2023Activity reportProjectTeamCAGE
RNSR: 201722536B Research center Inria Paris Centre at Sorbonne University
 In partnership with:CNRS, Sorbonne Université
 Team name: Control and Geometry
 In collaboration with:Laboratoire JacquesLouis Lions (LJLL)
 Domain:Applied Mathematics, Computation and Simulation
 Theme:Optimization and control of dynamic systems
Keywords
Computer Science and Digital Science
 A6. Modeling, simulation and control
 A6.1. Methods in mathematical modeling
 A6.1.1. Continuous Modeling (PDE, ODE)
 A6.4. Automatic control
 A6.4.1. Deterministic control
 A6.4.3. Observability and Controlability
 A6.4.4. Stability and Stabilization
 A6.4.5. Control of distributed parameter systems
 A6.4.6. Optimal control
Other Research Topics and Application Domains
 B2. Health
 B2.6. Biological and medical imaging
 B4.2.2. Fusion
 B5.2.4. Aerospace
 B5.11. Quantum systems
1 Team members, visitors, external collaborators
Research Scientists
 Mario Sigalotti [Team leader, INRIA, Senior Researcher, HDR]
 Ugo Boscain [CNRS, Senior Researcher, HDR]
 Barbara Gris [CNRS, Researcher]
 Kevin Le Balc'H [INRIA, ISFP]
Faculty Members
 JeanMichel Coron [UNIV PARIS, Emeritus]
 Ihab Haidar [ENSEA, Associate Professor Delegation, from Sep 2023]
 Emmanuel Trélat [Sorbonne Université, Professor, HDR]
PostDoctoral Fellows
 Wadim Gerner [INRIA, PostDoctoral Fellow]
 Jeremy Martin [INRIA, PostDoctoral Fellow]
 Jingrui Niu [INRIA, PostDoctoral Fellow, from Nov 2023]
 Tommaso Rossi [SORBONNE UNIVERSITE, PostDoctoral Fellow, from Oct 2023]
 Georgy Scholten [SORBONNE UNIVERSITE, PostDoctoral Fellow, until Aug 2023]
 Alessandro Socionovo [Sorbonne Université, from Nov 2023]
PhD Students
 Rameaux Agbo Bidi [SORBONNE UNIVERSITE]
 Xiangyu Ma [SORBONNE UNIVERSITE, from Oct 2023]
 Robin Roussel [SORBONNE UNIVERSITE]
 Liang Ruikang [POLYTECH SORBONNE]
 Lucia Tessarolo [SORBONNE UNIVERSITE, from Oct 2023]
Administrative Assistant
 Laurence Bourcier [INRIA]
Visiting Scientists
 Riccardo Adami [ECOLE POLYT. TURIN, until Apr 2023]
 Andrey Agrachev [SISSA, until Mar 2023]
2 Overall objectives
CAGE's activities take place in the field of mathematical control theory, with applications in several directions: control of quantum mechanical systems, stability and stabilization, in particular in presence of uncertain dynamics, optimal control, and geometric models for vision. Although control theory is nowadays a mature discipline, it is still the subject of intensive research because of its crucial role in a vast array of applications. Our focus is on the analytical and geometrical aspects of control applications.
At the core of the scientific activity of the team is the geometric control approach, that is, a distinctive viewpoint issued in particular from (elementary) differential geometry, to tackle questions of controllability, motion planning, stability, and optimal control. The emphasis of such a geometric approach is in intrinsic properties, and it is particularly well adapted to study nonlinear and nonholonomic phenomena 77, 53. The geometric control approach has historically been associated with the development of finitedimensional control theory. However, its impact in the study of distributed parameter control systems and, in particular, systems of controlled partial differential equations has been growing in the last decades, complementing analytical and numerical approaches by providing dynamical, qualitative, and intrinsic insight 69. CAGE has the ambition to be at the core of this development.
One of the features of the geometric control approach is its capability of exploiting symmetries and intrinsic structures of control systems. Symmetries and intrinsic structures (e.g., Lagrangian or Hamiltonian structures) can be used to characterize minimizing trajectories, prove regularity properties, and describe invariants. The geometric theory of quantum control, in particular, exploits the rich geometric structure encoded in the Schrödinger equation to design adapted control schemes and to characterize their qualitative properties.
3 Research program
3.1 Research domain
Our contributions are in the area of mathematical control theory, which is to say that we are interested in the analytical and geometrical aspects of control applications. In this approach, a control system is modeled by a system of equations (of many possible types: ordinary differential equations, partial differential equations, stochastic differential equations, difference equations,...), possibly not explicitly known in all its components, which are studied in order to establish qualitative and quantitative properties concerning the actuation of the system through the control.
Motion planning is, in this respect, a cornerstone property: it denotes the design and validation of algorithms for identifying a control law steering the system from a given initial state to (or close to) a target one. Initial and target positions can be replaced by sets of admissible initial and final states as, for instance, in the motion planning task towards a desired periodic solution. Many specifications can be added to the pure motion planning task, such as robustness to external or endogenous disturbances, obstacle avoidance or penalization criteria. A more abstract notion is that of controllability, which denotes the property of a system for which any two states can be connected by a trajectory corresponding to an admissible control law. In mathematical terms, this translates into the surjectivity of the socalled endpoint map, which associates with a control and an initial state the final point of the corresponding trajectory. The analytical and topological properties of endpoint maps are therefore crucial in analyzing the properties of control systems.
One of the most important additional objective which can be associated with a motion planning task is optimal control, which corresponds to the minimization of a cost (or, equivalently, the maximization of a gain) 105. Optimal control theory is clearly deeply interconnected with calculus of variations, even if the noninterchangeable nature of the timevariable results in some important specific features, such as the occurrence of abnormal extremals81. Research in optimal control encompasses different aspects, from numerical methods to dynamic programming and nonsmooth analysis, from regularity of minimizers to high order optimality conditions and curvaturelike invariants.
Another domain of control theory with countless applications is stabilization. The goal in this case is to make the system converge towards an equilibrium or some more general safety region. The main difference with respect to motion planning is that here the control law is constructed in feedback form. One of the most important properties in this context is that of robustness, i.e., the performance of the stabilization protocol in presence of disturbances or modeling uncertainties. A powerful framework which has been developed to take into account uncertainties and exogenous nonautonomous disturbances is that of hybrid and switched systems 92, 82, 98. The central tool in the stability analysis of control systems is that of control Lyapunov function. Other relevant techniques are based on algebraic criteria or dynamical systems. One of the most important stability property which is studied in the context of control system is inputtostate stability96, which measures how sensitive the system is to an external excitation.
One of the areas where control applications have nowadays the most impressive developments is in the field of biomedicine and neurosciences. Improvements both in modeling and in the capability of finely actuating biological systems have concurred in increasing the popularity of these subjects. Notable advances concern, in particular, identification and control for biochemical networks 90 and models for neural activity 74. Therapy analysis from the point of view of optimal control has also attracted a great attention 94.
Biological models are not the only one in which stochastic processes play an important role. Stockmarkets and energy grids are two major examples where optimal control techniques are applied in the nondeterministic setting. Sophisticated mathematical tools have been developed since several decades to allow for such extensions. Many theoretical advances have also been required for dealing with complex systems whose description is based on distributed parameters representation and partial differential equations. Functional analysis, in particular, is a crucial tool to tackle the control of such systems 102.
Let us conclude this section by mentioning another challenging application domain for control theory: the decision by the European Union to fund a flagship devoted to the development of quantum technologies is a symptom of the role that quantum applications are going to play in tomorrow's society. Quantum control is one of the bricks of quantum engineering, and presents many peculiarities with respect to standard control theory, as a consequence of the specific properties of the systems described by the laws of quantum physics. Particularly important for technological applications is the capability of inducing and reproducing coherent state superpositions and entanglement in a fast, reliable, and efficient way 75.
3.2 Scientific foundations
At the core of the scientific activity of the team is the geometric control approach. One of the features of the geometric control approach is its capability of exploiting symmetries and intrinsic structures of control systems. Symmetries and intrinsic structures can be used to characterize minimizing trajectories, prove regularity properties and describe invariants. An egregious example is given by mechanical systems, which inherently exhibit Lagrangian/Hamiltonian structures which are naturally expressed using the language of symplectic geometry 65. The geometric theory of quantum control, in particular, exploits the rich geometric structure encoded in the Schrödinger equation to engineer adapted control schemes and to characterize their qualitative properties. The Lie–Galerkin technique that we proposed starting in 66 builds on this premises in order to provide powerful tests for the controllability of quantum systems defined on infinitedimensional Hilbert spaces.
Although the focus of geometric control theory is on qualitative properties, its impact can also be disruptive when it is used in combination with quantitative analytical tools, in which case it can dramatically improve the computational efficiency. This is the case in particular in optimal control. Classical optimal control techniques (in particular, Pontryagin Maximum Principle, conjugate point theory, associated numerical methods) can be significantly improved by combining them with powerful modern techniques of geometric optimal control, of the theory of numerical continuation, or of dynamical system theory 100, 93. Geometric optimal control allows the development of general techniques, applying to wide classes of nonlinear optimal control problems, that can be used to characterize the behavior of optimal trajectories and in particular to establish regularity properties for them and for the cost function. Hence, geometric optimal control can be used to obtain powerful optimal syntheses results and to provide deep geometric insights into many applied problems. Numerical optimal control methods with geometric insight are in particular important to handle subtle situations such as rigid optimal paths and, more generally, optimal syntheses exhibiting abnormal minimizers.
Optimal control is not the only area where the geometric approach has a great impact. Let us mention, for instance, motion planning, where different geometric approaches have been developed: those based on the Lie algebra associated with the control system 86, 83, those based on the differentiation of nonlinear flows such as the return method70, 71, and those exploiting the differential flatness of the system 73.
Geometric control theory is not only a powerful framework to investigate control systems, but also a useful tool to model and study phenomena that are not a priori controlrelated. Two occurrences of this property play an important role in the activities of CAGE:
 geometric control theory as a tool to investigate properties of mathematical structures;
 geometric control theory as a modeling tool for neurophysical phenomena and for synthesizing biomimetic algorithms based on such models.
Examples of the first type, concern, for instance, hypoelliptic heat kernels 52 or shape optimization 56. Examples of the second type are inactivation principles in human motricity 58 or neurogeometrical models for image representation of the primary visual cortex in mammals 63.
A particularly relevant class of control systems, both from the point of view of theory and applications, is characterized by the linearity of the controlled vector field with respect to the control parameters. When the controls are unconstrained in norm, this means that the admissible velocities form a distribution in the tangent bundle to the state manifold. If the distribution is equipped with a pointdependent quadratic form (encoding the cost of the control), the resulting geometrical structure is said to be subRiemannian. SubRiemannian geometry appears as the underlying geometry of nonlinear control systems: in a similar way as the linearization of a control system provides local informations which are readable using the Euclidean metric scale, subRiemannian geometry provides an adapted nonisotropic class of lenses which are often much more informative. As such, its study is fundamental for control design. The importance of subRiemannian geometry goes beyond control theory and it is an active field of research both in differential geometry 85, geometric measure theory 54 and hypoelliptic operator theory 59.
4 Application domains
4.1 First axis: Quantum control
Quantum control is one of the bricks of quantum engineering, since manipulation of quantum mechanical systems is ubiquitous in applications such as quantum computation, quantum cryptography, and quantum sensing (in particular, imaging by nuclear magnetic resonance).
Quantum control presents many peculiarities with respect to standard control theory, as a consequence of the specific properties of the systems described by the laws of quantum physics. Particularly important for technological applications is the capability of inducing and reproducing coherent state superpositions and entanglement in a fast, reliable, and efficient way. The efficiency of the control action has a dramatic impact on the quality of the coherence and the robustness of the required manipulation. Minimal time constraints and interaction of time scales are important factors for characterizing the efficiency of a quantum control strategy. CAGE works for the improvement of quantum control paradigms, especially for what concerns quantum systems evolving in infinitedimensional Hilbert spaces. The controllability of quantum system is a wellestablished topic when the state space is finitedimensional 72, thanks to general controllability methods for leftinvariant control systems on compact Lie groups 64, 78. When the state space is infinitedimensional, it is known that in general the bilinear Schrödinger equation is not exactly controllable 103. The Lie–Galerkin technique 66 combines finitedimensional geometric control techniques and the distributed parameter framework in order to provide the most powerful available tests for the approximate controllability of quantum systems defined on infinitedimensional Hilbert spaces. Another important technique to the development of which we contribute is adiabatic quantum control. Adiabatic approximation theory and, in particular, adiabatic evolution 87, 99, 106 is wellknown to improve the robustness of the control strategy and is strongly related to time scales analysis. The advantage of the adiabatic control is that it is constructive and produces control laws which are both smooth and robust to parameter uncertainty 107, 80, 62.
4.2 Second axis: Stability and stabilization
A control application with a long history and still very challenging open problems is stabilization. For infinitedimensional systems, in particular nonlinear ones, the richness of the possible functional analytical frameworks makes feedback stabilization a challenging and active domain of research. Of particular interest are the different types of stabilization that may be obtained: exponential, polynomial, finitetime, ... Another important aspect of stabilization concerns control of systems with uncertain dynamics, i.e., with dynamics including possibly nonautonomous parameters whose value and dependence on time cannot be anticipated. Robustification, i.e., offsetting uncertainties by suitably designing the control strategy, is a widespread task in automatic control theory, showing up in many applicative domains such as electric circuits or aerospace motion planning. If dynamics are not only subject to static uncertainty, but may also change as time goes, the problem of controlling the system can be recast within the theory of switched and hybrid systems, both in a deterministic and in a probabilistic setting. Switched and hybrid systems constitute a broad framework for the description of the heterogeneous systems in which continuous dynamics (typically pertaining to physical quantities) interact with discrete/logical components. The development of the switched and hybrid paradigm has been motivated by a broad range of applications, including automotive and transportation industry 95, energy management 88 and congestion control 84. Even if both controllability 97 and observability 79 of switched and hybrid systems raise several important research issues, the central role in their study is played by uniform stability and stabilizabilization 82, 98. Uniformity is considered with respect to all signals in a given class, and it is wellknown that stability of switched systems depends not only on the dynamics of each subsystem but also on the properties of the considered class of switching signals. In many situations it is interesting for modeling purposes to specify the features of the switched system by introducing constrained switching rules. A typical constraint is that each mode is activated for at least a fixed minimal amount of time, called the dwelltime. Our approach to constrained switching is based on the idea of relating the analytical properties of the classes of constrained switching laws (shiftinvariance, compactness, closure under concatenation, ...) to the stability behavior of the corresponding switched systems. One can introduce probabilistic uncertainties by endowing the classes of admissible signals with suitable probability measures. The interest of this approach is that probabilistic stability analysis filters out highly `exceptional' worstcase trajectories. Although less explicitly characterized from a dynamical viewpoint than its deterministic counterpart, the probabilistic notion of uniform exponential stability can be studied using several reformulations of Lyapunov exponents proposed in the literature 57, 68, 104.
4.3 Third axis: Motion planning and optimal control
Geometric optimal control allows the development of general techniques, applying to wide classes of nonlinear optimal control problems, that can be used to characterize the behavior of optimal trajectories and in particular to establish regularity properties for them and for the cost function. Hence, geometric optimal control can be used to obtain powerful optimal syntheses results and to provide deep geometric insights into many applied problems. Geometric optimal control methods are in particular important to handle subtle situations such as rigid optimal paths and, more generally, optimal syntheses exhibiting abnormal minimizers.
Although the focus of geometric control theory is on qualitative properties, its impact can also be disruptive when it is used in combination with quantitative analytical tools, in which case it can dramatically improve the computational efficiency. This is the case in particular in optimal control. Classical optimal control techniques (in particular, Pontryagin Maximum Principle, conjugate point theory, associated numerical methods) can be significantly improved by combining them with powerful modern techniques of geometric optimal control, of the theory of numerical continuation, or of dynamical system theory 100, 93. Applications of optimal control theory considered by CAGE concern, in particular, motion planning problems for aerospace (atmospheric reentry, orbit transfer, low cost interplanetary space missions, ...) 60, 101.
4.4 Fourth axis: Geometric models for vision and subRiemannian geometry
Geometric control theory is not only a powerful framework to investigate control systems, but also a useful tool to model and study phenomena that are not a priori controlrelated. In particular, we use control theory to investigate the properties of subRiemannian structures, both for the sake of mathematical understanding and as a modeling tool for image and sound perception and processing . We recall that subRiemannian geometry is a geometric framework which is used to measure distances in nonholonomic contexts and which has a natural and powerful optimal control interpretation in terms controllinear systems with quadratic cost. SubRiemannian geometry, and in particular the theory of their associated (hypoelliptic) diffusive processes, plays a crucial role in the neurogeometrical model of the primary visual cortex due to Petitot, Citti and Sarti, based on the functional architecture first described by Hubel and Wiesel 76, 89, 67, 91. Such a model can be used as a powerful paradigm for bioinspired image processing, as already illustrated in the literature 63, 61. Our contributions to geometry of vision are based not only on this approach, but also on another geometric and subRiemannian framework for vision, based on pattern matching in the group of diffeomorphisms. In this case admissible diffeomorphisms correspond to deformations which are generated by vector fields satisfying a set of nonholonomic constraints. A subRiemannian metric on the infinitedimensional group of diffeomorphisms is induced by a length on the tangent distribution of admissible velocities 55. Nonholonomic constraints can be especially useful to describe distortions of sets of interconnected objects (e.g., motions of organs in medical imaging).
5 Highlights of the year
5.1 Awards
Rémi Robin was awarded with the Prix solennel de thèse de la chancellerie de Paris, the Prix de thèse PGMO 2023, and the Prix de thèse SMAIGAMNI for his PhD thesis defended in 2022 and obtained while being member of the team CAGE.
Daniele Cannarsa and Mario Sigalotti have been awarded the BrockettWillems Outstanding Paper Award 2023 for the best paper published in Systems & Control Letters during the twoyear period from January 2021 through December 2022 (paper written while Daniele Cannarsa was member of the team CAGE).
6 New results
6.1 Quantum control: new results
Let us list here our new results in quantum control theory.
 Achiral molecules can be made temporarily chiral by excitation with electric fields, in the sense that an average over molecular orientations displays a net chiral signal. In 46, we go beyond the assumption of molecular orientations to remain fixed during the excitation process. Treating both rotations and vibrations quantum mechanically, we identify conditions for the creation of chiral vibrational wavepackets – with net chiral signals – in ensembles of achiral molecules which are initially randomly oriented. Based on the analysis of symmetry and controllability, we derive excitation schemes for the creation of chiral wavepackets using a combination of (a) microwave and IR pulses and (b) a static field and a sequence of IR pulses. These protocols leverage quantum rotational dynamics for pumpprobe spectroscopy of chiral vibrational dynamics, extending the latter to regions of the electromagnetic spectrum other than the UV.
 In 48, we explore the controllability of a closed multiinput controlaffine quantum system. Previous studies have demonstrated that a spectrum connected by conical intersections which do not pile up yields exact controllability in finite dimension and approximate controllability in infinite dimension. Actually, the property that intersections between eigenvalues are conical and that they do not pile up is generic. However, in physical situations, due to symmetry of the system, the spectrum can exhibit intersections that are not conical and possibly pile up. We extend the controllability result to cover this type of situations under the hypothesis that the intersections have at least one conical direction and the piledup intersections have "rationally unrelated germs". Finally, we provide a testable firstorder sufficient condition for controllability. Physically relevant examples are provided.
 In 45, we obtain observability estimates for Schrödinger equations in the plane. More precisely, considering a periodic bounded potential, we prove that the evolution Schrödinger equation is observable from any periodic measurable set, in any small time. We then extend Taüffer's recent result in the twodimensional case to less regular observable sets and general bounded periodic potentials. The methodology of the proof is based on the use of the FloquetBloch transform, Strichartz estimates and semiclassical defect measures for the obtention of observability inequalities for a family of Schrödinger equations posed on the torus.
 In 20, we study, in the semiclassical sense, the global approximate controllability in small time of the quantum density and quantum momentum of the 1D semiclassical cubic Schrödinger equation with two controls between two states with positive quantum densities. We first control the asymptotic expansions of the zeroth and first order of the physical observables via the Agrachev–Sarychev method. Then we conclude the proof through techniques of semiclassical approximation of the nonlinear Schrödinger equation.
 In 26, we establish some properties of quantum limits on a product manifold, proving for instance that, under appropriate assumptions, the quantum limits on the product of manifolds are absolutely continuous if the quantum limits on each manifolds are absolutely continuous. On a product of Riemannian manifolds satisfying the minimal multiplicity property, we prove that a periodic geodesic can never be charged by a quantum limit.
6.2 Stability and stabilization: new results
Let us list here our new results about stability and stabilization of control and hybrid systems.
 In 23, we study some spectral properties of the scalar dynamical system defined by a linear delaydifferential equation with two positive delays. More precisely, the existing links between the delays and the maximal multiplicity of the characteristic roots are explored, as well as the dominancy of such roots compared with the spectrum localization. As a byproduct of the analysis, the pole placement issue is revisited with more emphasis on the role of the delays as control parameters in defining a partial pole placement guaranteeing the closedloop stability with an appropriate decay rate of the corresponding dynamical system.
 In 18, we consider the problem of determining the stability properties, and in particular assessing the exponential stability, of a singularly perturbed linear switching system. One of the challenges of this problem arises from the intricate interplay between the small parameter of singular perturbation and the rate of switching as both tend to zero. Our approach consists in characterizing suitable auxiliary linear systems that provide lower and upper bounds for the asymptotics of the maximal Lyapunov exponent of the linear switching system as the parameter of the singular perturbation tends to zero.
 In 29, we discuss the notion of universality for classes of candidate common Lyapunov functions of linear switched systems. On the one hand, we prove that a family of absolutely homogeneous functions is universal as soon as it approximates arbitrarily well every convex absolutely homogeneous function for the C0 topology of the unit sphere. On the other hand, we prove several obstructions for a class to be universal, showing, in particular, that families of piecewisepolynomial continuous functions whose construction involves at most l polynomials of degree at most m (for given positive integers l,m) cannot be universal.
 One of the central questions in control theory is achieving stability through feedback control. The paper 31 introduces a novel approach that combines Reinforcement Learning (RL) with mathematical analysis to address this challenge, with a specific focus on the Sterile Insect Technique (SIT) system. The objective is to find a feedback control that stabilizes the mosquito population model. Despite the mathematical complexities and the absence of known solutions for this specific problem, our RL approach identifies a candidate solution for an explicit stabilizing control. This study underscores the synergy between AI and mathematics, opening new avenues for tackling intricate mathematical problems.
 Consider a nonautonomous continuoustime linear system in which the timedependent matrix determining the dynamics is piecewise constant and takes finitely many values ${A}_{1},...,{A}_{N}$. The paper 19 studies the equality cases between the maximal Lyapunov exponent associated with the set of matrices $\{{A}_{1},...,{A}_{N}\}$, on the one hand, and the corresponding ones for piecewise deterministic Markov processes with modes ${A}_{1},\cdots ,{A}_{N}$, on the other hand. A fundamental step in this study consists in establishing a result of independent interest, namely, that any sequence of Markov processes associated with the matrices ${A}_{1},...,{A}_{N}$ converges, up to extracting a subsequence, to a Markov process associated with a suitable convex combination of those matrices.
 The article 39 deals with the stability of linear periodic difference delay systems, where the value at time $t$ of a solution is a linear combination with periodic coefficients of its values at finitely many delayed instants $t{\tau}_{1},...,t{\tau}_{N}$. We establish a necessary and sufficient condition for exponential stability of such systems when the coefficients have Höldercontinuous derivative, that generalizes the one obtained for difference delay systems with constant coefficients by Henry and Hale in the 1970s. This condition may be construed as analyticity, in a half plane, of the (operator valued) harmonic transfer function of an associated linear control system.
 In 35, we explicitly compute the maximal Lyapunov exponent for a switched system on $S{L}_{2}\left(\mathbb{R}\right)$. This computation is reduced to the characterization of optimal trajectories for an optimal control problem on the Lie group.
 In 38, we prove the (uniform) global exponential stabilization of the cubic defocusing Schrödinger equation on the torus ddimensional torus, for d=1, 2 or 3, with a linear damping localized in a subset of the torus satisfying some geometrical assumptions. In particular, this answers an open question of Dehman, Gérard, Lebeau from 2006. Our approach is based on three ingredients. First, we prove the wellposedness of the closedloop system in Bourgain spaces. Secondly, we derive new Carleman estimates for the nonlinear equation by directly including the cubic term in the conjugated operator. Thirdly, by conjugating with energy estimates and Morawetz multipliers method, we then deduce quantitative observability estimates leading to the uniform exponential decay of the total energy of the system. As a corollary of the global stabilization result, we obtain an upper bound of the minimal time of the global nullcontrollability of the nonlinear equation by using a stabilization procedure and a local nullcontrollability result.
 The Sterile Insect Technique or SIT is presently one of the most ecological methods for controlling insect pests responsible for disease transmission or crop destruction worldwide. This technique consists of releasing sterile males into the insect pest population. This approach aims at reducing fertility in the population and, consequently, reduce significantly the native insect population after a few generations. In the work 32, we study the global stabilization of a pest population at extinction equilibrium by the SIT method. We construct explicit feedback laws that stabilize the model and do numerical simulations to show the efficiency of our feedback laws. The different feedback laws are also compared taking into account their possible implementation in field interventions.
 In the article 24, we study the problem of stabilizing the traffic flow on a ring road to a uniform steadystate using autonomous vehicles (AV). Traffic is represented at a microscopic level via a BandoFollowtheLeader model capable of reproducing phantom jams. For the singlelane case, a single AV can stabilize an arbitrary large ring road with an arbitrary large number of cars. Moreover, this stabilization is exponentially quick with a decay rate independent of the number of cars and a control gain also independent of the number of cars. On the other side, the stabilization domain and stabilization time depend on the number of cars. Two types of controller algorithms are proposed: a proportional control and a proportionalintegral control. In both cases, the measurements used by the controller only depend on the local data around the AV, enabling an easy implementation. After numerical tests of the singlelane case, a multilane model is described using a safetyincentive mechanism for lane change. Numerical simulations for the multilane ring road suggest that the control strategy is also very efficient in such a setting, even with a single AV.
6.3 Motion planning and optimal control: new results
Let us list here our new results on controllability and motion planning algorithms, including optimal control, optimization beyond the quantum control framework.
 In 27, we address the problem of catching all speed 1 geodesics of a Riemannian manifold with a moving ball: given a compact Riemannian manifold $(M,g)$ and small parameters $\u03f5>0$ and $v>0$, is it possible to find $T>0$ and an absolutely continuous map $x:[0,T]\to M$,$t\mapsto x\left(t\right)$ satisfying $\parallel \dot{x}{\parallel}_{\infty}\le v$ and such that any geodesic of $(M,g)$ traveled at speed 1 meets the open ball ${B}_{g}(x\left(t\right),\u03f5)\subset M$ within time $T$? Our main motivation comes from the control of the wave equation: our results show that the controllability of the wave equation can sometimes be improved by allowing the domain of control to move adequately, even very slowly. We first prove that, in any Riemannian manifold $(M,g)$ satisfying a geodesic recurrence condition (GRC), our problem has a positive answer for any $\u03f5>0$ and $v>0$, and we give examples of Riemannian manifolds $(M,g)$ for which (GRC) is satisfied.
 In the lecture notes 51 we introduce controllability, tabilization and optimal control for systems in finite and infinite dimension.
 In 25, we prove the smalltime global nullcontrollability of forward (resp. backward) semilinear stochastic parabolic equations with globally Lipschitz nonlinearities in the drift and diffusion terms (resp. in the drift term). In particular, we solve the open question posed by S. Tang and X. Zhang, in 2009. We propose a new twist on a classical strategy for controlling linear stochastic systems. By employing a new refined Carleman estimate, we obtain a controllability result in a weighted space for a linear system with source terms. The main novelty here is that the Carleman parameters are made explicit and are then used in a Banach fixed point method. This allows to circumvent the wellknown problem of the lack of compactness embeddings for the solutions spaces arising in the study of controllability problems for stochastic PDEs.
 The article 42 deals with the controllability of linear onedimensional hyperbolic systems. Reformulating the problem in terms of linear difference equations and making use of infinitedimensional realization theory, we obtain both necessary and sufficient conditions for approximate and exact controllability, expressed in the frequency domain. The results are applied to flows in networks.
 In 36, we consider a linear quadratic (LQ) optimal control problem in both finite and infinite dimensions. We derive an asymptotic expansion of the value function as the fixed time horizon $T$ tends to infinity. The leading term in this expansion, proportional to $T$, corresponds to the optimal value attained through the classical turnpike theory in the associated static problem. The remaining terms are associated with optimal stabilization problems towards the turnpike.
 In 16, we deal with the global exact controllability to the trajectories of the Boussinesq system posed in 2D or 3D smooth bounded domains. The velocity field of the fluid must satisfy a Navier slipwithfriction boundary condition and a Robin boundary condition is im posed to the temperature. We assume that one can act on the velocity and the temperature on a small part of the boundary. For the proof, we first transform the boundary control problem into a distributed control problem. Then, we prove a global approximate controllability result by adapting the strategy of Coron et al [J. Eur. Math. Soc., 22 (2020), pp. 1625–1673]; this relies on the controllability properties of the inviscid Boussinesq system and the analysis of appropriate asymptotic boundary layer expansions. Finally, we conclude with a local control lability result; as in many other cases, this can be established as a consequence of the null controllability of a linearized system through a fixedpoint argument. Our contribution can be viewed as an extension of the results in [J. Eur. Math. Soc., 22 (2020), pp. 1625–1673], where thermal effects were not considered. Thus, we prove that the ideas behind the controllability properties of the Euler system and the wellprepared dissipation technique can be adapted to the present situation. Furthermore, we cover all the classical boundary conditions for the temperature, that is, those of the Robin, Neumann and Dirichlet kinds.
 The article 17 deals with the controllability of finitedimensional linear difference delay equations, i.e., dynamics for which the state at a given time $t$ is obtained as a linear combination of the control evaluated at time t and of the state evaluated at finitely many previous instants of time $t{\Lambda}_{1},...,t{\Lambda}_{N}$. Based on the realization theory developed by Y.Yamamoto for general infinitedimensional dynamical systems, we obtain necessary and sufficient conditions, expressed in the frequency domain, for the approximate controllability in finite time in ${L}^{q}$ spaces, $q\in [1,+\infty )$. We also provide a necessary condition for ${L}^{1}$ exact controllability, which can be seen as the closure of the ${L}^{1}$ approximate controllability criterion. Furthermore, we provide an explicit upper bound on the minimal times of approximate and exact controllability, given by $dmax\{{\Lambda}_{1},...,{\Lambda}_{N}\}$, where $d$ is the dimension of the state space.
 In 50, we consider the internal control of linear parabolic equations through onoff shape controls, i.e., controls of the form $M\left(t\right){\chi}_{\omega \left(t\right)}$ with $M\left(t\right)\ge 0$ and $\omega \left(t\right)$ with a prescribed maximal measure. We establish smalltime approximate controllability towards all possible final states allowed by the comparison principle with nonnegative controls. We manage to build controls with constant amplitude $M\left(t\right)\equiv \overline{M}$. In contrast, if the moving control set $\omega \left(t\right)$ is confined to evolve in some region of the whole domain, we prove that approximate controllability fails to hold for small times. The method of proof is constructive. Using FenchelRockafellar duality and the bathtub principle, the onoff shape control is obtained as the bangbang solution of an optimal control problem, which we design by relaxing the constraints. Our optimal control approach is outlined in a rather general form for linear constrained control problems, paving the way for generalisations and applications to other PDEs and constraints.
 The goal of 21 is to obtain observability estimates for nonhomogeneous elliptic equations in the presence of a potential, posed on a smooth bounded domain $\Omega $ in 2d and observed from a nonempty open subset $\omega \subset \Omega $. More precisely, for every realvalued bounded potential $V$, our main result shows that, when $\Omega $ has a finite number of holes, the observability constant of the elliptic operator $\Delta +V$, with domain ${H}^{2}\cap {H}_{0}^{1}\left(\Omega \right)$, is of the form ${C\mathrm{exp}\left(C\rightV}^{1/2}{log}^{1/2}\left(\rightV\left\right))$ where $C$ is a positive constant depending only on $\Omega $ and $\omega $. Our methodology of proof is crucially based on the one recently developed by Logunov, Malinnikova, Nadirashvili, and Nazarov, in the context of the Landis conjecture on exponential decay of solutions to homogeneous elliptic equations in the plane. The main difference and additional difficulty is that the zero set of the solutions to elliptic equations with source term can be very intricate and should be dealt with carefully. As a consequence of these new observability estimates, we obtain new results concerning control of semilinear elliptic equations in the spirit of FernándezCara, Zuazua's open problem concerning smalltime global nullcontrollability of slightly superlinear heat equations.
 In 33, we consider a smooth system of the form ${q}^{\text{'}}={f}_{0}\left(q\right)+{\sum}_{i=1}^{k}{u}_{i}{f}_{i}\left(q\right)$, $q\in M$, ${u}_{i}\in \mathbb{R}$, and study controllability issues on the group of diffeomorphisms of $M$. It is wellknown that the system can arbitrarily well approximate the movement in the direction of any Lie bracket polynomial of ${f}_{1},\cdots ,{f}_{k}$. Any Lie bracket polynomial of ${f}_{1},\cdots ,{f}_{k}$ is good in this sense. Moreover, some combinations of Lie brackets which involve the drift term ${f}_{0}$ are also good but surely not all of them. In this paper we try to characterize good ones and, in particular, all universal good combinations, which are good for any nilpotent truncation of any system.
 In 12, we consider a mechanical system of three ants on the floor, which move according to two independt rules: Rule A  forces the velocity of any given ant to always point at a neighboring ant, and Rule B  forces the velocity of every ant to be parallel to the line defined by the two other ants. We observe that Rule A equips the 6dimensional configuration space of the ants with a structure of a homogeneous (3,6) distribution, and that Rule B foliates this 6dimensional configuration space onto 5dimensional leaves, each of which is equiped with a homogeneous (2,3,5) distribution. The symmetry properties and BryantCartan local invariants of these distributions are determined. In the case of Rule B we study and determine the singular trajectories (abnormal extremals) of the corresponding distributions. We show that these satisfy an interesting system of two ODEs of Fuchsian type.
 In the work 43, we present a general framework which guarantees the existence of optimal domains for isoperimetric problems within the class of ${C}^{1,1}$regular domains satisfying a uniform ball condition as long as the desired objective function satisfies certain properties. We then verify that the helicity isoperimetric problem studied by Cantarella, DeTurck, Gluck and Teytel in 2002 satisfies the conditions of our framework and hence establish the existence of optimal domains within the given class of domains. We additionally use the same framework to prove the existence of optimal domains among uniform ${C}^{1,1}$domains for a first curl eigenvalue problem which has been studied recently for other classes of domains.
 In 44, we investigate properties of the image and kernel of the BiotSavart operator in the context of stellarator designs for plasma fusion. We first show that for any given coil winding surface (CWS) the image of the BiotSavart operator is ${L}^{2}$dense in the space of squareintegrable harmonic fields defined on a plasma domain surrounded by the CWS. Then we show that harmonic fields which are harmonic in a proper neighbourhood of the underlying plasma domain can in fact be approximated in any ${C}^{k}$norm by elements of the image of the BiotSavart operator. In the second part of this work we establish an explicit isomorphism between the space of harmonic Neumann fields and the kernel of the BiotSavart operator which in particular implies that the dimension of the kernel of the BiotSavart operator coincides with the genus of the coil winding surface and hence turns out to be a homotopy invariant among regular domains in 3space. Lastly, we provide an iterative scheme which we show converges weakly in ${W}^{\frac{1}{2},2}$topology to elements of the kernel of the BiotSavart operator.
 In 37, considering a general nonlinear dissipative finite dimensional optimal control problem in fixed time horizon $T$, we establish a twoterm asymptotic expansion of the value function as $T\to +\infty $. The dominating term is T times the optimal value obtained from the optimal static problem within the classical turnpike theory. The second term, of order unity, is interpreted as the sum of two values associated with optimal stabilization problems related to the turnpike.
 The turnpike phenomenon stipulates that the solution of an optimal control problem in large time, remains essentially close to a steadystate of the dynamics, itself being the optimal solution of an associated static optimal control problem. Under general assumptions, it is known that not only the optimal state and the optimal control, but also the adjoint state coming from the application of the Pontryagin maximum principle, are exponentially close to a steadystate, except at the beginning and at the end of the time frame. In such results, the turnpike set is a singleton, which is a steadystate. In the paper 30, we establish a turnpike result for finitedimensional optimal control problems in which some of the coordinates evolve in a monotone way, and some others are partial steadystates of the dynamics. We prove that the discrepancy between the optimal trajectory and the turnpike set is then linear, but not exponential: we thus speak of a linear turnpike theorem.
 Consider, on the one part, a general nonlinear finitedimensional optimal control problem and assume that it has a unique solution whose state is denoted by ${x}^{*}$. On the other part, consider the sampleddata control version of it. Under appropriate assumptions, in 41, we prove that the optimal state of the sampleddata problem converges uniformly to ${x}^{*}$ as the norm of the corresponding partition tends to zero. Moreover, applying the Pontryagin maximum principle to both problems, we prove that, if ${x}^{*}$ has a unique weak extremal lift with a costate $p$ that is normal, then the costate of the sampleddata problem converges uniformly to $p$. In other words, under a nondegeneracy assumption, control sampling commutes, at the limit of small partitions, with the application of the Pontryagin maximum principle.
 In this paper 34, we prove Morse index theorems for a big class of constrained variational problems on graphs. Such theorems are useful in various physical and geometric applications. Our formulas compute the difference of Morse indices of two Hessians related to two different graphs or two different sets of boundary conditions. Several applications such as the iteration formulas or lower bounds for the index are proved.
 The work 49 tackles the open pit planning problem in an optimal control framework. We study the optimality conditions for the socalled continuous formulation using Pontryagin’s Maximum Principle, and introduce a new, semicontinuous formulation that can handle the optimization of a twodimensional mine profile. Numerical simulations are provided for several test cases, including global optimization for the onedimensional final open pit, and first results for the twodimensional sequential open pit. Theses indicate a good consistency between the different approaches, and with the theoretical optimality conditions.
 In the paper 14, we consider a measuretheoretical formulation of the training of NeurODEs in the form of a meanfield optimal control with ${L}^{2}$regularization of the control. We derive first order optimality conditions for the NeurODE training problem in the form of a meanfield maximum principle, and show that it admits a unique control solution, which is Lipschitz continuous in time. As a consequence of this uniqueness property, the meanfield maximum principle also provides a strong quantitative generalization error for finite sample approximations. Our derivation of the meanfield maximum principle is much simpler than the ones currently available in the literature for meanfield optimal control problems, and is based on a generalized Lagrange multiplier theorem on convex sets of spaces of measures. The latter is also new, and can be considered as a result of independent interest.
6.4 Geometric models for vision and subRiemannian geometry: new results
Let us list here our new results in the geometry of vision axis and, more generally, on hypoelliptic diffusion and subRiemannian geometry.
 In the article 28, we study the observability (or, equivalently, the controllability) of some subelliptic evolution equations depending on their step. This sheds light on the speed of propagation of these equations, notably in the “degenerated directions” of the subelliptic structure. First, for any $\gamma \ge 1$, we establish a resolvent estimate for the BaouendiGrushintype operator ${\Delta}_{\gamma}={\partial}_{x}^{2}+{\leftx\right}^{2\gamma}{\partial}_{y}^{2}$, which has step $\gamma +1$. We then derive consequences for the observability of the Schrodinger type equation $i{\partial}_{t}u{({\Delta}_{\gamma})}^{s}u=0$ where $s\in \mathbb{N}$. We identify three different cases: depending on the value of the ratio $(\gamma +1)/s$, observability may hold in arbitrarily small time, or only for sufficiently large times, or even fail for any time. As a corollary of our resolvent estimate, we also obtain observability for heattype equations ${\partial}_{t}u+{({\Delta}_{\gamma})}^{s}u=0$ and establish a decay rate for the damped wave equation associated with ${\Delta}_{\gamma}$.
 In 40, we consider the evolution of a free quantum particle on the Grushin cylinder, under different type of quantizations. In particular we are interested to understand if the particle can cross the singular set, i.e., the set where the structure is not Riemannian. We consider intrinsic and extrinsic quantizations, where the latter are obtained by embedding the Grushin structure isometrically in ${\mathbb{R}}^{3}$ (with singularities). As a byproduct we provide formulas to embed the Grushin cylinder in ${\mathbb{R}}^{3}$ that could be useful for other purposes. Such formulas are not global, but permit to study the embedding arbitrarily close to the singular set. We extend these results to the case of $\alpha $Grushin cylinders.
 In 47, we establish two results concerning the Quantum Limits (QLs) of some subLaplacians. First, under a commutativity assumption on the vector fields involved in the definition of the sub Laplacian, we prove that it is possible to split any QL into several pieces which can be studied separately, and which come from wellcharacterized parts of the associated sequence of eigenfunctions. Secondly, building upon this result, we study in detail the QLs of a particular family of subLaplacians defined on products of compact quotients of Heisenberg groups. We express the QLs through a disintegration of measure result which follows from a natural spectral decomposition of the subLaplacian in which harmonic oscillators appear. Both results are based on the construction of an adequate elliptic operator commuting with the subLaplacian, and on the associated joint spectral calculus. They illustrate the fact that, because of the possible high degeneracies in the spectrum, the spectral theory of subLaplacians is very rich.
 In 15, we consider surfaces embedded in a 3D contact subRiemannian manifold and the problem of the finiteness of the induced distance (i.e., the infimum of the length of horizontal curves that belong to the surface). Recently it has been proved that for a surface having the topology of a sphere embedded in a tight coorientable structure, the distance is always finite. In this paper we study closed surfaces of genus larger than 1, proving that such surfaces can be embedded in such a way that the induced distance is finite or infinite. We then study the structural stability of the finiteness/notfiniteness of the distance.
 The relative heat content associated with a subset $\Omega \subset M$ of a subRiemannian manifold, is defined as the total amount of heat contained in $\Omega $ at time $t$, with uniform initial condition on Ω, allowing the heat to flow outside the domain. In the work 13, we obtain a fourthorder asymptotic expansion in square root of t of the relative heat content associated with relatively compact noncharacteristic domains. Compared to the classical heat content that we studied in [Rizzi, Rossi  J. Math. Pur. Appl., 2021], several difficulties emerge due to the absence of Dirichlet conditions at the boundary of the domain. To overcome this lack of information, we combine a rough asymptotic for the temperature function at the boundary, coupled with stochastic completeness of the heat semigroup. Our technique applies to any (possibly rankvarying) subRiemannian manifold that is globally doubling and satisfies a global weak Poincaré inequality, including in particular subRiemannian structures on compact manifolds and Carnot groups.
 In 22, we study the isoperimetric problem for anisotropic leftinvariant perimeter measures on ${\mathbb{R}}^{3}$, endowed with the Heisenberg group structure. The perimeter is associated with a leftinvariant norm $\varphi $ on the horizontal distribution. We first prove a representation formula for the $\varphi $perimeter of regular sets and, assuming some regularity on $\varphi $ and on its dual norm ${\varphi}_{*}$, we deduce a foliation property by subFinsler geodesics of ${C}^{2}$smooth surfaces with constant $\varphi $curvature. We then prove that the characteristic set of ${C}^{2}$smooth surfaces that are locally extremal for the isoperimetric problem is made of isolated points and horizontal curves satisfying a suitable differential equation. Based on such a characterization, we characterize ${C}^{2}$smooth $\varphi $isoperimetric sets as the subFinsler analogue of Pansu's bubbles. We also show, under suitable regularity properties on $\varphi $, that such subFinsler candidate isoperimetric sets are indeed ${C}^{2}$smooth. By an approximation procedure, we finally prove a conditional minimality property for the candidate solutions in the general case (including the case where $\varphi $ is crystalline).
7 Bilateral contracts and grants with industry
Participants: Emmanuel Trélat, Veljko Askovic, Georgy Scholten.
7.1 Bilateral contracts with industry
Contract with MBDA (Palaiseau), 2021–2023. Subject: “Contrôle optimal pour la planification de trajectoires et l’estimation des ensembles accessibles". Pariticpants: V. Askovic (MBDA & CAGE), E. Trélat (coordinator).
7.2 Bilateral grants with industry
Grant by AFOSR (Air Force Office of Scientific Research), 2020–2023. Participants : Mohab Safey El Din (LIP6), E. Trélat.
8 Partnerships and cooperations
8.1 International research visitors
8.1.1 Visits of international scientists
Inria International Chair
Andrei Agrachev (SISSA, Trieste, Italy) made two visits to CAGE (16/1–15/3 and 19/9–18/11) in the framework of his Inria International Chair 20202024.
Other international visits to the team
Riccardo Adami (Politecnico di Torino, Italy), March.
8.2 National initiatives
8.2.1 ANR
 ANR TRECOS, for New Trends in Control and Stabilization: Constraints and nonlocal terms, coordinated by Sylvain Ervedoza, University of Bordeaux. The ANR started in 2021 and runs up to 2025. TRECOS' focus is on control theory for partial differential equations, and in particular models from ecology and biology.
 ANR QUACO, for QUAntum COntrol: PDE systems and MRI applications, coordinated by Thomas Chambrion, started in 2017 and finished in June 2023. Other partners: Burgundy University. QUACO contributed to quantum control theory in two directions: improving the comprehension of the dynamical properties of controlled quantum systems in infinitedimensional state spaces, and improving the efficiency of control algorithms for MRI.
 ANR/DFG CoRoMo for Efficient quantum control of molecular rotations – time and controllability, 2023–2025. The grant is cocoordinated by Ugo Boscain (CAGE) and Christiane Koch (Berlin). In this project, we seek to elucidate the role of time in quantum control, using the important benchmark of molecular rotations as testbed. We will leverage controllability analysis to tackle the role of time in quantum control, combining physical intuition from the control of molecular rotations with recent advances of mathematical methods.
 ANR EINSTEINPPF for Contraintes d'Einstein : passé', présent et futur, coordinated by Philippe Lefloch. Relying on a close collaboration between analysts and geometers, the ANR project is aimed at advancing our knowledge of the analytic and geometric properties of Einstein spacetimes, especially when the metrics under consideration have low regularity.
8.2.2 Other national initatives
 The Inria Exploratory Action “StellaCage” is supporting since Spring 2020 a collaboration between CAGE, Yannick Privat (Inria team TONUS), and the startup Renaissance Fusion, based in Grenoble. StellaCage approaches the problem of designing better stellarators (yielding better confinement, with simpler coils, capable of higher fields) by combining geometrical properties of magnetic field lines from the control perspective with shape optimization techniques.
 The 80 prime project BioSpeech (2023–2024), coordinated by Ugo Boscain, studies a bioinspired geometric model for speech sound reconstruction. It is a collaboration between mathematicians, automatic control scientists, and linguists.
8.3 Regional initiatives
The Bourse Emergence(s) de la Ville de Paris “Morphométrie sous contrainte pour l’analyse de données biologiques : un nouvel outil pour la communauté scientifique”, whose principal investigator is Barbara Gris, runs from 2022 to 2025.
9 Dissemination
9.1 Promoting scientific activities
9.1.1 Scientific events: organisation
 Ugo Boscain, JeanMichel Coron, Kévin Le Balc’h, Mario Sigalotti, and Emmanuel Trélat are members of the scientific committee of the Groupe de Travail Contrôle. Emmanuel Trélat is the main organizer of this regular seminar.
Member of the organizing and scientific committees
 Ugo Boscain was organizer (together with Domenico D'Alessandro) of the triple session “Geometric Control Theory with Quantum and Classical Applications” at the SIAM Conference on Control and Its Applications, Philadelphia, USA, July.
 Ugo Boscain was organizer (together with Giovanni Marelli) of the CIMPA school “Contemporary Geometry”. Windhoeck Namibia, January.
 Ugo Boscain and Mario Sigalotti were organizers (with D. Barilari, D. Prandi, L. Rizzi, Y. Sachkov, A. Sarychev) of the conference “Geometry and Control in Cortona”, Palazzone, Cortona Italy, March.
 Barbara Gris was in the dans local organizing committee of the conference of the FoCM society.
 Kévin Le Balc'h was coorganizer of the workhsop “Contrôle, Stabilisation et EDP” in Rennes, June.
 Emmanuel Trélat is in the scientific committee of the next SMAI Mode conference, Lyon.
 Emmanuel Trélat was in the scientific committee of the conference “New Trends and Challenges in Optimization Theory Applied to Space Engineering”, l’Aquila, Itay, December.
9.1.2 Journal
Member of the editorial boards
 Ugo Boscain is Associate editor of SIAM Journal on Control and Optimization and he is Corresponding editor of the special section “Control of Quantum Mechanical Systems”.
 Ugo Boscain is Managing editor of Journal of Dynamical and Control Systems
 JeanMichel Coron is Editorinchief of Comptes Rendus Mathématique
 JeanMichel Coron is Associate editor of Journal of Evolution Equations
 JeanMichel Coron is Associate editor of Asymptotic Analysis
 JeanMichel Coron is Associate editor of ESAIM: Control, Optimisation and Calculus of Variations
 JeanMichel Coron is Associate editor of Applied Mathematics Research Express
 JeanMichel Coron is Associate editor of Advances in Differential Equations
 JeanMichel Coron is Associate editor of Mathematics of Control, Signals, and Systems
 JeanMichel Coron is Associate editor of Annales de l'IHP, Analyse non linéaire
 Mario Sigalotti is Associate editor of SIAM Journal on Control and Optimization
 Mario Sigalotti is Associate editor of ESAIM: Control, Optimisation and Calculus of Variations
 Mario Sigalotti is Associate editor of Journal on Dynamical and Control Systems
 Emmanuel Trélat is Editorinchief of ESAIM: Control, Optimisation and Calculus of Variations
 Emmanuel Trélat is Associate editor of SIAM Review
 Emmanuel Trélat is Associate editor of Systems & Control Letters
 Emmanuel Trélat is Associate editor of Journal on Dynamical and Control Systems
 Emmanuel Trélat is Associate editor of Bollettino dell'Unione Matematica Italiana
 Emmanuel Trélat is Associate editor of ESAIM: Mathematical Modelling and Numerical Analysis
 Emmanuel Trélat is Editor of BCAM Springer Briefs
 Emmanuel Trélat is Associate editor of IEEE Transactions on Automatic Control
 Emmanuel Trélat is Associate editor of Journal of Optimization Theory and Applications
 Emmanuel Trélat is Associate editor of Mathematical Control & Related Fields
 Emmanuel Trélat is Associate editor of Mathematics of Control, Signals, and Systems
 Emmanuel Trélat is Associate editor of Optimal Control Applications and Methods
 Emmanuel Trélat is Associate editor of Advances in Continuous and Discrete Models: Theory and Modern Applications
9.1.3 Invited talks
 Ugo Boscain was invited speaker at the Journée Colloquium de Mathématiques, Laboratoire de Mathématiques d’Avignon.
 Ugo Boscain was invited speaker at ENS de Lyon, Workshop Defi EQIP 2023.
 Ugo Boscain was invited speaker at the conference “Optimization and Control in Burgundy”.
 Barbara Gris was invited speaker at the séminaire de modélisation mathématique en sciences de la vie et santé (LAGA).
 Barbara Gris was invited speaker at the journée annuelle du groupe thématique SIGMA de la SMAI.
 Kévin Le Balc'h was invited speaker at the Workshop “Control and Related Fields”, University of Sevilla, Spain.
 Kévin Le Balc'h was invited speaker at the Colloquium UNAM, Mexico City, Mexico.
 Kévin Le Balc'h was invited speaker at the Online seminar of Dortmund, Germany.
 Kévin Le Balc'h was invited speaker at at the Workshop EDP Cosy, Toulouse.
 Kévin Le Balc'h was invited speaker at the seminar of the numberical analysis and PDEs team, Sevilla, Spain.
 Mario Sigalotti was invited speaker at the Workshop EDPCOSy, Toulouse.
 Mario Sigalotti was invited speaker at the seminar of the Math department of the HumboldtUniversität zu Berlin, Germany.
 Emmanuel Trélat was plenary speaker at SCINDIS 2023, Wuppertal, Germany.
 Emmanuel Trélat was plenary speaker at SMAI 2023, Guadeloupe.
 Emmanuel Trélat was invited speaker at the conference “Control of Partial Differential Equations in HautsdeFrance”, Valenciennes.
 Emmanuel Trélat was invited speaker at the Workshop EDPCOSy, Toulouse.
 Emmanuel Trélat was invited speaker at the seminar MBDA, Le PlessisRobinson.
 Emmanuel Trélat was invited speaker at Texas A& M, College Station.
 Emmanuel Trélat was invited speaker at the francocorean weminar.
 Emmanuel Trélat was invited speaker at ENS Ker Lann.
 Emmanuel Trélat was invited speaker at Fédération Charles Hermite, Nancy.
 Emmanuel Trélat was invited speaker at the seminar of the Institut Jean Le Rond d’Alembert.
 Emmanuel Trélat was invited speaker at the seminar PDE, LJK, Grenoble.
9.1.4 Leadership within the scientific community
 Ugo Boscain is Délégueé Scientifique at INSMI in charge of interdisciplinarity and member of the Comité de pilotage of the Mission pour les initiatives transverses et interdisciplinaires (MITI).
 Emmanuel Trélat is Head of the Laboratoire JacquesLouis Lions (LJLL).
9.1.5 Scientific expertise
 Emmanuel Trélat is member of the conseil scientifique de la Fédération de Mathématiques de CentraleSupelec.
 Emmanuel Trélat is member of the Advisory Board of the Department of Data Science, FAU (Erlangen), Germany.
9.1.6 Research administration
 Kévin Le Balc'h is SMAI correspondent for the Laboratoire JacquesLouis Lions.
 Emmanuel Trélat is member of the Bureau de comité des équipesprojets, Inria Paris center.
9.2 Teaching  Supervision  Juries
9.2.1 Teaching
 Ugo Boscain thought “ Geometric Control Theory” to PhD students at SISSA, Trieste, Italy.
 Ugo Boscain thought “Complements on subRiemannian geometry” at the CIMPA PhD school “Contemporary Geometry”, Windhoeck Namibia.
 Ugo Boscain and Mario Sigalotti thought “Geometric control theory” at the M2 Mathématiques de la Modélisation, Sorbonne Université.
 Barbara Gris was in charge of the supervision of projects for l3 students,Sorbonne Université.
 Kévin Le Balc'h thought Encadrement de leçons d'agrégation externe de mathématiques to M2 students at Sorbonne Université.
 Kévin Le Balc'h thought “Approximation des EDP elliptiques” to M1 students at Sorbonne Université.
 Kévin Le Balc'h thought “Agrégation (analyse, probabilités)” to M2 students at Sorbonne Université.
 Kévin Le Balc'h thought “Analyse numérique” to L3 students at Sorbonne Université.
 Kévin Le Balc'h was the tutor of a M2 student at Sorbonne Université.
 Emmanuel Trélat thought “Contrôle en dimension finie et infinie” to M2 students at Sorbonne Université
 Emmanuel Trélat thought “Optimisation numérique et sciences des données” to M1 students at Sorbonne Université
9.2.2 Supervision
 PhD: Veljko Askovic, “Aerial vehicle guidance problem by the Pontryagin Maximum Principle and Hamilton Jacobi Bellman approach”, December 2023. Supervisors: Emmanuel Trélat and Hasnaa Zidani (INSA, Rouen).
 PhD in progress: Kala Agbo Bidi, “Robust pest control strategies”. Supervisors: Luis Almeida and JeanMichel Coron.
 PhD in progress: Liangying Chen, “Sensitivity, Verification and Conjugate Times in Stochastic Optimal Control”, started in 2021. Supervisors: Emmanuel Trélat and Xu Zhang (Chengdu, China).
 PhD in progress: Ruikang Liang, “The quantum speed limit in Quantum Control”, started in 2022. Supervisors: Ugo Boscain and Mario Sigalotti.
 PhD in progress: Xiangyu Ma, “A bioinspired geometric model for speech sound reconstruction”, started in 2023. Supervisors: Ugo Boscain, Dario Prandi, and Giuseppina Turco.
 PhD in progress: Rayane Mouhli, “L'ontogénèse par grandes déformations”, started in 2023. Supervisors: Barbara Gris and Irène Kaltenmark.
 PhD in progress: Robin Roussel, “Magnetic field lines and confinement in stellarators: a Hamiltonian perspective”, started in 2021. Supervisors: Ugo Boscain and Mario Sigalotti.
 PhD in progress: Lucia Tessarolo, “Sub Riemannian geometry and pinwheels”, started in 2023. Supervisor: Ugo Boscain.
 Kévin Le Balc'h was member of the comités de suivi of the PhD theses of Cristobal Loboya and Ivan Hasenohr.
9.2.3 Juries
 Mario Sigalotti was member of the PhD jury of Gautier Roman, Sorbonne Université.
 Mario Sigalotti and Emmanuel Trélat were members of the PhD jury of Veljko Askovic, Sorbonne Université.
 Emmanuel Trélat was president of the HDR jury of Ihab Haidar, Univiversité de Cergy.
 Emmanuel Trélat was member of the HDR jury of C. J. Silva, University of Aveiro, Portugal.
 Emmanuel Trélat was member of the HDR jury of Amaury Hayat, Université ParisDauphine.
 Emmanuel Trélat was member of the PhD jury of R. Prébet, Sorbonne Université.
 Emmanuel Trélat was referee and member of the PhD jury of R. Loyer, Université du Littoral.
 Emmanuel Trélat was member of the PhD jury of M. Harakeh, Université d’Orléans.
 Emmanuel Trélat was referee and member of the PhD jury of A. Bouali, Université d’Avignon.
 Emmanuel Trélat was referee and member of the PhD jury of A. Herasimenka, Université Côte d'Azur.
 Emmanuel Trélat was referee and member of the PhD jury of L. Mascolo, Politecnico di Torino, Italy.
 Emmanuel Trélat was referee and member of the PhD jury of H. Ménou, Ecole des Mines de Paris.
10 Scientific production
10.1 Major publications
 1 articleOn the regularity of abnormal minimizers for rank 2 subRiemannian structures.Journal de Mathématiques Pures et Appliquées1332020, 118138HALDOI
 2 articleOptimal Control of EndoAtmospheric Launch Vehicle Systems: Geometric and Computational Issues.IEEE Transactions on Automatic Control6562020, 24182433HALDOI
 3 miscSpectral asymptotics for subRiemannian Laplacians.December 2022HAL
 4 articleStabilization of the linearized water tank system.Archive for Rational Mechanics and Analysis24432022, 1019–1097HAL
 5 articleSmalltime global exact controllability of the NavierStokes equation with Navier slipwithfriction boundary conditions.Journal of the European Mathematical Society225May 2020, 16251673HALDOI
 6 articleOptimal time for the controllability of linear hyperbolic systems in one dimensional space.SIAM Journal on Control and Optimization572April 2019, 11271156HALDOI
 7 articleReachability results for perturbed heat equations.Journal of Functional Analysis28310November 2022HAL
 8 articleFull quantum control of enantiomerselective state transfer in chiral molecules despite degeneracy.Communications PhysicsMay 2022HALDOI
 9 articleImage reconstruction through metamorphosis.Inverse Problems362020HALDOI
 10 articleOptimal shape of stellarators for magnetic confinement fusion.Journal de Mathématiques Pures et Appliquées2022HALDOI
 11 articleEnsemble qubit controllability with a single control via adiabatic and rotating wave approximations.Journal of Differential Equations318May 2022HALDOI
10.2 Publications of the year
International journals
 12 articleAnts and bracket generating distributions in dimension 5 and 6.Automatica1472023HALback to text
 13 articleRelative heat content asymptotics for subRiemannian manifolds.Analysis & PDE2023HALback to text
 14 articleA Measure Theoretical Approach to the Meanfield Maximum Principle for Training NeurODEs.Nonlinear Analysis: Theory, Methods and Applications2272023, 113161HALDOIback to text

15
articleSurfaces of genus
$g1$ in 3D contact subRiemannian manifolds.ESAIM: Control, Optimisation and Calculus of Variations29November 2023, 79HALDOIback to text  16 articleGlobal Controllability of the Boussinesq System with NavierSlipwithFriction and Robin Boundary Conditions.SIAM Journal on Control and Optimization612March 2023, 484510HALDOIback to text
 17 articleHautusYamamoto criteria for approximate and exact controllability of linear difference delay equations.Discrete and Continuous Dynamical Systems  Series A439September 2023, 33063337HALDOIback to text
 18 articleUpper and lower bounds for the maximal Lyapunov exponent of singularly perturbed linear switching systems.Automatica1552023, 111151HALDOIback to text
 19 articleOn the gap between deterministic and probabilistic Lyapunov exponents for continuoustime linear systems.Electronic Journal of Probability282023, Paper No. 43, 39 pp.HALDOIback to text
 20 articleOn the global approximate controllability in small time of semiclassical 1D Schrödinger equations between two states with positive quantum densities.Journal of Differential Equations345February 2023, 144HALDOIback to text
 21 articleCost of observability inequalities for elliptic equations in 2d with potentials and applications to control theory.Communications in Partial Differential Equations484April 2023, 623677HALDOIback to text

22
articleThe isoperimetric problem for regular and crystalline norms in
${}^{1}$ .The Journal of Geometric Analysis2023HALDOIback to text  23 articleOn the pole placement of scalar linear delay systems with two delays.IMA Journal of Mathematical Control and Information401February 2023, 81–105HALDOIback to text
 24 articleDissipation of traffic jams using a single autonomous vehicle on a ring road.SIAM Journal on Applied Mathematics833January 2023HALDOIback to text
 25 articleGlobal nullcontrollability for stochastic semilinear parabolic equations.Annales de l'Institut Henri Poincaré C, Analyse non linéaireJanuary 2023, 14151455HALDOIback to text
 26 articleQuantum Limits on product manifolds.Indiana University Mathematics Journal7222023, 757783HALDOIback to text
 27 articleCatching all geodesics of a manifold with moving balls and application to controllability of the wave equation.Annali della Scuola Normale Superiore di Pisa, Classe di ScienzeXXIV2023, 15HALDOIback to text
 28 articleObservability of BaouendiGrushinType Equations Through Resolvent Estimates.Journal of the Institute of Mathematics of Jussieu2222023, 541579HALDOIback to text
 29 articleOn universal classes of Lyapunov functions for linear switched systems.Automatica1552023, 111155HALDOIback to text
 30 articleLinear turnpike theorem.Mathematics of Control, Signals, and Systems3532023, 685739HALback to text
International peerreviewed conferences
 31 inproceedingsReinforcement Learning in Control Theory: A New Approach to Mathematical Problem Solving.The 3rd Workshop on Mathematical Reasoning and AI at NeurIPS'233rd Workshop on Mathematical Reasoning and AI at NeurIPS'23New Orleans (LA), United StatesDecember 2023HALback to text
Reports & preprints
 32 miscGlobal stabilization of sterile insect technique model by feedback laws.July 2023HALback to text
 33 misc"Good Lie Brackets" for Control Affine Systems.May 2023HALback to text
 34 miscIndex theorems for graphparametrized optimal control problems.January 2022HALback to text
 35 miscLyapunov Exponents of Linear Switched Systems.December 2023HALback to text
 36 miscLinear quadratic optimal control turnpike in finite and infinite dimension: twoterm expansion of the value function.December 2023HALback to text
 37 miscTwoterm largetime asymptotic expansion of the value function for dissipative nonlinear optimal control problems.2023HALback to text
 38 miscGlobal stabilization of the cubic defocusing nonlinear Schrödinger equation on the torus.October 2023HALback to text
 39 miscExponential stability of linear periodic differencedelay equations.2023HALback to text

40
miscEmbedding the Grushin Cylinder in
${\mathbf{R}}^{3}$ and Schroedinger evolution.April 2023HALback to text  41 miscConvergence in nonlinear optimal sampleddata control problems.2023HALback to text
 42 miscApproximate and exact controllability criteria for linear onedimensional hyperbolic systems.October 2023HALback to text
 43 miscExistence of optimal domains for the helicity maximisation problem among domains satisfying a uniform ball condition.May 2023HALback to text
 44 miscProperties of the BiotSavart operator acting on surface currents.November 2023HALback to text
 45 miscObservability estimates for the Schrödinger equation in the plane with periodic bounded potentials from measurable sets.April 2023HALback to text
 46 miscQuantum control of rovibrational dynamics and application to lightinduced molecular chirality.October 2023HALback to text
 47 miscQuantum limits of subLaplacians via joint spectral calculus.April 2023HALback to text
 48 miscControllability of quantum systems having weakly conically connected spectrum.October 2023HALback to text
 49 miscOptimal control approaches for Open Pit planning.March 2023HALback to text
 50 miscApproximate control of parabolic equations with onoff shape controls by Fenchel duality.December 2023HALback to text
 51 miscControl in finite and infinite dimension.December 2023HALback to text
10.3 Cited publications
 52 articleThe intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups.J. Funct. Anal.25682009, 26212655URL: https://doi.org/10.1016/j.jfa.2009.01.006DOIback to text
 53 bookControl theory from the geometric viewpoint.87Encyclopaedia of Mathematical SciencesControl Theory and Optimization, IISpringerVerlag, Berlin2004, xiv+412URL: https://doi.org/10.1007/9783662064047DOIback to text
 54 bookTopics on analysis in metric spaces.25Oxford Lecture Series in Mathematics and its ApplicationsOxford University Press, Oxford2004, viii+133back to text
 55 articleShape deformation analysis from the optimal control viewpoint.J. Math. Pures Appl. (9)10412015, 139178URL: https://doi.org/10.1016/j.matpur.2015.02.004DOIback to text
 56 articleAnalytical parameterization of rotors and proof of a Goldberg conjecture by optimal control theory.SIAM J. Control Optim.4762008, 30073036DOIback to text
 57 articleQualitative properties of certain piecewise deterministic Markov processes.Ann. Inst. Henri Poincaré Probab. Stat.5132015, 10401075URL: https://doi.org/10.1214/14AIHP619DOIback to text
 58 articleThe inactivation principle: mathematical solutions minimizing the absolute work and biological implications for the planning of arm movements.PLoS Comput. Biol.4102008, e1000194, 25URL: https://doi.org/10.1371/journal.pcbi.1000194DOIback to text
 59 bookStratified Lie groups and potential theory for their subLaplacians.Springer Monographs in MathematicsSpringer, Berlin2007, xxvi+800back to text
 60 bookMécanique céleste et contrôle des véhicules spatiaux.51Mathématiques & Applications (Berlin) [Mathematics & Applications]SpringerVerlag, Berlin2006, xiv+276back to text
 61 articleHypoelliptic diffusion and human vision: a semidiscrete new twist.SIAM J. Imaging Sci.722014, 669695DOIback to text
 62 articleAdiabatic control of the Schroedinger equation via conical intersections of the eigenvalues.IEEE Trans. Automat. Control5782012, 19701983back to text
 63 articleAnthropomorphic image reconstruction via hypoelliptic diffusion.SIAM J. Control Optim.5032012, 13091336DOIback to textback to text
 64 articleSystem theory on group manifolds and coset spaces.SIAM J. Control101972, 265284back to text
 65 bookGeometric control of mechanical systems.49Texts in Applied MathematicsModeling, analysis, and design for simple mechanical control systemsSpringerVerlag, New York2005, xxiv+726DOIback to text
 66 articleControllability of the discretespectrum Schrödinger equation driven by an external field.Ann. Inst. H. Poincaré Anal. Non Linéaire2612009, 329349URL: https://doi.org/10.1016/j.anihpc.2008.05.001DOIback to textback to text
 67 articleA cortical based model of perceptual completion in the rototranslation space.J. Math. Imaging Vision2432006, 307326URL: http://dx.doi.org/10.1007/s1085100536302DOIback to text
 68 articleDecay rates for stabilization of linear continuoustime systems with random switching.Math. Control Relat. Fields2019back to text
 69 bookControl and nonlinearity.136Mathematical Surveys and MonographsAmerican Mathematical Society, Providence, RI2007, xiv+426back to text
 70 articleGlobal asymptotic stabilization for controllable systems without drift.Math. Control Signals Systems531992, 295312URL: https://doi.org/10.1007/BF01211563DOIback to text
 71 inproceedingsOn the controllability of nonlinear partial differential equations.Proceedings of the International Congress of Mathematicians. Volume IHindustan Book Agency, New Delhi2010, 238264back to text
 72 bookIntroduction to quantum control and dynamics.Chapman & Hall/CRC Applied Mathematics and Nonlinear Science SeriesChapman & Hall/CRC, Boca Raton, FL2008, xiv+343back to text
 73 articleFlatness and defect of nonlinear systems: introductory theory and examples.Internat. J. Control6161995, 13271361URL: https://doi.org/10.1080/00207179508921959DOIback to text
 74 articleA threescale model of spatiotemporal bursting.SIAM J. Appl. Dyn. Syst.1542016, 21432175DOIback to text
 75 articleTraining Schrödinger's cat: quantum optimal control. Strategic report on current status, visions and goals for research in Europe.European Physical Journal D692015, 279DOIback to text
 76 bookBrain and Visual Perception: The Story of a 25Year Collaboration.OxfordOxford University Press2004back to text
 77 bookGeometric control theory.52Cambridge Studies in Advanced MathematicsCambridge University Press, Cambridge1997, xviii+492back to text
 78 articleControl systems on Lie groups.J. Differential Equations121972, 313329URL: https://doi.org/10.1016/00220396(72)900356DOIback to text
 79 articleSwitch observability for switched linear systems.Automatica J. IFAC872018, 121127URL: https://doi.org/10.1016/j.automatica.2017.09.024DOIback to text
 80 articleAdiabatic passage and ensemble control of quantum systems.Journal of Physics B44152011back to text
 81 bookCalculus of variations and optimal control theory.A concise introductionPrinceton University Press, Princeton, NJ2012, xviii+235back to text
 82 bookSwitching in systems and control.Systems & Control: Foundations & ApplicationsBirkhäuser Boston, Inc., Boston, MA2003, xiv+233URL: https://doi.org/10.1007/9781461200178DOIback to textback to text
 83 articleAveraging theorems for highly oscillatory differential equations and iterated Lie brackets.SIAM J. Control Optim.3561997, 19892020DOIback to text
 84 articleStability of distributed congestion control with heterogeneous feedback delays.IEEE Trans. Automat. Control476Special issue on systems and control methods for communication networks2002, 895902URL: https://doi.org/10.1109/TAC.2002.1008356DOIback to text
 85 bookA tour of subriemannian geometries, their geodesics and applications.91Mathematical Surveys and MonographsAmerican Mathematical Society, Providence, RI2002, xx+259back to text
 86 articleNonholonomic motion planning: steering using sinusoids.IEEE Trans. Automat. Control3851993, 700716URL: https://doi.org/10.1109/9.277235DOIback to text
 87 articleOn the adiabatic theorem of quantum mechanics.J. Phys. A1321980, L15L18URL: http://stacks.iop.org/03054470/13/L15back to text
 88 articleAlternative control methods for DCDC converters: an application to a fourlevel threecell DCDC converter.Internat. J. Robust Nonlinear Control21102011, 11121133URL: https://doi.org/10.1002/rnc.1651DOIback to text
 89 bookNeurogéomètrie de la vision. Modèles mathématiques et physiques des architectures fonctionnelles.Les Éditions de l'École Polythechnique2008back to text
 90 articleMomentbased methods for parameter inference and experiment design for stochastic biochemical reaction networks.ACM Trans. Model. Comput. Simul.2522015, Art. 8, 25URL: https://doi.org/10.1145/2688906DOIback to text
 91 articleThe symplectic structure of the primary visual cortex.Biol. Cybernet.9812008, 3348URL: http://dx.doi.org/10.1007/s0042200701949DOIback to text
 92 bookAn introduction to hybrid dynamical systems.251Lecture Notes in Control and Information SciencesSpringerVerlag London, Ltd., London2000, xiv+174URL: https://doi.org/10.1007/BFb0109998DOIback to text
 93 bookGeometric optimal control.38Interdisciplinary Applied MathematicsTheory, methods and examplesSpringer, New York2012, xx+640URL: https://doi.org/10.1007/9781461438342DOIback to textback to text
 94 bookOptimal control for mathematical models of cancer therapies.42Interdisciplinary Applied MathematicsAn application of geometric methodsSpringer, New York2015, xix+496URL: https://doi.org/10.1007/9781493929726DOIback to text
 95 articleA design methodology for switched discrete time linear systems with applications to automotive roll dynamics control.Automatica J. IFAC4492008, 23582363URL: https://doi.org/10.1016/j.automatica.2008.01.014DOIback to text
 96 incollectionInput to state stability: basic concepts and results.Nonlinear and optimal control theory1932Lecture Notes in Math.Springer, Berlin2008, 163220URL: https://doi.org/10.1007/9783540776536_3back to text
 97 articleControllability and reachability criteria for switched linear systems.Automatica J. IFAC3852002, 775786URL: https://doi.org/10.1016/S00051098(01)002679DOIback to text
 98 bookStability theory of switched dynamical systems.Communications and Control Engineering SeriesSpringer, London2011, xx+253URL: https://doi.org/10.1007/9780857292568DOIback to textback to text
 99 bookAdiabatic perturbation theory in quantum dynamics.1821Lecture Notes in MathematicsBerlinSpringerVerlag2003, vi+236back to text
 100 bookContrôle optimal.Mathématiques Concrètes. [Concrete Mathematics]Théorie & applications. [Theory and applications]Vuibert, Paris2005, vi+246back to textback to text
 101 articleOptimal control and applications to aerospace: some results and challenges.J. Optim. Theory Appl.15432012, 713758URL: https://doi.org/10.1007/s1095701200505DOIback to text
 102 bookObservation and control for operator semigroups.Birkhäuser Advanced Texts: Basler Lehrbücher. [Birkhäuser Advanced Texts: Basel Textbooks]Birkhäuser Verlag, Basel2009, xii+483URL: https://doi.org/10.1007/9783764389949DOIback to text
 103 inproceedingsOn the controllability of bilinear quantum systems.Mathematical models and methods for ab initio Quantum Chemistry74Lecture Notes in ChemistrySpringer2000back to text
 104 bookLectures on Lyapunov exponents.145Cambridge Studies in Advanced MathematicsCambridge University Press, Cambridge2014, xiv+202URL: https://doi.org/10.1017/CBO9781139976602DOIback to text
 105 bookOptimal control.Systems & Control: Foundations & ApplicationsBirkhäuser Boston, Inc., Boston, MA2000, xviii+507back to text
 106 inproceedingsQuantum control using diabatic and adiabatic transitions.AIP Conference Proceedings9632AIP2007, 840842back to text
 107 articleTopology of adiabatic passage.Phys. Rev. A652002, 043407, 7back to text