2025Activity report‌​‌Project-TeamCAGE

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​​​‌ so-called end-point 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) 136. Optimal​​ control theory is clearly​​​‌ deeply interconnected with calculus‌ of variations, even if‌​‌ the non-interchangeable nature of​​ the time-variable results in​​​‌ some important specific features,‌ such as the occurrence‌​‌ of abnormal extremals112​​. Research in optimal​​​‌ control encompasses different aspects,‌ from numerical methods to‌​‌ dynamic programming and non-smooth​​ analysis, from regularity of​​​‌ minimizers to high order‌ optimality conditions and curvature-like‌​‌ 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 non-autonomous disturbances is​​ that of hybrid and​​​‌ switched systems 123,​ 113, 129.​‌ 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 input-to-state stability127​‌, 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 121​​ and models for neural​​​‌ activity 104. Therapy​ analysis from the point​‌ of view of optimal​​ control has also attracted​​​‌ a great attention 125​.

Biological models are​‌ not the only one​​ in which stochastic processes​​​‌ play an important role.​ Stock-markets and energy grids​‌ are two major examples​​ where optimal control techniques​​​‌ are applied in the​ non-deterministic 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​​ 133.

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 105.​​

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 95​​. 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 96 builds​​​‌ on this premises in‌ order to provide powerful‌​‌ tests for the controllability​​ of quantum systems defined​​​‌ on infinite-dimensional 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 131​​, 124. 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 117, 114‌​‌, those based on​​ the differentiation of nonlinear​​​‌ flows such as the‌ return method100,‌​‌ 101, and those​​ exploiting the differential flatness​​​‌ of the system 103‌.

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 control-related. 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 83 or​​ shape optimization 87.​​​‌ Examples of the second‌ type are inactivation principles‌​‌ in human motricity 89​​ or neurogeometrical models for​​​‌ image representation of the‌ primary visual cortex in‌​‌ mammals 93.

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 point-dependent​​​‌ quadratic form (encoding the​ cost of the control),​‌ the resulting geometrical structure​​ is said to be​​​‌ sub-Riemannian. Sub-Riemannian 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, sub-Riemannian​ geometry provides an adapted​‌ non-isotropic class of lenses​​ which are often much​​​‌ more informative. As such,​ its study is fundamental​‌ for control design. The​​ importance of sub-Riemannian geometry​​​‌ goes beyond control theory​ and it is an​‌ active field of research​​ both in differential geometry​​​‌ 116, geometric measure​ theory 85 and hypoelliptic​‌ operator theory 90.​​

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​‌ infinite-dimensional Hilbert spaces. The​​ controllability of quantum system​​​‌ is a well-established topic​ when the state space​‌ is finite-dimensional 102,​​ thanks to general controllability​​​‌ methods for left-invariant control​ systems on compact Lie​‌ groups 94, 109​​. When the state​​​‌ space is infinite-dimensional, it​ is known that in​‌ general the bilinear Schrödinger​​ equation is not exactly​​​‌ controllable 134. The​ Lie–Galerkin technique 96 combines​‌ finite-dimensional 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 infinite-dimensional​ Hilbert spaces. Another important​‌ technique to the development​​ of which we contribute​​​‌ is adiabatic quantum control​. Adiabatic approximation theory​‌ and, in particular, adiabatic​​ evolution 118, 130​​​‌, 137 is well-known​ 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​​ 138, 111,​​​‌ 92.

4.2 Second​ axis: Stability and stabilization​‌

A control application with​​ a long history and​​​‌ still very challenging open​ problems is stabilization.​‌ For infinite-dimensional 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,​​ finite-time, ... Another important​​​‌ aspect of stabilization concerns‌ control of systems with‌​‌ uncertain dynamics, i.e., with​​ dynamics including possibly non-autonomous​​​‌ 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 126‌​‌, energy management 119​​ and congestion control 115​​​‌. Even if both‌ controllability 128 and observability‌​‌ 110 of switched and​​ hybrid systems raise several​​​‌ important research issues, the‌ central role in their‌​‌ study is played by​​ uniform stability and stabilizabilization​​​‌ 113, 129.‌ Uniformity is considered with‌​‌ respect to all signals​​ in a given class,​​​‌ and it is well-known‌ 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 dwell-time. Our approach​​ to constrained switching is​​​‌ based on the idea‌ of relating the analytical‌​‌ properties of the classes​​ of constrained switching laws​​​‌ (shift-invariance, 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' worst-case 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 88​​​‌, 98, 135‌.

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​ 131, 124.​‌ Applications of optimal control​​ theory considered by CAGE​​​‌ concern, in particular, motion​ planning problems for aerospace​‌ (atmospheric re-entry, orbit transfer,​​ low cost interplanetary space​​​‌ missions, ...) 91,​ 132.

4.4 Fourth​‌ axis: Geometric models for​​ vision and sub-Riemannian 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​​ control-related. In particular, we​​​‌ use control theory to​ investigate the properties of​‌ sub-Riemannian structures, both for​​ the sake of mathematical​​​‌ understanding and as a​ modeling tool for image​‌ and sound perception and​​ processing . We recall​​​‌ that sub-Riemannian 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​​ control-linear systems with quadratic​​​‌ cost. Sub-Riemannian geometry turns​ out to be a​‌ powerful tool for studying​​ geometry of vision,​​​‌ either from the perspective​ of the neurogeometrical model​‌ of the primary visual​​ cortex inspired by Hubel​​​‌ and Wiesel 106 and​ proposed by Petitot, Citti​‌ and Sarti 120,​​ 97, 122 or​​​‌ from the point of​ view of pattern matching​‌ in the group of​​ diffeomorphisms 86. Nonholonomic​​​‌ constraints are used in​ this setting to describe​‌ distortions of sets of​​ interconnected objects (e.g., motions​​​‌ of organs in medical​ imaging).

4.5 Fifth axis:​‌ Magnetic confinement in stellarators​​

Another domain on which​​​‌ the team has been​ active since before the​‌ last evaluation is the​​ mathematics of magnetic confinement​​​‌ in stellarators. The​ latter are toroidal devices​‌ whose goal is to​​ achieve nuclear fusion, alternative​​​‌ to tokamaks. In stellarators,​ the twist in the​‌ confining magnetic fields is​​ obtained without inducing any​​​‌ current (contrary to tokamaks),​ relying instead on a​‌ much more complex shape​​ and magnetic field structure.​​​‌ While stellarators are expected​ to be easier to​‌ operate (they can in​​ principle achieve steady-state operation),​​​‌ their design is considerably​ more challenging to realize.​‌ The design of stellarators​​ still faces numerous problems,​​​‌ many of which are​ highly complex from a​‌ mathematical perspective 107.​​ Our goal is to​​ improve the understanding of​​​‌ the dynamical properties of‌ magnetic fields in toroidal‌​‌ domains at magneto-hydrodynamic equilibrium​​ and to optimize the​​​‌ shape of stellarators in‌ order to get magnetic‌​‌ fields with the best​​ confining properties.

5.1‌ Impact of research results‌​‌

The collaboration with Renaissance​​ Fusion on the topic​​​‌ of magnetic confinement has‌ the objective of accelerating‌​‌ the development of stellarators,​​ which have the potential​​​‌ of producing low-carbon energy‌ with little radioactive waste‌​‌ and abundant fuel.

7.1‌ Quantum control: new results‌​‌

Participants: Ugo Boscain,​​ Bettina Kazandjian, Kévin​​​‌ Le Balc'h, Ruikang‌ Liang, Mario Sigalotti‌​‌, Emmanuel Trélat.​​

Let us list here​​​‌ our new results in‌ quantum control theory.

• The‌​‌ work 20, entitled​​ Good Lie Brackets for​​​‌ classical and quantum harmonic‌ oscillators, develops new‌​‌ structural results on the​​ Lie algebra generated by​​​‌ harmonic-oscillator Hamiltonians. It identifies‌ classes of “good” Lie‌​‌ brackets that play a​​ central role in controllability​​​‌ analysis for both classical‌ and quantum linear systems.‌​‌
• The work 28,​​ entitled Schrödinger eigenfunctions sharing​​​‌ the same modulus and‌ applications to the control‌​‌ of quantum systems,​​ investigates pairs of eigenfunctions​​​‌ with identical modulus and‌ shows how such structures‌​‌ can be used to​​ design control strategies for​​​‌ quantum dynamics, with implications‌ for inverse problems and‌​‌ quantum identification.
• The work​​ 65, entitled A​​​‌ meaningful optimal control problem‌ in quantum and classical‌​‌ physics, proposes an​​ optimal control formulation rooted​​​‌ in physical observability principles.‌ The paper establishes well-posedness‌​‌ results and provides examples​​ showing how meaningful performance​​​‌ criteria arise naturally in‌ both quantum and classical‌​‌ settings.
• The work 34​​, entitled Controllability of​​​‌ quantum systems having weakly‌ conically connected spectrum,‌​‌ proves controllability results for​​ finite-dimensional quantum systems whose​​​‌ spectra satisfy a weak‌ conical connectivity condition. This‌​‌ extends classical Lie-algebraic criteria​​ and gives new tools​​​‌ for systems with spectral‌ degeneracies.
• The work 35‌​‌, entitled Ensemble control​​ of $n$-level quantum​​​‌ systems with a scalar‌ control, addresses the‌​‌ simultaneous control of a​​ continuum of $n$-level​​​‌ quantum systems driven by‌ a common scalar field.‌​‌ It provides constructive controllability​​ results and discusses implications​​​‌ for robust manipulation of‌ quantum ensembles.
• The work‌​‌ 71, entitled Enhancing​​ the controllability of quantum​​​‌ systems via a static‌ field, shows how‌​‌ adding a suitably chosen​​ static Hamiltonian term can​​​‌ enlarge the effective Lie‌ algebra and thereby improve‌​‌ the controllability of quantum​​ systems. The article provides​​​‌ explicit conditions and illustrative‌ examples.
• The work 45‌​‌, entitled Controllability and​​ ensemble control design for​​​‌ quantum systems, is‌ a comprehensive study of‌​‌ controllability and ensemble-control methods​​ for quantum dynamics. It​​​‌ combines Lie-algebraic criteria, adiabatic‌ arguments, and constructive algorithms,‌​‌ with applications to multi-level​​ systems and robust control.​​​‌
• The work 41,‌ entitled An approach to‌​‌ control design for two-level​​​‌ quantum ensemble systems,​ introduces a design methodology​‌ for controlling ensembles of​​ two-level systems subject to​​​‌ inhomogeneities. The paper develops​ control laws ensuring uniform​‌ performance across the ensemble​​ and analyzes their robustness.​​​‌

7.2 Magnetic confinement in​ stellarators: new results

Participants:​‌ Ugo Boscain, Wadim​​ Gerner.

Let us​​​‌ list here our new​ results on magnetic confinement​‌ in stellarators.

• The work​​ 27, entitled Charged​​​‌ particle motion in a​ strong magnetic field: Applications​‌ to plasma confinement,​​ provides a detailed analysis​​​‌ of charged-particle dynamics in​ the strong-field regime. By​‌ deriving accurate asymptotic models​​ and characterizing effective drift​​​‌ motions, the paper contributes​ to a better understanding​‌ of confinement mechanisms in​​ magnetized plasmas, with direct​​​‌ applications to the study​ and design of stellarators.​‌
• The work 60,​​ entitled Kernel and image​​​‌ of the Biot-Savart operator​ and their applications in​‌ stellarator designs, investigates​​ the functional-analytic properties of​​​‌ the Biot–Savart operator relevant​ for magnetic-field generation. The​‌ characterization of its kernel​​ and image leads to​​​‌ new insights into the​ degrees of freedom available​‌ in magnetic-field shaping, offering​​ mathematical tools applicable to​​​‌ the optimization and geometric​ design of stellarators.

7.3​‌ Stability and stabilization: new​​ results

Participants: Kala Agbo​​​‌ Bidi, Jean-Michel Coron​, Ihab Haidar,​‌ Kévin Le Balc'h,​​ Rayane Mouhli, Mario​​​‌ Sigalotti, Emmanuel Trélat​.

Let us list​‌ here our new results​​ about stability and stabilization​​​‌ of control and hybrid​ systems.

• The work 72​‌, entitled Stabilizability with​​ bounded feedback for analytic​​​‌ linear control systems,​ establishes conditions guaranteeing stabilizability​‌ by bounded control laws​​ in the analytic setting.​​​‌ The paper clarifies the​ relation between analytic structure,​‌ spectral constraints, and achievable​​ closed-loop decay rates.
• The​​​‌ work 17, entitled​ Global stabilization of a​‌ Sterile Insect Technique model​​ by feedback laws,​​​‌ analyzes a nonlinear population-dynamics​ model arising in Sterile​‌ Insect Technique strategies. It​​ proposes explicit stabilizing feedback​​​‌ laws ensuring the eradication​ of the wild population​‌ under biologically meaningful assumptions.​​
• The work 47,​​​‌ entitled Feedback stabilization for​ a spatial-dependent Sterile Insect​‌ Technique model with Allee​​ Effect, extends stabilization​​​‌ results to a spatially​ distributed PDE model incorporating​‌ an Allee effect. The​​ article provides sufficient conditions​​​‌ and constructive feedback designs​ guaranteeing global asymptotic stabilization.​‌
• The work 44,​​ entitled Feedback stabilisation of​​​‌ a sterile insect control​ system: Applications to mosquito-borne​‌ disease control, offers​​ a comprehensive study of​​​‌ feedback-based stabilization strategies for​ sterile insect models, combining​‌ PDE and ODE frameworks,​​ with applications to mosquito​​​‌ population control and vector-borne​ disease mitigation.
• The work​‌ 23, entitled Exponential​​ stability of linear periodic​​​‌ difference-delay equations, develops​ new criteria for exponential​‌ stability in linear systems​​ combining periodicity and delay​​​‌ effects. The results allow​ for precise characterization of​‌ the spectral properties ensuring​​ uniform decay.
• The work​​​‌ 42, entitled Dynamics​ and Stability of Continuous-Time​‌ Switched Linear Systems,​​ provides a systematic analysis​​​‌ of stability properties for​ continuous-time switched linear systems.​‌ It characterizes dynamical behaviors​​ under arbitrary, constrained, or​​ optimized switching, with emphasis​​​‌ on Lyapunov and spectral‌ criteria.
• The work 54‌​‌, entitled Stability characterization​​ of impulsive linear switched​​​‌ systems, studies linear‌ systems subject to both‌​‌ switching and impulsive effects.​​ It establishes conditions for​​​‌ stability and boundedness, revealing‌ interactions between impulsive actions,‌​‌ switching signals, and system​​ matrices.
• The work 61​​​‌, entitled Stability criteria‌ for hybrid linear systems‌​‌ with singular perturbations,​​ examines hybrid systems involving​​​‌ multiple time scales and‌ discontinuities. The article provides‌​‌ stability criteria capturing the​​ combined influence of switching,​​​‌ fast–slow dynamics, and perturbation‌ parameters.
• The work 40‌​‌, entitled Sampled-data global​​ asymptotic stabilization of globally​​​‌ Lipschitz retarded switched systems‌, derives stabilizing sampled-data‌​‌ feedback laws for a​​ large class of switched​​​‌ systems with delays. The‌ results guarantee global asymptotic‌​‌ stability under mild Lipschitz​​ and switching assumptions.
• The​​​‌ work 69, entitled‌ Boundary output feedback stabilization‌​‌ of a cascade of​​ $N$ heat equations,​​​‌ proposes an output-feedback law‌ achieving exponential stabilization of‌​‌ a multi-equation heat cascade​​ through boundary measurements only.​​​‌ The approach relies on‌ tailored Lyapunov functionals and‌​‌ backstepping constructions.
• The work​​ 66, entitled Optimal​​​‌ dynamical stabilization, introduces‌ a framework for designing‌​‌ stabilizing controls that are​​ optimal with respect to​​​‌ dynamical performance criteria. The‌ article connects stabilization, optimality,‌​‌ and energy shaping through​​ a unified variational perspective.​​​‌
• The work 74,‌ entitled Decoupling actions of‌​‌ finite-dimensional groups of diffeomorphisms​​ in the large deformation​​​‌ framework, investigates stability‌ and decoupling phenomena for‌​‌ group actions in large-deformation​​ models. It provides structural​​​‌ and geometric insights relevant‌ for stabilization in nonlinear‌​‌ shape analysis problems.
• The​​ work 24, entitled​​​‌ The usefulness of viscosity‌ for the robustness of‌​‌ boundary feedback control of​​ an unstable fluid flow​​​‌ system, shows how‌ adding viscosity terms enhances‌​‌ robustness properties of boundary-feedback​​ controllers in fluid-flow models.​​​‌ The study quantifies the‌ stabilizing effect of dissipative‌​‌ mechanisms.
• The work 22​​, entitled Lyapunov Exponents​​​‌ of Linear Switched Systems‌, analyzes the Lyapunov‌​‌ spectrum of linear switched​​ systems under various switching​​​‌ rules. It provides new‌ formulas and bounds for‌​‌ Lyapunov exponents, offering deeper​​ insight into stability mechanisms​​​‌ for switched dynamics.

7.4‌ Controllability, observability, and motion‌​‌ planning: new results

Participants:​​ Jean-Michel Coron, Bettina​​​‌ Kazandjian, Kévin Le‌ Balc'h, Jingrui Niu‌​‌, Mario Sigalotti,​​ Emmanuel Trélat.

Let​​​‌ us list here our‌ new results on controllability,‌​‌ observability, and motion planning.​​

• The work 77,​​​‌ entitled Observability and controllability‌ for Schrödinger equations in‌​‌ the semi-periodic setting,​​ develops new observability and​​​‌ controllability results for Schrödinger‌ dynamics on semi-periodic domains.‌​‌ The analysis combines Fourier​​ decomposition techniques with refined​​​‌ propagation estimates.
• The work‌ 67, entitled Geometric‌​‌ condition for the observability​​ of electromagnetic Schrödinger operators​​​‌ on ${𝕋}^2$,‌ establishes a geometric condition‌​‌ ensuring observability for Schrödinger​​ equations with electromagnetic potentials​​​‌ on the two-dimensional torus.‌ The result extends classical‌​‌ geometric control principles to​​ the magnetic setting.
• The​​​‌ work 59, entitled‌ Control of blow-up profiles‌​‌ for the mass-critical focusing​​​‌ nonlinear Schrödinger equation on​ bounded domains, investigates​‌ how controls can influence​​ blow-up dynamics in the​​​‌ mass-critical NLS. The article​ describes mechanisms allowing one​‌ to modify or steer​​ blow-up profiles through appropriately​​​‌ chosen forcing.
• The work​ 33, entitled Quantitative​‌ propagation of smallness and​​ spectral estimates for the​​​‌ Schrödinger operator, provides​ new quantitative results on​‌ propagation of smallness for​​ Schrödinger eigenfunctions. These yield​​​‌ refined spectral estimates with​ implications for observability and​‌ control.
• The work 49​​, entitled The Graph​​​‌ Geometric Control Condition,​ introduces a graph-theoretic interpretation​‌ of geometric control conditions​​ for PDEs. It provides​​​‌ a unified framework for​ understanding how geometric propagation​‌ interacts with control and​​ observation regions.
• The work​​​‌ 29, entitled Global​ controllability and stabilization of​‌ the wave maps equation​​ from a circle to​​​‌ a sphere, proves​ global controllability and stabilization​‌ results for the wave​​ maps equation in a​​​‌ one-dimensional geometric setting. The​ analysis relies on the​‌ interplay between energy methods​​ and geometric properties of​​​‌ the target manifold.
• The​ work 30, entitled​‌ Global controllability to harmonic​​ maps of the heat​​​‌ flow from a circle​ to a sphere,​‌ establishes global controllability toward​​ harmonic maps for the​​​‌ heat flow between the​ circle and the sphere.​‌ The result highlights how​​ geometry influences the reachable​​​‌ set.
• The work 58​, entitled Wave maps​‌ from circle to Riemannian​​ manifold: global controllability is​​​‌ equivalent to homotopy,​ provides a characterization of​‌ global controllability in geometric​​ wave-map systems, showing that​​​‌ controllability reduces to topological​ properties of homotopy classes.​‌
• The work 70,​​ entitled Controllability and Stabilization​​​‌ of a Wave–Heat Cascade​ System, analyzes a​‌ coupled wave–heat cascade and​​ proves both controllability and​​​‌ stabilization results using boundary​ actions and appropriate energy​‌ estimates.
• The work 68​​, entitled Boundary control​​​‌ of heat–heat cascades,​ develops boundary control strategies​‌ for cascaded heat equations,​​ providing explicit feedback constructions​​​‌ and demonstrating exponential stabilization.​
• The work 76,​‌ entitled Small-time local controllability​​ of a KdV system​​​‌ for all critical lengths​, proves small-time local​‌ controllability for KdV dynamics​​ at every critical length,​​​‌ resolving an open question​ and extending classical boundary-control​‌ results.
• The work 75​​, entitled The periodic​​​‌ KdV with control on​ space-time measurable sets,​‌ establishes controllability of periodic​​ KdV equations with controls​​​‌ acting on general measurable​ subsets of space-time, using​‌ advanced observability and unique​​ continuation arguments.
• The work​​​‌ 31, entitled Controlling​ the rates of a​‌ chain of harmonic oscillators​​ with a point Langevin​​​‌ thermostat, analyzes controllability​ properties in chains of​‌ harmonic oscillators coupled to​​ a thermostat. It characterizes​​​‌ how localized stochastic forcing​ influences the global energy​‌ distribution.
• The work 32​​, entitled Internal control​​​‌ of the transition kernel​ for stochastic lattice dynamics​‌, studies internal control​​ mechanisms for stochastic lattice​​​‌ systems. It provides results​ on how controls shape​‌ the transition kernel and​​ long-term behavior of the​​​‌ system.
• The work 39​, entitled On the​‌ dimension of observable sets​​ for the heat equation​​, investigates how the​​​‌ size and geometry of‌ observation sets influence observability‌​‌ for the heat equation,​​ providing new bounds on​​​‌ the minimal dimension of‌ sets enabling full observation.‌​‌
• The work 21,​​ entitled Generic controllability of​​​‌ equivariant systems and applications‌ to particle systems and‌​‌ neural networks, establishes​​ generic controllability results for​​​‌ systems with symmetry. Applications‌ include controlled particle systems‌​‌ and models of neural​​ dynamics exhibiting equivariance.
• The​​​‌ work 64, entitled‌ Orbits and attainable Hamiltonian‌​‌ diffeomorphisms of mechanical Liouville​​ equations, characterizes the​​​‌ reachable sets and attainable‌ Hamiltonian diffeomorphisms associated with‌​‌ mechanical Liouville equations. The​​ results clarify how geometric​​​‌ constraints shape controllability in‌ Hamiltonian systems.

7.5 Optimization,‌​‌ optimal control, and sub-Riemannian​​ models: new results

Participants:​​​‌ Barbara Gris, Ugo‌ Boscain, Bettina Kazandjian‌​‌, Xiangyu Ma,​​ Rayane Mouhli, Mario​​​‌ Sigalotti, Alessandro Socionovo‌, Lucia Tessarolo,‌​‌ Emmanuel Trélat.

Let​​ us list here our​​​‌ new results on optimization,‌ optimal control, and sub-Riemannian‌​‌ models.

• The work 36​​, entitled Turnpike property​​​‌ of linear quadratic control‌ problems with unbounded control‌​‌ operators, establishes turnpike​​ phenomena for infinite-dimensional LQ​​​‌ problems involving unbounded control‌ operators. The result identifies‌​‌ conditions ensuring exponential attraction​​ to steady-state optimal profiles.​​​‌
• The work 38,‌ entitled The exponential turnpike‌​‌ property for periodic linear​​ quadratic optimal control problems​​​‌ in infinite dimension,‌ demonstrates exponential turnpike behavior‌​‌ in periodic infinite-dimensional LQ​​ settings. The article provides​​​‌ precise estimates for the‌ convergence rate toward periodic‌​‌ optimal trajectories.
• The work​​ 81, entitled Turnpike​​​‌ in optimal control and‌ beyond: a survey,‌​‌ offers a comprehensive survey​​ of turnpike theory across​​​‌ finite- and infinite-dimensional optimal‌ control. It highlights general‌​‌ mechanisms, frameworks, and recent​​ applications.
• The work 19​​​‌, entitled Optimal Control‌ for Linear Systems with‌​‌ $L^1$-norm Cost​​, studies optimal control​​​‌ problems with $L^{\mathrm{1‌}}$-type performance criteria. It‌​‌ characterizes optimal solutions, their​​ sparsity properties, and the​​​‌ geometry of associated Hamiltonian‌ flows.
• The work 50‌​‌, entitled Numerical solving​​ of an optimal control​​​‌ problem in large time‌ horizon: the aerial vehicle‌​‌ guidance, develops numerical​​ methods for long-horizon optimal​​​‌ control with an application‌ to aerial-vehicle trajectory planning.‌​‌ The approach combines shooting,​​ continuation, and sensitivity tools.​​​‌
• The work 43,‌ entitled PDE-constrained optimization within‌​‌ FreeFEM, presents algorithms​​ and software tools for​​​‌ PDE-constrained optimization implemented in‌ FreeFEM. It illustrates the‌​‌ methodology through applications in​​ shape optimization and inverse​​​‌ problems.
• The work 80‌, entitled Probabilistic algorithm‌​‌ for computing all local​​ minimizers of Morse functions​​​‌ on a compact domain‌, proposes a probabilistic‌​‌ algorithm capable of detecting​​ all local minima of​​​‌ Morse functions. The method‌ has potential applications in‌​‌ global optimization and parameter-estimation​​ problems.
• The work 56​​​‌, entitled Not all‌ sub-Riemannian minimizing geodesics are‌​‌ smooth, provides examples​​ showing that minimizing geodesics​​​‌ in sub-Riemannian manifolds may‌ lack smoothness. This sheds‌​‌ light on the subtleties​​ of regularity in optimal​​​‌ control and geometric analysis.‌
• The work 63,‌​‌ entitled A note on​​​‌ pliability and the openness​ of the multiexponential map​‌ in Carnot groups,​​ studies the multiexponential map​​​‌ in Carnot groups and​ introduces new insights on​‌ pliability and openness properties​​ relevant to controllability and​​​‌ geometric flows.
• The work​ 74, entitled Decoupling​‌ actions of finite-dimensional groups​​ of diffeomorphisms in the​​​‌ large deformation framework,​ analyzes the geometry of​‌ large-deformation models and provides​​ decoupling results for group​​​‌ actions, with implications for​ shape analysis and geometric​‌ optimal control.
• The work​​ 46, entitled Schrödinger​​​‌ evolution on surfaces in​ 3D contact sub-Riemannian manifolds​‌, investigates Schrödinger dynamics​​ on submanifolds embedded in​​​‌ contact sub-Riemannian structures. It​ provides geometric insights into​‌ propagation and controllability phenomena​​ in degenerate settings.
• The​​​‌ work 25, entitled​ Embedding the Grushin Cylinder​‌ in ${𝐑}^3$ and​​ Schroedinger evolution, studies​​​‌ embeddings of the Grushin​ cylinder into Euclidean space​‌ and analyzes associated Schrödinger​​ equations. The work connects​​​‌ geometric degeneracies with quantum​ propagation properties.
• The work​‌ 79, entitled Universal​​ approximations of quasilinear PDEs​​​‌ by finite distinguishable particle​ systems, shows how​‌ quasilinear PDEs can be​​ approximated by interacting particle​​​‌ systems. It establishes convergence​ results and explores implications​‌ for numerical simulation and​​ control.
• The work 78​​​‌, entitled Infinite-wise interactions:​ mean-field and graph limits​‌ for multiple-wise distinguishable agent​​ systems, analyzes systems​​​‌ with higher-order interactions and​ proves propagation-of-chaos results. The​‌ macroscopic limits obtained have​​ applications in collective dynamics​​​‌ and optimal control.
• The​ work 37, entitled​‌ Existence of surfaces optimizing​​ geometric and PDE shape​​​‌ functionals under reach constraint​, establishes existence results​‌ for shape-optimization problems under​​ reach constraints. The work​​​‌ blends geometric measure theory​ with PDE-based optimization.
• The​‌ work 51, entitled​​ A solution to the​​​‌ mystery of the sub-harmonic​ combination tone via a​‌ linear mathematical model of​​ the cochlea, proposes​​​‌ a linear cochlear model​ explaining the emergence of​‌ sub-harmonic combination tones. The​​ analysis uses geometric and​​​‌ dynamical tools relevant to​ sub-Riemannian auditory models.

8.1 Bilateral​​​‌ contracts with industry

Participants:​ Emmanuel Trélat.

Grant​‌ by AFOSR (Air Force​​ Office of Scientific Research),​​​‌ 2025–2028, coordinated by Emmanuel​ Trélat . The focus​‌ of the project was​​ on optimization and optimal​​​‌ control problems having an​ algebraic structure, involving for​‌ instance polynomial or semi-algebraic​​ dynamics and cost functionals,​​​‌ or switches between polynomial​ models. Motion planning under​‌ obstacles is one of​​ the main targeted problems.​​​‌

9.1 International initiatives

Participants:​‌ Emmanuel Trélat, Kévin​​ Le Balc'h.

9.2 National initiatives

9.3 Regional initiatives

Participants:‌ Barbara Gris, Rayane‌​‌ Mouhli.

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”, 2022–2025, coordinated‌ by Barbara Gris .‌​‌ Members for CAGE: Barbara​​ Gris and Rayane Mouhli​​​‌ .

9.4 Public policy‌ support

Participants: Emmanel Trélat‌​‌.

Emmanel Trélat is​​ member of the scientific​​​‌ committee CERT at CNES‌, headed by Sébastien‌​‌ Candel (Académie des Sciences).​​

10.1 Promoting​​​‌ scientific activities

10.2 Teaching -‌​‌ Supervision - Juries -​​ Educational and pedagogical outreach​​​‌

• Ugo Boscain and Mario‌ Sigalotti taught “Geometric control‌​‌ theory” to M2 students​​ at Sorbonne Université (15h​​​‌ équivalent TD each).
• Kévin‌ Le Balc'h taught “Agrégation‌​‌ (analyse, probabilités)” to M2​​ students at Sorbonne Université​​​‌ (16h équivalent TD).‌
• Kévin Le Balc'h taught‌​‌ “Oraux blancs analyse probabilités”​​ to M2 students at​​​‌ Sorbonne Université (20h équivalent‌ TD).
• Kévin Le‌​‌ Balc'h taught “Optimisation, Contrôle,​​ Données” to M2 students​​​‌ at Sorbonne Université (24h‌ équivalent TD).
• Mario‌​‌ Sigalotti taught “Introduction to​​ Geometric Control Theory” to​​​‌ PhD students at SISSA,‌ Trieste, Italy (30h équivalent‌​‌ TD).
• Emmanuel Trélat​​ taught “Contrôle en dimension​​​‌ finie et infinie” to‌ M2 students at Sorbonne‌​‌ Université (36h équivalent TD​​).
• Emmanuel Trélat taught​​​‌ “Optimisation numérique et sciences‌ des données” to M1‌​‌ students at Sorbonne Université​​ (36h équivalent TD).​​​‌

10.3 Popularization

11.1 Major publications​​​‌

• 1 articleD.Davide​ Barilari, U.Ugo​‌ Boscain, D.Daniele​​ Cannarsa and K.Karen​​​‌ Habermann. Stochastic processes​ on surfaces in three-dimensional​‌ contact sub-Riemannian manifolds.​​Annales de l'Institut Henri​​​‌ Poincaré (B) Probabilités et​ Statistiques25 pages, 2​‌ figures2021HALDOI​​
• 2 articleD.Davide​​​‌ Barilari, Y.Yacine​ Chitour, F.Frédéric​‌ Jean, D.Dario​​ Prandi and M.Mario​​​‌ Sigalotti. On the​ regularity of abnormal minimizers​‌ for rank 2 sub-Riemannian​​ structures.Journal de​​ Mathématiques Pures et Appliquées​​​‌1332020, 118-138‌HALDOI
• 3 article‌​‌M.Marcelo Bertalmio,​​ L.Luca Calatroni,​​​‌ V.Valentina Franceschi,‌ B.Benedetta Franceschiello and‌​‌ D.Dario Prandi.​​ Cortical-inspired Wilson-Cowan-type equations for​​​‌ orientation-dependent contrast perception modelling‌.Journal of Mathematical‌​‌ Imaging and VisionJune​​ 2020HALDOI
• 4​​​‌ articleR.Riccardo Bonalli‌, B.Bruno Hérissé‌​‌ and E.Emmanuel Trélat​​. Optimal Control of​​​‌ Endo-Atmospheric Launch Vehicle Systems:‌ Geometric and Computational Issues‌​‌.IEEE Transactions on​​ Automatic Control656​​​‌2020, 2418--2433HAL‌DOI
• 5 articleU.‌​‌Ugo Boscain, E.​​Eugenio Pozzoli and M.​​​‌Mario Sigalotti. Classical‌ and quantum controllability of‌​‌ a rotating 3D symmetric​​ molecule.SIAM Journal​​​‌ on Control and Optimization‌2020HAL
• 6 misc‌​‌Y.Yves Colin de​​ Verdìère, L.Luc​​​‌ Hillairet and E.Emmanuel‌ Trélat. Spectral asymptotics‌​‌ for sub-Riemannian Laplacians.​​December 2022HAL
• 7​​​‌ articleJ.-M.Jean-Michel Coron‌, A.Amaury Hayat‌​‌, S.Shengquan Xiang​​ and C.Christophe Zhang​​​‌. Stabilization of the‌ linearized water tank system‌​‌.Archive for Rational​​ Mechanics and Analysis244​​​‌32022, 1019–1097‌HAL
• 8 articleJ.-M.‌​‌Jean-Michel Coron, F.​​Frédéric Marbach and F.​​​‌Franck Sueur. Small-time‌ global exact controllability of‌​‌ the Navier-Stokes equation with​​ Navier slip-with-friction boundary conditions​​​‌.Journal of the‌ European Mathematical Society22‌​‌5May 2020,​​ 1625--1673HALDOI
• 9​​​‌ articleJ.-M.Jean-Michel Coron‌ and H.-M.Hoai-Minh Nguyen‌​‌. Finite-time stabilization in​​ optimal time of homogeneous​​​‌ quasilinear hyperbolic systems in‌ one dimensional space.‌​‌ESAIM: Control, Optimisation and​​ Calculus of Variations26​​​‌2020, 119HAL‌DOI
• 10 articleJ.-M.‌​‌Jean-Michel Coron and H.-M.​​Hoai-Minh Nguyen. Optimal​​​‌ time for the controllability‌ of linear hyperbolic systems‌​‌ in one dimensional space​​.SIAM Journal on​​​‌ Control and Optimization57‌2April 2019,‌​‌ 1127-1156HALDOI
• 11​​ articleS.Sylvain Ervedoza​​​‌, K.Kévin Le‌ Balc’h and M.Marius‌​‌ Tucsnak. Reachability results​​ for perturbed heat equations​​​‌.Journal of Functional‌ Analysis28310November‌​‌ 2022HAL
• 12 article​​M.Monika Leibscher,​​​‌ E.Eugenio Pozzoli,‌ C.Cristobal Pérez,‌​‌ M.Melanie Schnell,​​ M.Mario Sigalotti,​​​‌ U.Ugo Boscain and‌ C. P.Christiane P.‌​‌ Koch. Full quantum​​ control of enantiomer-selective state​​​‌ transfer in chiral molecules‌ despite degeneracy.Communications‌​‌ PhysicsMay 2022HAL​​DOI
• 13 articleJ.​​​‌Jérôme Lohéac, E.‌Emmanuel Trélat and E.‌​‌Enrique Zuazua. Nonnegative​​ control of finite-dimensional linear​​​‌ systems.Annales de‌ l'Institut Henri Poincaré (C)‌​‌ Non Linear Analysis38​​2021, 301--346HAL​​​‌DOI
• 14 articleO.‌Ozan Öktem, B.‌​‌Barbara Gris and C.​​Chong Chen. Image​​​‌ reconstruction through metamorphosis.‌Inverse Problems362020‌​‌HALDOI
• 15 article​​Y.Yannick Privat,​​​‌ R.Rémi Robin and‌ M.Mario Sigalotti.‌​‌ Optimal shape of stellarators​​ for magnetic confinement fusion​​​‌.Journal de Mathématiques‌ Pures et Appliquées2022‌​‌HALDOI
• 16 article​​​‌R.Rémi Robin,​ N.Nicolas Augier,​‌ U.Ugo Boscain and​​ M.Mario Sigalotti.​​​‌ Ensemble qubit controllability with​ a single control via​‌ adiabatic and rotating wave​​ approximations.Journal of​​​‌ Differential Equations318May​ 2022HALDOI

11.2​‌ Publications of the year​​

11.3 Cited publications

• 83​ articleA.Andrei Agrachev​‌, U.Ugo Boscain​​, J.-P.Jean-Paul Gauthier​​​‌ and F.Francesco Rossi​. The intrinsic hypoelliptic​‌ Laplacian and its heat​​ kernel on unimodular Lie​​​‌ groups.J. Funct.​ Anal.25682009​‌, 2621--2655URL: https://doi.org/10.1016/j.jfa.2009.01.006​​DOIback to text​​
• 84 bookA. A.​​​‌Andrei A. Agrachev and‌ Y. L.Yuri L.‌​‌ Sachkov. Control theory​​ from the geometric viewpoint​​​‌.87Encyclopaedia of‌ Mathematical SciencesControl Theory‌​‌ and Optimization, IISpringer-Verlag,​​ Berlin2004, xiv+412​​​‌URL: https://doi.org/10.1007/978-3-662-06404-7DOIback‌ to text
• 85 book‌​‌L.Luigi Ambrosio and​​ P.Paolo Tilli.​​​‌ Topics on analysis in‌ metric spaces.25‌​‌Oxford Lecture Series in​​ Mathematics and its Applications​​​‌Oxford University Press, Oxford‌2004, viii+133back‌​‌ to text
• 86 article​​S.Sylvain Arguillère,​​​‌ E.Emmanuel Trélat,‌ A.Alain Trouvé and‌​‌ L.Laurent Younes.​​ Shape deformation analysis from​​​‌ the optimal control viewpoint‌.J. Math. Pures‌​‌ Appl. (9)1041​​2015, 139--178URL:​​​‌ https://doi.org/10.1016/j.matpur.2015.02.004DOIback to‌ text
• 87 articleT.‌​‌Térence Bayen. Analytical​​ parameterization of rotors and​​​‌ proof of a Goldberg‌ conjecture by optimal control‌​‌ theory.SIAM J.​​ Control Optim.476​​​‌2008, 3007--3036DOI‌back to text
• 88‌​‌ articleM.Michel Benaim​​, S.Stéphane Le​​​‌ Borgne, F.Florent‌ Malrieu and P.-A.Pierre-André‌​‌ Zitt. Qualitative properties​​ of certain piecewise deterministic​​​‌ Markov processes.Ann.‌ Inst. Henri Poincaré Probab.‌​‌ Stat.5132015​​, 1040--1075URL: https://doi.org/10.1214/14-AIHP619​​​‌DOIback to text‌
• 89 articleB.Bastien‌​‌ Berret, C.Christian​​ Darlot, F.Frédéric​​​‌ Jean, T.Thierry‌ Pozzo, C.Charalambos‌​‌ Papaxanthis and J. P.​​Jean Paul Gauthier.​​​‌ The inactivation principle: mathematical‌ solutions minimizing the absolute‌​‌ work and biological implications​​ for the planning of​​​‌ arm movements.PLoS‌ Comput. Biol.410‌​‌2008, e1000194, 25​​URL: https://doi.org/10.1371/journal.pcbi.1000194DOIback​​​‌ to text
• 90 book‌A.A. Bonfiglioli,‌​‌ E.E. Lanconelli and​​ F.F. Uguzzoni.​​​‌ Stratified Lie groups and‌ potential theory for their‌​‌ sub-Laplacians.Springer Monographs​​ in MathematicsSpringer, Berlin​​​‌2007, xxvi+800back‌ to text
• 91 book‌​‌B.Bernard Bonnard,​​ L.Ludovic Faubourg and​​​‌ E.Emmanuel Trélat.‌ Mécanique céleste et contrôle‌​‌ des véhicules spatiaux.​​51Mathématiques & Applications​​​‌ (Berlin) [Mathematics & Applications]‌Springer-Verlag, Berlin2006,‌​‌ xiv+276back to text​​
• 92 articleU.Ugo​​​‌ Boscain, F.Francesca‌ Chittaro, P.Paolo‌​‌ Mason and M.Mario​​ Sigalotti. Adiabatic control​​​‌ of the Schroedinger equation‌ via conical intersections of‌​‌ the eigenvalues.IEEE​​ Trans. Automat. Control57​​​‌82012, 1970--1983‌back to text
• 93‌​‌ articleU.Ugo Boscain​​, J.Jean Duplaix​​​‌, J.-P.Jean-Paul Gauthier‌ and F.Francesco Rossi‌​‌. Anthropomorphic image reconstruction​​ via hypoelliptic diffusion.​​​‌SIAM J. Control Optim.‌5032012,‌​‌ 1309--1336DOIback to​​ text
• 94 articleR.​​​‌ W.R. W. Brockett‌. System theory on‌​‌ group manifolds and coset​​ spaces.SIAM J.​​​‌ Control101972,‌ 265--284back to text‌​‌
• 95 bookF.Francesco​​ Bullo and A. D.​​​‌Andrew D. Lewis.‌ Geometric control of mechanical‌​‌ systems.49Texts​​ in Applied MathematicsModeling,​​​‌ analysis, and design for‌ simple mechanical control systems‌​‌Springer-Verlag, New York2005​​​‌, xxiv+726DOIback​ to text
• 96 article​‌T.Thomas Chambrion,​​ P.Paolo Mason,​​​‌ M.Mario Sigalotti and​ U.Ugo Boscain.​‌ Controllability of the discrete-spectrum​​ Schrödinger equation driven by​​​‌ an external field.​Ann. Inst. H. Poincaré​‌ Anal. Non Linéaire26​​12009, 329--349​​​‌URL: https://doi.org/10.1016/j.anihpc.2008.05.001DOIback​ to textback to​‌ text
• 97 articleG.​​G. Citti and A.​​​‌A. Sarti. A​ cortical based model of​‌ perceptual completion in the​​ roto-translation space.J.​​​‌ Math. Imaging Vision24​32006, 307--326​‌URL: http://dx.doi.org/10.1007/s10851-005-3630-2DOIback​​ to text
• 98 article​​​‌F.Fritz Colonius and​ G.Guilherme Mazanti.​‌ Decay rates for stabilization​​ of linear continuous-time systems​​​‌ with random switching.​Math. Control Relat. Fields​‌2019back to text​​
• 99 bookJ.-M.Jean-Michel​​​‌ Coron. Control and​ nonlinearity.136Mathematical​‌ Surveys and MonographsAmerican​​ Mathematical Society, Providence, RI​​​‌2007, xiv+426back​ to text
• 100 article​‌J.-M.Jean-Michel Coron.​​ Global asymptotic stabilization for​​​‌ controllable systems without drift​.Math. Control Signals​‌ Systems531992​​, 295--312URL: https://doi.org/10.1007/BF01211563​​​‌DOIback to text​
• 101 inproceedingsJ.-M.Jean-Michel​‌ Coron. On the​​ controllability of nonlinear partial​​​‌ differential equations.Proceedings​ of the International Congress​‌ of Mathematicians. Volume I​​Hindustan Book Agency, New​​​‌ Delhi2010, 238--264​back to text
• 102​‌ bookD.Domenico D'Alessandro​​. Introduction to quantum​​​‌ control and dynamics.​Chapman & Hall/CRC Applied​‌ Mathematics and Nonlinear Science​​ SeriesChapman & Hall/CRC,​​​‌ Boca Raton, FL2008​, xiv+343back to​‌ text
• 103 articleM.​​Michel Fliess, J.​​​‌Jean Lévine, P.​Philippe Martin and P.​‌Pierre Rouchon. Flatness​​ and defect of non-linear​​​‌ systems: introductory theory and​ examples.Internat. J.​‌ Control6161995​​, 1327--1361URL: https://doi.org/10.1080/00207179508921959​​​‌DOIback to text​
• 104 articleA.Alessio​‌ Franci and R.Rodolphe​​ Sepulchre. A three-scale​​​‌ model of spatio-temporal bursting​.SIAM J. Appl.​‌ Dyn. Syst.154​​2016, 2143--2175DOI​​​‌back to text
• 105​ articleS. ..S​‌ .J. Glaser, U.​​U. Boscain, T.​​​‌T. Calarco, C.​ ..C .P. Koch​‌, W.W. Köckenberger​​, R.R. Kosloff​​​‌, I.I. Kuprov​, B.B. Luy​‌, S.S. Schirmer​​, T.T. Schulte-Herbrüggen​​​‌, D.D. Sugny​ and F. ..F​‌ .K. Wilhelm. Training​​ 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
• 106 book​​D.D.H. Hubel and​​​‌ T.T.N. Wiesel.​ Brain and Visual Perception:​‌ The Story of a​​ 25-Year Collaboration.Oxford​​​‌Oxford University Press2004​back to text
• 107​‌ bookL.-M.Lise-Marie Imbert-Gérard​​, E. J.Elizabeth​​​‌ J. Paul and A.​ M.Adelle M. Wright​‌. An introduction to​​ stellarators---from magnetic fields to​​​‌ symmetries and optimization.​With a foreword by​‌ David Bindel and Matt​​ LandremanSociety for Industrial​​ and Applied Mathematics, Philadelphia,​​​‌ PA2025, xviii+290‌back to text
• 108‌​‌ bookV.Velimir Jurdjevic​​. Geometric control theory​​​‌.52Cambridge Studies‌ in Advanced MathematicsCambridge‌​‌ University Press, Cambridge1997​​, xviii+492back to​​​‌ text
• 109 articleV.‌Velimir Jurdjevic and H.‌​‌ J.Héctor J. Sussmann​​. Control systems on​​​‌ Lie groups.J.‌ Differential Equations121972‌​‌, 313--329URL: https://doi.org/10.1016/0022-0396(72)90035-6​​DOIback to text​​​‌
• 110 articleF.Ferdinand‌ Küsters and S.Stephan‌​‌ Trenn. Switch observability​​ for switched linear systems​​​‌.Automatica J. IFAC‌872018, 121--127‌​‌URL: https://doi.org/10.1016/j.automatica.2017.09.024DOIback​​ to text
• 111 article​​​‌Z.Z. Leghtas,‌ A.A. Sarlette and‌​‌ P.P. Rouchon.​​ Adiabatic passage and ensemble​​​‌ control of quantum systems‌.Journal of Physics‌​‌ B44152011​​back to text
• 112​​​‌ bookD.Daniel Liberzon‌. Calculus of variations‌​‌ and optimal control theory​​.A concise introduction​​​‌Princeton University Press, Princeton,‌ NJ2012, xviii+235‌​‌back to text
• 113​​ bookD.Daniel Liberzon​​​‌. Switching in systems‌ and control.Systems‌​‌ & Control: Foundations &​​ ApplicationsBirkhäuser Boston, Inc.,​​​‌ Boston, MA2003,‌ xiv+233URL: https://doi.org/10.1007/978-1-4612-0017-8DOI‌​‌back to textback​​ to text
• 114 article​​​‌W.Wensheng Liu.‌ Averaging theorems for highly‌​‌ oscillatory differential equations and​​ iterated Lie brackets.​​​‌SIAM J. Control Optim.‌3561997,‌​‌ 1989--2020DOIback to​​ text
• 115 articleL.​​​‌L. Massoulié. Stability‌ of distributed congestion control‌​‌ with heterogeneous feedback delays​​.IEEE Trans. Automat.​​​‌ Control476Special‌ issue on systems and‌​‌ control methods for communication​​ networks2002, 895--902​​​‌URL: https://doi.org/10.1109/TAC.2002.1008356DOIback‌ to text
• 116 book‌​‌R.Richard Montgomery.​​ A tour of subriemannian​​​‌ geometries, their geodesics and‌ applications.91Mathematical‌​‌ Surveys and MonographsAmerican​​ Mathematical Society, Providence, RI​​​‌2002, xx+259back‌ to text
• 117 article‌​‌R. M.Richard M.​​ Murray and S. S.​​​‌S. Shankar Sastry.‌ Nonholonomic motion planning: steering‌​‌ using sinusoids.IEEE​​ Trans. Automat. Control38​​​‌51993, 700--716‌URL: https://doi.org/10.1109/9.277235DOIback‌​‌ to text
• 118 article​​G.G. Nenciu.​​​‌ On the adiabatic theorem‌ of quantum mechanics.‌​‌J. Phys. A13​​21980, L15--L18​​​‌URL: http://stacks.iop.org/0305-4470/13/L15back to‌ text
• 119 articleD.‌​‌Diego Patino, M.​​Mihai Bâja, P.​​​‌Pierre Riedinger, H.‌Hervé Cormerais, J.‌​‌Jean Buisson and C.​​Claude Iung. Alternative​​​‌ control methods for DC-DC‌ converters: an application to‌​‌ a four-level three-cell DC-DC​​ converter.Internat. J.​​​‌ Robust Nonlinear Control21‌102011, 1112--1133‌​‌URL: https://doi.org/10.1002/rnc.1651DOIback​​ to text
• 120 book​​​‌J.Jean Petitot.‌ Neurogéomètrie de la vision.‌​‌ Modèles mathématiques et physiques​​ des architectures fonctionnelles.​​​‌Les Éditions de l'École‌ Polythechnique2008back to‌​‌ text
• 121 articleJ.​​Jakob Ruess and J.​​​‌John Lygeros. Moment-based‌ methods for parameter inference‌​‌ and experiment design for​​ stochastic biochemical reaction networks​​​‌.ACM Trans. Model.‌ Comput. Simul.252‌​‌2015, Art. 8,​​​‌ 25URL: https://doi.org/10.1145/2688906DOI​back to text
• 122​‌ articleA.Alessandro Sarti​​, G.Giovanna Citti​​​‌ and J.Jean Petitot​. The symplectic structure​‌ of the primary visual​​ cortex.Biol. Cybernet.​​​‌9812008,​ 33--48URL: http://dx.doi.org/10.1007/s00422-007-0194-9DOI​‌back to text
• 123​​ bookA.Arjan van​​​‌ der Schaft and H.​Hans Schumacher. An​‌ introduction to hybrid dynamical​​ systems.251Lecture​​​‌ Notes in Control and​ Information SciencesSpringer-Verlag London,​‌ Ltd., London2000,​​ xiv+174URL: https://doi.org/10.1007/BFb0109998DOI​​​‌back to text
• 124​ bookH.Heinz Schättler​‌ and U.Urszula Ledzewicz​​. Geometric optimal control​​​‌.38Interdisciplinary Applied​ MathematicsTheory, methods and​‌ examplesSpringer, New York​​2012, xx+640URL:​​​‌ https://doi.org/10.1007/978-1-4614-3834-2DOIback to​ textback to text​‌
• 125 bookH.Heinz​​ Schättler and U.Urszula​​​‌ Ledzewicz. Optimal control​ for mathematical models of​‌ cancer therapies.42​​Interdisciplinary Applied MathematicsAn​​​‌ application of geometric methods​Springer, New York2015​‌, xix+496URL: https://doi.org/10.1007/978-1-4939-2972-6​​DOIback to text​​​‌
• 126 articleS.Selim​ Solmaz, R.Robert​‌ Shorten, K.Kai​​ Wulff and F.Fiacre​​​‌ Ó Cairbre. A​ design methodology for switched​‌ discrete time linear systems​​ with applications to automotive​​​‌ roll dynamics control.​Automatica J. IFAC44​‌92008, 2358--2363​​URL: https://doi.org/10.1016/j.automatica.2008.01.014DOIback​​​‌ to text
• 127 incollection​E. D.E. D.​‌ Sontag. Input to​​ state stability: basic concepts​​​‌ and results.Nonlinear​ and optimal control theory​‌1932Lecture Notes in​​ Math.Springer, Berlin2008​​​‌, 163--220URL: https://doi.org/10.1007/978-3-540-77653-6_3​back to text
• 128​‌ articleZ.Zhendong Sun​​, S. S.S.​​​‌ S. Ge and T.​ H.T. H. Lee​‌. Controllability and reachability​​ criteria for switched linear​​​‌ systems.Automatica J.​ IFAC3852002​‌, 775--786URL: https://doi.org/10.1016/S0005-1098(01)00267-9​​DOIback to text​​​‌
• 129 bookZ.Zhendong​ Sun and S. S.​‌Shuzhi Sam Ge.​​ Stability theory of switched​​​‌ dynamical systems.Communications​ and Control Engineering Series​‌Springer, London2011,​​ xx+253URL: https://doi.org/10.1007/978-0-85729-256-8DOI​​​‌back to textback​ to text
• 130 book​‌S.S. Teufel.​​ Adiabatic perturbation theory in​​​‌ quantum dynamics.1821​Lecture Notes in Mathematics​‌BerlinSpringer-Verlag2003,​​ vi+236back to text​​​‌
• 131 bookE.Emmanuel​ Trélat. Contrôle optimal​‌.Mathématiques Concrètes. [Concrete​​ Mathematics]Théorie & applications.​​​‌ [Theory and applications]Vuibert,​ Paris2005, vi+246​‌back to textback​​ to text
• 132 article​​​‌E.E. Trélat.​ Optimal control and applications​‌ to aerospace: some results​​ and challenges.J.​​​‌ Optim. Theory Appl.154​32012, 713--758​‌URL: https://doi.org/10.1007/s10957-012-0050-5DOIback​​ to text
• 133 book​​​‌M.Marius Tucsnak and​ G.George Weiss.​‌ Observation and control for​​ operator semigroups.Birkhäuser​​​‌ Advanced Texts: Basler Lehrbücher.​ [Birkhäuser Advanced Texts: Basel​‌ Textbooks]Birkhäuser Verlag, Basel​​2009, xii+483URL:​​​‌ https://doi.org/10.1007/978-3-7643-8994-9DOIback to​ text
• 134 inproceedingsG.​‌Gabriel Turinici. On​​ the controllability of bilinear​​​‌ quantum systems.Mathematical​ models and methods for​‌ ab initio Quantum Chemistry​​74Lecture Notes in​​ ChemistrySpringer2000back​​​‌ to text
• 135 book‌M.Marcelo Viana.‌​‌ Lectures on Lyapunov exponents​​.145Cambridge Studies​​​‌ in Advanced MathematicsCambridge‌ University Press, Cambridge2014‌​‌, xiv+202URL: https://doi.org/10.1017/CBO9781139976602​​DOIback to text​​​‌
• 136 bookR.Richard‌ Vinter. Optimal control‌​‌.Systems & Control:​​ Foundations & ApplicationsBirkhäuser​​​‌ Boston, Inc., Boston, MA‌2000, xviii+507back‌​‌ to text
• 137 inproceedings​​D.DA Wisniacki,​​​‌ G.GE Murgida and‌ P.PI Tamborenea.‌​‌ Quantum control using diabatic​​ and adiabatic transitions.​​​‌AIP Conference Proceedings963‌2AIP2007,‌​‌ 840--842back to text​​
• 138 articleL.L.P.​​​‌ Yatsenko, S.S.‌ Guérin and H.H.R.‌​‌ Jauslin. Topology of​​ adiabatic passage.Phys.​​​‌ Rev. A652002‌, 043407, 7back‌​‌ to text