2023Activity reportProjectTeamVALSE
RNSR: 201923115X Research center Inria Centre at the University of Lille
 In partnership with:Ecole Centrale de Lille, Université de Lille
 Team name: Finitetime control and estimation for distributed systems
 In collaboration with:Centre de Recherche en Informatique, Signal et Automatique de Lille
 Domain:Applied Mathematics, Computation and Simulation
 Theme:Optimization and control of dynamic systems
Keywords
Computer Science and Digital Science
 A5.9.2. Estimation, modeling
 A6.4.1. Deterministic control
 A6.4.4. Stability and Stabilization
 A6.4.5. Control of distributed parameter systems
 A9.5. Robotics
Other Research Topics and Application Domains
 B1.1.8. Mathematical biology
 B2.1. Well being
 B5.6. Robotic systems
 B7.2.1. Smart vehicles
1 Team members, visitors, external collaborators
Research Scientists
 Denis Efimov [Team leader, INRIA, Senior Researcher, HDR]
 Jin Gyu Lee [INRIA, ISFP]
 Andrey Polyakov [INRIA, Researcher, HDR]
 Rosane Ushirobira [INRIA, Researcher, HDR]
PostDoctoral Fellow
 Jesus Mendoza Avila [INRIA, until Nov 2023]
PhD Students
 Mohamed Yassine Arkhis [INRIA, from Oct 2023]
 Mericel Ayamou [UNIV LILLE]
 Mahugnon Dadjo [INRAE]
 Min Li [CSC Scholarship]
 Danilo Rodrigues De Lima [INRIA]
 Yu Zhou [CSC Scholarship]
Technical Staff
 Gerald Dherbomez [CNRS, Engineer]
Administrative Assistant
 Lucille Leclercq [INRIA, from Feb 2023]
Visiting Scientists
 Leonid Fridman [UNAM, until Jan 2023]
 Ariana Gutierrez [IT Laguna, from Aug 2023 until Oct 2023]
 Ankit Kumar [IIT Delhi, from Mar 2023 until May 2023]
 Manuel Mera [Instituto Politécnico Nacional, from Aug 2023 until Sep 2023]
 Jose Antonio Ortega [UNAM, from Aug 2023 until Oct 2023]
 Hector Rios Barajas [IT Laguna, from Aug 2023 until Sep 2023]
2 Overall objectives
The Valse team studies the estimation and control problems arising in the analysis and the design of distributed, uncertain, and interconnected dynamical systems:
 Using the concepts of finitetime/fixedtime/hyperexponential convergence and stability, the main idea is to separate and hierarchize in time the control and estimation processes, which are distributed in space. This greatly simplifies their analysis and the design for largescale solutions.
 The main areas of investigation and application are the Internet of Things (IoT) and CyberPhysical Systems (CPS).
 The team aims to draw up algorithms for decentralized finitetime control and estimation. The methodology to be developed includes extensions of the theory of homogeneous systems and of finitetime/fixedtime/hyperexponential convergence and stability notions. Particular attention is given to applications in realworld scenarios.
 It is a joint proposal with the CNRS CRIStAL UMR 9189.
3 Research program
The Valse team works in the domains of control science: dynamical systems, stability analysis, estimation, and automatic control. Our developments are focused on the theoretical and applied aspects related to the control and estimation of largescale multisensor and multiactuator systems based on the use of the theories of finitetime/fixedtime/hyperexponential convergence and homogeneous systems. The Lyapunov function method and other methods of analysis of dynamical systems form a basis for the studies in the Valse team.
The key idea of the research program for the team is that a fast (nonasymptotic) convergence of the regulation and estimation errors increases the reliability of intelligent distributed actuators and sensors in complex scenarios, such as interconnected cyberphysical systems (CPSs).
The expertise of Valse's members in theoretical developments of control and estimation theory (finitetime control and estimation algorithms in centralized context 84, 70, 81, 80, 77, homogeneity framework for differential equations 85, 72, 71, 73, 75, 86, 82, timedelay systems 74, 76, 89, distributed systems 83 and algebraicbased methods for estimation 87, 88) is an essential ingredient to achieve our objective.
The generic chart of different goals and tasks included in the scientific work program of Valse and interrelations between them are presented in Fig. 1. We have selected three main objectives to pursue with the related tasks to fulfill:
 The first objective is to design control and estimation solutions for CPS and IoT, which is the principal aim of Valse. It will contain the main outcomes of our research.
 The second objective is more theoretical and needed to make the basement for our design and analysis parts in the last goal.
 The third objective deals with applications, which will drive the team and motivate the theoretical studies and selected design performances.
All these objectives are interconnected: from a particular problem in an IoT application, it is planned to design control or estimation algorithms, leading to the development of theoretical tools; and vice versa, a new theoretical advance can provide a possibility for the development of novel tools which can be used in applications.
To explain our motivation: why use finite time? Applying any method for control/estimation has a price in terms of its advantages and disadvantages. There is no universal framework that is the best always and everywhere. Finitetime may appear as a luxurious property for a physical system, requiring nonlinear tools. Of course, if an asymptotic convergence and a linear model are enough for solving a given problem, then there is no reason to develop something else. However, most of the present problems in CPS and IoT are nonlinear (i.e., they have various local behaviors that cannot be collected in only one linear model). Design and analysis of various local linearized models and solutions are luxurious, too. The theory of homogeneity can go beyond linearity, offering many new features while not appearing as severe as other nonlinear tools and having almost all hints of the linear framework. Suppose that, thanks to the homogeneity theory, finitetime/fixedtime can be obtained with little difficulty while adding the bonuses of stronger robustness and faster convergence compared to the linear case? We are convinced that the price of going beyond linear control and estimation can be strongly dropped by maturing the theory of homogeneity and finite/fixedtime convergence. We are also convinced that it will be compensated in terms of robustness and speed, which can be demanded in the new areas of application such as IoT for example.
4 Application domains
An objective of the team is the application of the developed control and estimation algorithms for different scenarios in IoT or CPSs. Participation in various potential applications allows the Valse team to better understand the features of CPSs and their required performances, and to properly formulate the control and estimation problems that must be solved. Here is a list of ongoing, past and potential applications addressed by the team:
 smart bivalvebased biosensor for water quality monitoring (ANR project WaQMoS, the developed sensor is shown in Fig. 2): in living beings, the presence of persistent external perturbations may be difficult to measure, and important model uncertainties render the application of conventional techniques complicated; another issue for estimation is the consensusseeking between animals for contamination detection 68;
 control and estimation for flying vehicles, e.g. quadrotors or blimps given in Fig. 3: the nonlinearity of the model and its uncertainty coupled with important aerodynamic perturbations have to be compensated by fast (finite or fixedtime) and robust control and estimation algorithms;
 human behavior modeling and identification with the posterior design of algorithms for humancomputer interaction (HCI, with the Inria team LOKI): robust finitetime differentiators demonstrate good estimation capabilities needed for prediction in this application 88, 69;
 human physiological characteristics estimation (like emotion detection, galvanic skin response filtering, fatigue evaluation in collaborations with Neotrope and Ellcie Healthy): intelligent robust filtering and finitetime distributed estimation are key features in these scenarios;
 path planning for autonomous vehicles taking into account the behavior of humans (with the Inria team SCOOL): application of interval and finitetime adaptive estimation and prediction techniques allows for treating the uncertainty of the environment by reducing the computational complexity of reinforcement learning 791;
 flow control 78: the case of control and estimation of a distributedparameter system with very fast and uncertain dynamics, where finitetime solutions developed by Valse are necessary (an example of results is given in Fig. 4);
 control of bioreactors (in the framework of IPL COSY): here again, the problem is an important uncertainty of the model, which can be handled by robust sliding mode control algorithms, or by applying adaptive finitetime estimation and identification tools;
It is worth highlighting a widespread distribution of various scientific domains in the list of applications for the team given above. Such interdisciplinarity for Valse is unsurprising since control theory is a science of systems whose interest today is, by nature, to interface with other disciplines and their fields of application. This is also well aligned with the domain of CPSs, which by its origin requires multidisciplinary competencies.
5 Social and environmental responsibility
Activities of the team related with social responsibility:
 Engaging in outreach programs to promote mathematics education and awareness in local communities: Rosane Ushirobira participes in the work of CIMPA
 Collaborating with educational institutions to support the development of math skills for young generation: Rosane Ushirobira made several CHICHE sessions in high schools of Lille and metropolitan area
 Participating in mentorship programs to encourage underrepresented groups to pursue careers in mathematics and related fields: Rosane Ushirobira organized the days of young girls in informatics and mathematics (RJMI)
 Contributing to interdisciplinary research that addresses societal challenges, such as healthcare, by applying mathematical modeling and analysis: a new ANR project NOCIME has been accepted with participation of the team on analysis of epidimiological models, in addition, there are publications on this subject
 Mentoring and supporting earlycareer researchers to foster a diverse and inclusive research community
Activities of the team related with environmental responsibility:
 Developing mathematical models and the methods for their design and analysis to support sustainable energy systems: ANR project SyNPiD devoted to this issue
 Collaborating with environmental scientists, engineers, and policymakers to provide mathematical insights and solutions for environmental challenges and their mitigations: a PhD student is supervised with INRAE on the waste water treatment problems
Overall, social and environmental responsibility for researchers in the team involves using mathematical expertise to address societal issues, promote inclusivity, and contribute to environmental sustainability through research, collaboration, and outreach efforts.
6 Highlights of the year
 ANR Project NOCIME has been accepted
 Regional project STARS of Jin Gyu Lee has been accepted
 Almost all members of the team visited IEEE CDC in Singapore, where our team kept $1\%$ of the total number of accepted publications
 Among 28 journal publications of the team this year, 7 are in Automatica and 10 in IEEE TAC (the top journals in the domain of the theory of control), which is $60\%$ of scientific production
7 New software, platforms, open data
7.1 New software
7.1.1 HCS Toolbox

Name:
Homogeneous Systems Control Toolbox (HSC Toolbox) for MATLAB

Keywords:
Control design, Matlab, Homogeneity

Functional Description:
Homogeneous Systems Control Toolbox (HCS Toolbox) for MATLAB is a collection of functions for design and tuning of control systems with improved control quality (faster convergences, better robustness, smaller overshoots, etc) based on the concept of a dilation symmetry (homogeneity). Homogeneous controllers/observers design well as procedures for upgrading of existing linear controllers/observers to nonlinear (homogeneous) ones are developed for both SingleInput SingleOutput (SISO) and MultiplyInput MultiplyOutput (MIMO) systems.

Release Contributions:
HCS Toolbox for MATLAB ver. 0.1
This is the first release of HCS Toolbox for MATLAB. The list of MATLAB functions provided for homogeneous control systems design: (Homogeneous Objects) hnorm  computation of homogeneous norm hproj  computation of homogeneous projection hcurve  generation of points of a homogeneous curve hsphere  generation of a random grid on a homogeneous sphere (Homogeneous Control Design) hpc_design  Homogeneous Proportional Control (HPC) design hpci_design  Homogeneous ProportionalIntegral Control (HPIC) design hsmc_design  Homogeneous Sliding Mode Controller (HSMC) design hsmci_design  design of HSMC with Integral action fhpc_design  Fixedtime HPC design fhpic_design  Fixedtime HPIC design lpc2hpc  upgrading Linear Proportional Control (LPC) to HPC lpic2hpc  upgrading Linear PI control (LPIC) to HPIC (Discretization of Homogeneous Control) e_hpc  explicit discretization of HPC e_hpc  semiimplicit discretization of HPC c_hpc  consistent discretization of HPC e_hpic  explicit discretization of HPIC e_hsmc  explicit discretization of HSMC si_hsmc  semiimplicit explicit discretization of HSMC e_hsmci  explicit discretization of HSMC with Integral action e_fhpc  explicit discretization of Fixedtime HPC si_fhpc  semiimplicit discretization of Fixedtime HPC e_fhpic  explicit discretization of Fixedtime HPIC (Homogeneous Observer Design) ho_design  Homogeneous Observer (HO) design fho_design  Fixedtime HO design lo2ho  upgrading Linear Observer (LO) to HO (Discretization of Homogeneous Observer) e_ho  explicit Euler discretization of HO e_fho  explicit Euler discretization of FHO si_ho  semiimplicit discretization of HO si_fho  semiimplicit discretization of FHO (Block forms ) block_con  transformation to block controlability form bloc_obs  transformation to block bservability form trans_con  transformation to partial block controlability form trans_con  transformation to partial block observability form output_form  transformation to reduced order output control system (Examples) demo_hnorm  demo of computation of a homogeneous norm demo_hsphere  plot of homogeneous balls in 2D demo_hpc  demo of HPC design and simulation demo_hpic  demo of HPIC design and simulation demo_hsmc  demo of HSMC design and simulation demo_hsmci  demo of HSMCI design and simulation demo_fhpc  demo of FHPC design and simulation demo_fhpic  demo of FHPIC design and simulation demo_lpc2hpc  demo of upgrading LPC to HPC/FHPC demo_lpic2hpic  demo of upgrading LPIC to HPIC/FHPIC demo_ho  demo of HO design and simulation demo_fho  demo of FHO design and simulation demo_lo2ho  demo of upgrading LO to HO/FHO For more details please read the documentation: HCS_doc.pdf
 URL:

Author:
Andrey Polyakov

Contact:
Andrey Polyakov
8 New results
8.1 Analysis and design of homogeneous and finitetime stable systems
Participants: Denis Efimov, Andrey Polyakov.
Inputtostate stability (ISS) is one of the most utilizable robust stability properties for nonlinear dynamical systems, while (nearly) fixedtime convergence is a kind of decay for trajectories of disturbancefree systems that is independent in initial conditions. The presence of both these features for a system can be checked by existence of a proper Lyapunov function. The objective of 10 was to provide the conditions for a converse result that (nearly) fixedtime inputtostate stable systems admit a respective Lyapunov function. Similar auxiliary results for uniform finitetime stability and uniform (nearly) fixedtime stability are obtained.
Usually, singularly perturbed models are used to justify the decomposition of the interconnected systems into the Main Dynamics (MD) and the Parasitic Dynamics (PD). In 20, the effect of a homogeneous PD on the stability of a homogeneous MD, when homogeneity degrees are possibly different, is studied via ISS approach in the framework of singular perturbations. Proposed analysis discovers three kinds of stability in the behavior of such an interconnection by assuming that both, regulated MD and unforced PD, are globally asymptotically stable.
The paper 33 develops control algorithms for a class of affine nonlinear systems using the socalled canonical homogeneous representation. It is demonstrated that such a representation exists for any homogeneous vector field bounded on the unit sphere. It is shown that canonical homogeneous representation is useful for LMIbased control design and stability analysis of nonlinear systems.
Nonovershooting stabilization is a form of safe control where the setpoint chosen by the user is at the boundary of the safe set. Exponential nonovershooting stabilization, including suitable extensions to systems with deterministic and stochastic disturbances, has been solved previously. In 25, we develop homogeneous feedback laws for fixedtime nonovershooting stabilization of nonlinear systems that are inputoutput linearizable with a full relative degree, i.e., for systems that are diffeomorphically equivalent to the chain of integrators. These homogeneous feedback laws can also assume the secondary role of 'fixedtime safety filters' (FxTSf filters) which keep the system within the closed safe set for all time but, in the case where the user's nominal control commands approach to the unsafe set, allow the system to reach the boundary of the safe set no later than a desired time that is independent of nominal control and independent of the value of the state at the time the nominal control begins to be overridden.
The problem of finitetime stabilization of a linear plant with an optimization of both a settling time and an averaged/weighted control energy is studied using the concept of generalized homogeneity in 23. It is shown that the optimal finitetime stabilizing control in this case can be designed by means of solving a simple linear algebraic equation. Robustness of the obtained control law is studied.
The paper 11 addresses the problem of inputtostate stabilization for heat equation with external input via boundary control strategy. Following our previous results, based on the backstepping approach, a switching boundary control law depending on the system state is designed. By estimating the upper bound of kernel functions, switching levels are determined and commutation law is further constructed. For the chosen switched control, the wellposedness property is verified. It is proved that the resulting system is ISS, and the solutions of the system will not exceed the highest admissible level dependent on the disturbance amplitude. Meanwhile, a stronger result is also obtained, that is the finitetime stability for the disturbancefree system.
8.2 Analysis and design for timedelay systems
Participants: Denis Efimov.
For a class of nonlinear systems with homogeneous righthand sides of nonzero degree and distributed delays, the problem of stability robustness of the zero solution with respect to timevarying perturbations multiplied by a nonlinear functional gain is studied in 7. It is assumed that the disturbancefree and delayfree system (that results after substitution of nondelayed state for the delayed one) is globally asymptotically stable. First, it is demonstrated that in the disturbancefree case the zero solution is either locally asymptotically stable or practically globally asymptotically stable, depending on the homogeneity degree of the delayfree counterpart. Second, using averaging tools several variants of the timevarying perturbations are considered and the respective conditions are derived evaluating the stability margins in the system. The results are obtained by a careful choice and comparison of LyapunovKrasovskii and LyapunovRazumikhin approaches. Finally, the obtained theoretical findings are illustrated on two mechanical systems.
For inputaffine nonlinear dynamical systems, an ISS analysis with respect to (weighted) average values of exogenous perturbations is proposed in 9. The timedelay method is used to represent the system in a suitable form for investigation: a kind of neutraltype differential equation. The introduced approach allows the asymptotic gains with respect to zeromean periodic signals to be evaluated for nonlinear systems (an analogue of Bode magnitude plot), as well as for integral ISS (iISS) systems with periodic inputs. The results are illustrated on the class of homogeneous systems.
8.3 Discretisation of homogeneous systems
Participants: Denis Efimov, Andrey Polyakov.
The paper 22 proposes a discretization (sampledtime implementation) algorithm for a class of homogeneous controllers for linear timeinvariant systems preserving the finitetime and nearly fixedtime stability properties. The sampling period is assumed to be constant. Both singleinput and multipleinput cases are considered. The robustness (ISS) of the obtained sampledtime control system is studied as well.
The paper 21 is dedicated to the experimental analysis of discretetime differentiators implemented in closedloop control systems. To this end, two laboratory setups, namely an electropneumatic system and a rotary inverted pendulum have been used to implement 25 different differentiators. Since the selected laboratory setups behave differently in the case of dynamic response and noise characteristics, it is expected that the results remain valid for a wide range of control applications. The validity of several theoretical results, which have been already reported in the literature using mathematical analysis and numerical simulations, has been investigated, and several comments are provided to allow one to select an appropriate differentiation scheme in practical closedloop control systems.
8.4 Homogenization through controls
Participants: Andrey Polyakov.
In 18, the leaderfollowing consensus problem for multiagent systems is considered. Each agent is assumed to be modeled by a linear multiinput system. A novel (generalized homogeneous) consensus control protocol is designed under the assumption that there are some uncertainties in the dynamic of the leader. Some LMIs are derived to select the control parameters in order to ensure the ISS and global finitetime stability of the consensus errors with desired homogeneity degrees.
The methodology of the unit sliding mode control design (known since 1970s) for linear systems is revised based on the concept of the generalized homogeneity in 24. The restriction about a consistency of the number of control inputs with the dimension of the sliding surface is eliminated. A simple procedure of control tuning based on a known maximal magnitude of matched perturbations is developed. To deal with perturbations of unknown magnitude, a homogeneous sliding mode control with integral action is designed as well.
A generalized homogeneous control with integral action for a multipleinput plant operating under uncertainty conditions is designed in 31. The stability analysis is essentially based on a special version of the nonsmooth Lyapunov function theorem for differential equations with discontinuous righthand sides. A Lyapunov function for analysis of the closedloop system is presented. For negative homogeneity degree, this Lyapunov function becomes a strict Lyapunov function allowing an advanced analysis to be provided. In particular, the maximum control magnitude and the settlingtime of the closedloop system are estimated and a class of disturbances to be rejected by the control law is characterized. The control parameters are tuned by solving a system of LMIs, whose feasibility is proved at least for small (close to zero) homogeneity degrees.
8.5 Control and estimation for Persidskii systems
Participants: Denis Efimov, Rosane Ushirobira.
Generalized Persidskii systems (or Lur'e systems) represent the dynamics described by the superposition of a linear part with multiple sector nonlinearities and exogenous perturbations. They can be used to model many physical and engineering phenomena.
The paper 19 studies the trajectory behavior evaluation for generalized Persidskii systems with an essentially bounded input on a finite time interval. Also, the notions of annular settling and output annular settling for general nonlinear systems are introduced, and the respective stability conditions are porposed. These conditions are based on the verification of linear matrix inequalities. An application to recurrent neural networks illustrates the usefulness of the proposed notions and conditions.
The paper 12 considers the state estimation problem for a class of nonautonomous nonlinear systems. We propose conditions on the existence and stability of a nonlinear observer based on the invariant manifold approach in both continuous and discretetime scenarios. The requirements are formulated using linear matrix equalities and LMIs. We present two possible applications of the result: a reducedorder observer (e.g., an observer for unmeasured states) and regression in linear and nonlinear, continuousand discretetime settings. With nonlinear regression being a sophisticated case, the parameter estimation problem for a particular output equation (when the fusion of linear and nonlinear sensors is weighted) is investigated.
The article 27 deals with the problem of timevarying parameter identification in dynamical regression models affected by disturbances. The disturbances comprise timedependent external perturbations and nonlinear unmodeled dynamics. With this aim in mind, we propose a robust nonlinear adaptive observer. The algorithm ensures the asymptotic convergence of the parameter identification error to an acceptably small region around the origin in the presence of disturbances. The synthesis of the adaptive observer is given in terms of linear matrix inequalities since the error dynamics is reduced to Persidskii form, providing a constructive design method.
8.6 Control of robotic systems
Participants: Andrey Polyakov.
The paper 32 deals with the tracking problem for the unicycle mobile robot with slippage effects. A homogeneous controller is developed based on a particular cascade control strategy. The robustness of the closedloop system is studied. The design is essentially based on the canonical homogeneous norm being a Lyapunov function of the system. The (finitetime or exponential) convergence rate of the homogeneous controller can be tuned by a proper selection of the socalled homogeneity degree. Some experimental results illustrate the performance of the proposed homogeneous control in the UMR QBot2 by Quanser.
The paper 28 contributes to the design of a second order slidingmode controller for the trajectory tracking problem in perturbed unicycle mobile robots. The proposed strategy takes into account the design of two particular sliding variables, which ensure the convergence of the tracking error to the origin in a finite time despite the effect of some external perturbations. The straightforward structure of the controller is simple to tune and implement. The global, uniform and finitetime stability of the closedloop tracking error dynamics is demonstrated by means of Lyapunov functions. Furthermore, the performance of the proposed approach is validated through some experiments using a QBot2 unicycle mobile robot.
8.7 Estimation under communication constraints
Participants: Denis Efimov.
In the paper 30, an approach is proposed for the remote observation of a dynamical system through a datarate constrained communication channel. The focus is put on discretetime systems with a Lipschitz nonlinearity, driven by an external signal, and subject to bounded state perturbation and measurement error. The problem at hand is providing estimates of system's state at a remote location, which is connected via a channel, which can only sent limited numbers of bits per unit of time. A solution, named observation scheme, is proposed in the form of several interacting agents. This solution is designed such that the maximum observation error is upperbounded by a computable quantity dependent on system constants and selectable parameters. The scheme is designed in an eventtriggered fashion, such that the actual communication rate is sometimes much lower than the theoretically evaluated maximum one.
8.8 Synchronization and multistability
Participants: Denis Efimov, Rosane Ushirobira, Jin Gyu Lee.
We present new results for global boundedness of state periodic systems in 29. Thereby, we address both the case of systems, whose dynamics is periodic with respect to a part of the state vector and the case of systems, whose dynamics is periodic with respect to all state variables. Both classes of systems are of high relevance in diverse and timely applications. To derive the results the notion of strong Leonov functions is refined. The main results are complemented by a number of relaxations based on the concpet of weak Leonov functions.
In the paper 8, we study the problem of robust stabilization of affine nonlinear multistable systems in the presence of exogenous disturbances. The results are based on the theory of ISS and iISS for systems with multiple invariant sets. The notions of ISS and iISS control Lyapunov functions (CLFs) and the small control property are extended within the multistability framework. Such properties are also complemented by the concept of a weak iISS CLF and corresponding small control property. It is verified that the universal control formula can be applied to yield the ISS (iISS) property for the closedloop system. The efficiency of the extended CLF framework in the multistable sense is illustrated for a Duffing system and in application to a noiseinduced transition in a semiconductorgasdischarge gap system.
When a group of heterogeneous node dynamics are diffusively coupled with a high coupling gain, the group exhibits a collective emergent behavior which is governed by a simple algebraic average of the node dynamics called the blended ones. This finding has been utilized for designing heterogeneous multiagent systems by building the desired blended dynamics first and then splitting it into the node dynamics. However, to compute the magnitude of the coupling gain, each agent needs to know global information such as the number of participating nodes, the graph structure, and so on, which prevents a fully decentralized design of the node dynamics in conjunction with the coupling laws. To resolve this issue, the idea of funnel control, which is a method for adaptive gain selection, was exploited in 16.
A discretetime version of the blended dynamics theorem is proposed in 13 that can be used for design of distributed computation algorithms. The blended dynamics theorem enables to predict the behavior of heterogeneous multiagent systems. Therefore, once we get a blended dynamics for a particular computational task, design idea of node dynamics for individual heterogeneous agents can easily occur. In the continuoustime case, prediction by blended dynamics was enabled by high coupling gain among neighboring agents. In the discretetime case, we propose an equivalent action.
The paper 17 examines how weak synaptic coupling can achieve rapid synchronization in heterogeneous networks. The assumptions aim at capturing the key mathematical properties that make this possible for biophysical networks. In particular, the combination of nodal excitability and synaptic coupling are shown to be essential to the phenomenon.
The paper 15 investigates the finitetime stability and nearly fixedtime stability of nonlinear impulsive systems with destabilizing impulses. A Lyapunov inequality with linear terms has been used to derive sufficient conditions based on the dwell time (DT) and average dwell time (ADT) properties of impulsive sequences to ensure stability of the system. The main results of this paper are applied to the synchronization problem of impulsive neural networks with destablizing impulses.
9 Bilateral contracts and grants with industry
9.1 Bilateral contracts with industry
Participants: Denis Efimov, Rosane Ushirobira.
 52 Hertz is a startup (Brest, France) that develops an underwater communication device for divers. The goal of this contract was to develop an intelligent filtering algorithm that compensates for the voice deformation during underwater vocal communication through the device. The code for the filter was written in Matlab, with further help for its adaptation in Python and C.
10 Partnerships and cooperations
10.1 International initiatives
10.1.1 Participation in other International Programs
ECOSNord, Mexico
Participants: Denis Efimov, Andrey Polyakov, Rosane Ushirobira.

Title:
Artificial Intelligencebased Control Approaches for Multiple Mobile Robots

Partner Institution(s):
 IT Laguna, Mexico
 Instituto Politécnico Nacional, Mexico

Date/Duration:
2021–2023

Additionnal info/keywords:
This project was focused on studying several tracking tasks for autonomous mobile robot systems, particularly unmanned aerial vehicles and wheeled mobile robots. This project aimed to develop robust control and navigation schemes by combining the methods of artificial intelligence and control theory.
PHC Aurora
Participants: Denis Efimov, Andrey Polyakov, Rosane Ushirobira, Jin Gyu Lee.

Title:
Equivalent nonlinear control methods for digitalization in robotics and autonomous systems

Partner Institution(s):
 University of Agder, Norway

Date/Duration:
20232024

Additionnal info/keywords:
The robotic and autonomous systems rely heavily on the complex, often distributed, and hierarchical control systems, which ensure main functionalities with a flexible and safe operation. The classical automatic controllers with feedback from the acquisition and perception devices continue to experience the new challenges coming from an increasing complexity in the dynamic behavior of the systems to be controlled on the one hand, and from the digitalization and associated transformations of data, their spatial availability and communication time delays on the other hand. To propose the advanced nonlinear control methods which, however, would be equivalent (in terms of simplicity of tuning and implementation) to the widely accepted standard linear controls (such as PID), and in this way would be more accessible for future applications, is the scientific scope of this project.
10.2 International research visitors
10.2.1 Visits of international scientists
Inria International Chair
Participants: Denis Efimov, Andrey Polyakov, Rosane Ushirobira, Jin Gyu Lee.
Leonid Fridman, UNAM, until Jan 2023
Other international visits to the team
Ariana Gutierrez

Status:
PhD

Institution of origin:
IT Laguna

Country:
Mexico

Dates:
from Aug 2023 until Oct 2023

Context of the visit:
ECOS Nord

Mobility program/type of mobility:
research stay
Jose Antonio Ortega

Status:
PhD

Institution of origin:
UNAM

Country:
Mexico

Dates:
from May 2023 until Jun 2023

Context of the visit:
Consyt grant

Mobility program/type of mobility:
research stay
Hector Rios Barajas

Status:
researcher

Institution of origin:
IT Laguna

Country:
Mexico

Dates:
from Aug 2023 until Sep 2023

Context of the visit:
ECOS Nord

Mobility program/type of mobility:
research stay
Manuel Mera

Status:
researcher

Institution of origin:
Instituto Politécnico Nacional

Country:
Mexico

Dates:
from Aug 2023 until Sep 2023

Context of the visit:
Inria invited professor

Mobility program/type of mobility:
research stay
Ankit Kumar

Status:
PhD

Institution of origin:
IIT Delhi

Country:
India

Dates:
from Mar 2023 until May 2023

Context of the visit:
CEFIPRA mobility grant

Mobility program/type of mobility:
research stay
10.3 National initiatives
10.3.1 ANR
 NOCIME (New Observation and Control Issues Motivated by Epidemiology), coordinator PierreAlexandre Bliman (Inria, Paris)
 SyNPiD (Synchronization in power networks with periodic dynamics), coordinators Denis Efimov (Inria, France) and J. Schiffer (Brandenburg University of Technology CottbusSenftenberg, Germany)
10.4 Regional initiatives
 Project STARS "Practical design for interconnected CPSs by synchronization enforcement" of Jin Gyu Lee
11 Dissemination
The members of the team serve as reviewers for major journals and conferences in the field of the theory of control and automation.
11.1 Promoting scientific activities
11.1.1 Scientific events: organisation
Member of the conference program committees
 Denis Efimov , IFAC World Congress, Yokohama, Japan
11.1.2 Journal
Member of the editorial boards
 Denis Efimov , Associate editor, IFAC Journal on Nonlinear Analysis: Hybrid Systems
 Denis Efimov , Associate editor, IEEE Transactions on Automatic Control
 Denis Efimov , Associate editor, Automatica
 Rosane Ushirobira , Associate editor, Asian Journal of Control
 Rosane Ushirobira , Associate editor, Trends in Computational and Applied Mathematics (TEMA)
11.1.3 Invited talks
 Denis Efimov , Hangzhou Dianzi University, China
 Denis Efimov , Xidian University, Xi'an, China
 Andrey Polyakov , Xidian University, Xi'an, China
11.1.4 Leadership within the scientific community
 Denis Efimov , Senior member IEEE
 Denis Efimov , Member of IFAC TC 1.2. Adaptive and Learning Systems
 Denis Efimov , Publication vicechair of IFAC TC 9.2. Systems and Control for Societal Impact
 Denis Efimov , Executive committee member, IEEE CSS Technical Committee on Variable Structure and Sliding Mode Control
 Denis Efimov , Cochair of European PhD Award on Control for Complex and Heterogeneous Systems
 Rosane Ushirobira , Scientific Officer at CIMPA (Centre International de Mathématiques Pures et Appliquées)
11.1.5 Research administration
 Rosane Ushirobira , Elected member of the CE Inria
 Rosane Ushirobira , President of the CER (Commission des emplois de recherche) Inria Lille
 Andrey Polyakov, Jury member of the CRCN/ISFP Inria Lille
 Rosane Ushirobira, Jury member of the CRCN/ISFP Inria Lyon; CoS MCF CNU 61 IUT Lille
11.2 Teaching  Supervision  Juries
11.2.1 Teaching
 Licence: Rosane Ushirobira , Basic courses in Linear algebra and Calculus, 71h, L3, Polytech Lille
 Master: Jin Gyu Lee , Dynamical systems, 17h, M2, Université de Lille
11.2.2 Juries
The members of the team participated in numerous juries for Ph.D. defense.
11.3 Popularization
11.3.1 Internal or external Inria responsibilities
 Denis Efimov , Member of IES comittee
 Rosane Ushirobira , Scientific Officer for Scientific Popularization
 Rosane Ushirobira , Organizer of 30 min. of science (monthly seminar for scientists in the center)
11.3.2 Interventions
 Rosane Ushirobira , Organizer of CHICHE sessions in Lille Academy, gave 13 talks to highschool students within this framework
 Rosane Ushirobira , Organizer of the 3rd Rendezvous des Jeunes Mathématiciennes et Informaticiennes (RJMI) Inria Lille
12 Scientific production
12.1 Major publications
 1 articleDesign of Finite/Fixedtime ISSLyapunov Functions for Mechanical Systems.Mathematics of Control, Signals, and Systems2022HAL
 2 articleAccelerated convergence with improved robustness for discretetime parameter estimation.Systems and Control Letters5512October 2022, 324329HALDOI
 3 articleOn Computer Mouse Pointing Model Online Identification and Endpoint Prediction.IEEE Transactions on HumanMachine Systems525October 2022HAL
 4 articleHyperexponential and fixedtime stability of timedelay systems: LyapunovRazumikhin method.IEEE Transactions on Automatic Control2022HALDOI
 5 articleQuadrotor stabilization under time and space constraints using implicit PID controller.Journal of The Franklin InstituteJanuary 2022HAL
12.2 Publications of the year
International journals
 6 articleOn local ISS of nonlinear secondorder timedelay systems without damping †.International Journal of Robust and Nonlinear Control2024HAL
 7 articleStability of homogeneous systems with distributed delay and timevarying perturbations.Automatica153July 2023, 111058HALDOIback to text
 8 articleControl Lyapunov function method for robust stabilization of multistable affine nonlinear systems.International Journal of Robust and Nonlinear ControlMarch 2023HALback to text
 9 articleOn ISS with respect to average value of disturbances: a timedelay approach.IEEE Transactions on Automatic Control2023HALback to text
 10 articleOn converse Lyapunov theorem for fixedtime inputtostate stability.SIAM Journal on Control and Optimization2023HALback to text
 11 articleInputtostate stability analysis of heat equation with boundary finitetime control.Automatica2023HALback to text
 12 articleOn robust observer design for a class of timevarying continuousand discretetime Persidskii systems.IEEE Transactions on Automatic Control2023HALback to text
 13 articleA Design Method of Distributed Algorithms via Discretetime Blended Dynamics Theorem.Automatica2023HALback to text
 14 articleA note on fixedand discretetime estimation via the DREM method.IEEE Transactions on Automatic ControlJanuary 2023HAL
 15 articleFinite/nearly FixedTime stability of Nonlinear Impulsive Systems with Destabilizing Impulses and its Application to Neural Networks.Communications in Nonlinear Science and Numerical Simulations2023HALback to text
 16 articleEdgewise funnel output synchronization of heterogeneous agents with relative degree one.Automatica156October 2023, 111204HALDOIback to text
 17 articleRapid and robust synchronization via weak synaptic coupling.Automatica2023HALback to text
 18 articleOn Generalized Homogeneous Leaderfollowing Consensus Control for Multiagent Systems.IEEE Transactions on Control of Network Systems2024HALDOIback to text
 19 articleOn annular shorttime stability conditions for generalized Persidskii systems.International Journal of ControlSeptember 2023HALback to text
 20 articleOn Stability of Homogeneous Systems in Presence of Parasitic Dynamics.IEEE Transactions on Automatic Control11November 2023HALback to text
 21 articleDiscretetime differentiators in closedloop control systems: experiments on electropneumatic system and rotary inverted pendulum.Control Engineering Practice1362023, 128HALDOIback to text
 22 articleConsistent discretization of homogeneous finite/fixedtime controllers for LTI systems.Automatica155September 2023, 111118HALback to text
 23 articleEnergetically optimal finitetime stabilization of generalized homogeneous linear systems.IEEE Transactions on Automatic Control2023HALback to text
 24 articleHomogeneous Unit Sliding Mode Control.IEEE Transactions on Automatic ControlMay 2023HALDOIback to text
 25 articleFiniteand FixedTime Nonovershooting Stabilizers and Safety Filters by Homogeneous Feedback.IEEE Transactions on Automatic ControlJanuary 2023, 116HALDOIback to text
 26 articleFixedtime Stabilization with a Prescribed Constant Settling Time by Static Feedback for DelayFree and Input Delay Systems.International Journal of Robust and Nonlinear Control2024HAL
 27 articleAn LMIbased Robust Nonlinear Adaptive Observer for Disturbed Regression Models.IEEE Transactions on Automatic Control2023HALback to text
 28 articlePerturbed Unicycle Mobile Robots: A SecondOrder SlidingMode Trajectory Tracking Control.IEEE Transactions on Industrial ElectronicsMay 2023, 19HALDOIback to text
 29 articleStrong and weak Leonov functions for global boundedness of state periodic systems.IEEE Transactions on Automatic Control2023HALback to text
 30 articleRemote State Estimation of Steered Systems with Limited Communications: an EventTriggered Approach.IEEE Transactions on Automatic Control2023HALback to text
 31 articleGeneralized homogeneous control with integral action.International Journal of Robust and Nonlinear ControlJanuary 2023HALDOIback to text
 32 articleHomogeneityBased Control Strategy for Trajectory Tracking in Perturbed Unicycle Mobile Robots.IEEE Transactions on Control Systems Technology3212024, 274281HALDOIback to text
 33 articleHomogeneous Systems Stabilization Based on Convex Embedding ⋆.Automatica154August 2023, 111108HALback to text
International peerreviewed conferences
 34 inproceedingsAnalysis of homogeneous systems with distributed delay using averaging approach.IFAC 2023  22nd IFAC World CongressYokohama, JapanJuly 2023HAL
 35 inproceedingsOn stability of secondorder nonlinear timedelay systems without damping.CDC 2023  62nd IEEE Conference on Decision and ControlSingapore, SingaporeDecember 2023HAL
 36 inproceedingsOn DREM regularization and unexcited linear regression estimation.62nd IEEE Conference on Decision and ControlSINGAPORE, SingaporeDecember 2023HAL
 37 inproceedingsAn adaptive observer for timevarying nonlinear systems  application to a crop irrigation model.62nd IEEE Conference on Decision and ControlSingapore, SingaporeDecember 2023HAL
 38 inproceedingsHomogeneity with respect to a part of variables and accelerated stabilization.CDC 2023  62nd IEEE Conference on Decision and ControlSingapore, SingaporeDecember 2023HAL
 39 inproceedingsOn hyperexponential stabilization of double integrator in continuous and discrete time.IFAC 2023  22nd IFAC World CongressYokohama, JapanJuly 2023HAL
 40 inproceedingsNonlinear Adaptive Observers for an SIS System Counting Primoinfections.22nd World Congress of the International Federation of Automatic ControlYokohama, JapanJuly 2023HAL
 41 inproceedingsAn Interval Predictorbased Robust Control for a Class of Constrained Nonlinear Systems.62nd IEEE Conference on Decision and ControlSINGAPORE, SingaporeDecember 2023HAL
 42 inproceedingsA Robust Interval MPC for Uncertain LPV Systems via Integral SlidingMode Control.CDC 2023  62nd IEEE Conference on Decision and ControlSingapore, SingaporeDecember 2023HAL
 43 inproceedingsOn observer design for a class of Persidskii systems based on steadystate estimation.IFAC 2023  22nd IFAC World CongressYokohama, JapanJuly 2023HAL
 44 inproceedingsFixedtime parameter estimation via the discretetime DREM method.IFACPapersOnLine22nd IFAC World Congress562YOKOHAMA, JapanJuly 2023, 40134018HALDOI
 45 inproceedingsRealization from moments: The linear case.IEEE Conference on Decision and ControlSingapore, SingaporeDecember 2023HAL
 46 inproceedingsOn Prescribedtime Cooperative State Estimation of LTI Plants.IFAC 2023  22nd World Congress of the International Federation of Automatic ControlYokohama, JapanJuly 2023HAL
 47 inproceedingsCommand governorbased adaptive control for constrained linear systems in presence of unmodelled dynamics.ACC 2023  American Control ConferenceSan Diego, United StatesIEEEMay 2023, 23872392HALDOI
 48 inproceedingsDesign of Controls for Boundedness of Trajectories of Multistable State Periodic Systems.Proc. 62th IEEE Conference on Decision and Control (CDC)Singapore, SingaporeDecember 2023HAL
 49 inproceedingsDesign of controls for ISS and Integral ISS Stabilization of Multistable State Periodic.IFAC 2023  The 22nd World Congress of the International Federation of Automatic ControlYokohama, JapanJuly 2023HAL
 50 inproceedingsA Control Leonov Function Guaranteeing Global ISS of Two Coupled Synchronverters.Proc. 62th IEEE Conference on Decision and Control (CDC)Singapore, FranceDecember 2023HAL
 51 inproceedingsA Leonov Function for Almost Global Synchronization Conditions in Acyclic Networks of Heterogeneous Kuramoto Oscillators.IFAC 2023  22nd IFAC World CongressYokohama, JapanJuly 2023HAL
 52 inproceedingsGeneralized Homogeneous Unit Control.IFAC 2023  22nd World Congress of the International Federation of Automatic ControlYokohama, JapanJuly 2023HAL
 53 inproceedingsA New FiniteTime SlidingMode Controller for a Class of SecondOrder NonLinear Systems.IFAC 2023  22nd World Congress of the International Federation of Automatic ControlYokohama, JapanJuly 2023HAL
 54 inproceedingsAn Integral SlidingModebased Robust Interval Predictive Control for Perturbed Unicycle Mobile Robots.CDC 2023  62nd IEEE Conference on Decision and ControlSingapore, SingaporeDecember 2023HAL
 55 inproceedingsConstructing annihilators for parameter estimation in nonlinearly parameterized signals.IFAC 2023  22nd IFAC World CongressYokohama, JapanJuly 2023HAL
 56 inproceedingsTrajectory Tracking in Unicycle Mobile Robots: A Homogeneitybased Control Approach.IFAC 2023  22nd World Congress of the International Federation of Automatic ControlYokohama, JapanJuly 2023HAL
 57 inproceedingsOn finitetime observers for linear systems.IFAC 2023  22nd IFAC World CongressYokohama, JapanJuly 2023HAL
 58 inproceedingsFinitetime control protocol for uniform allocation of secondorder agents.CDC 2023  62nd IEEE Conference on Decision and ControlSingapore, SingaporeDecember 2023HAL
 59 inproceedingsStability analysis and stabilization of systems with hyperexponential rates.IFAC 2023  22nd IFAC World CongressYokohama, JapanJuly 2023HAL
Scientific book chapters
Reports & preprints
 61 miscLocally Homogeneous Finitetime Stabilization of QuasiLinear Systems.June 2023HAL
 62 miscWaterminimizing strategies under viability constraint for a crop fertirrigation model.October 2023HAL
 63 miscInterval Observation and Control for ContinuousTime Persidskii Systems.September 2023HAL
 64 miscHomogeneous Artificial Neural Network.November 2023HAL
 65 miscLearning linear dynamical systems under convex constraints.August 2023HAL
 66 miscRobust Stability Analysis for ContinuousTime ParameterVarying Persidskii Systems.October 2023HAL
 67 reportHomogeneous Systems Stabilization Based on Convex Embedding.Inria2023HAL
12.3 Cited publications
 68 articleVelocity estimation of valve movement in oysters for water quality surveillance.IFACPapersOnLine482015, 333338back to text
 69 conferenceFrequency Domain Forecasting Approach for Latency Reduction in Direct HumanComputer Interaction.Proc. 56th IEEE Conference on Decision and Control (CDC)Melbourne2017back to text
 70 articleRobust finitetime output feedback stabilization of the double integrator.International Journal of Control8832015, 451460back to text
 71 articleOn Homogeneity and Its Application in Sliding Mode.Int. J. Franklin Institute35142014, 18661901back to text
 72 articleVerification of ISS, iISS and IOSS properties applying weighted homogeneity.Systems & Control Letters622013, 11591167back to text
 73 articleOn conditions of oscillations and multihomogeneity.Mathematics of Control, Signals, and Systems2812015, 137URL: http://dx.doi.org/10.1007/s004980150157yback to text
 74 articleDevelopment of Homogeneity Concept For TimeDelay Systems.SIAM Journal on Optimization and Control5232014, 14031808back to text
 75 articleRealization and Discretization of Asymptotically Stable Homogeneous Systems.IEEE Trans. Automatic Control62112017, 59625969back to text
 76 articleWeighted Homogeneity for TimeDelay Systems: FiniteTime and Independent of Delay Stability.IEEE Trans. Automatic Control6112016, 210215back to text
 77 articleBoundary timevarying feedbacks for fixedtime stabilization of constantparameter reactiondiffusion systems.Automatica1032019, 398407URL: https://doi.org/10.1016/j.automatica.2019.02.013back to text
 78 articleSISO modelbased control of separated flows: Sliding mode and optimal control approaches.International Journal of Robust and Nonlinear Control27182017, 50085027back to text
 79 conferenceInterval Prediction for ContinuousTime Systems with Parametric Uncertainties.Proc. 58th IEEE Conference on Decision and Control (CDC)Nice2019back to text
 80 articleFinitetime and Fixedtime Observer Design: Implicit Lyapunov function approach.Automatica8712018, 5260back to text
 81 articleOn Homogeneous FiniteTime Control for Linear Evolution Equation in Hilbert Space.IEEE Transactions on Automatic Control2018back to text
 82 articleConsistent Discretization of Finitetime and Fixedtime Stable Systems.SIAM Journal on Optimization and Control5712019, 78103back to text
 83 articleOn Homogeneous Distributed Parameter Systems.IEEE Trans. Automatic Control61112016, 36573662back to text
 84 articleFinitetime and fixedtime stabilization: Implicit Lyapunov function approach.Automatica512015, 332340back to text
 85 articleNonlinear feedback design for fixedtime stabilization of linear control systems.IEEE Transactions on Automatic Control57(8)2012, 21062110back to text
 86 articleTimeVarying Parameter Identification Algorithms: Finite and FixedTime Convergence.IEEE Transactions on Automatic Control6272017, 36713678URL: https://dx.doi.org/10.1109/TAC.2017.2673413back to text
 87 conferenceEstimating the infection rate of a SIR epidemic model via differential elimination.Proceedings of ECCNaples2019back to text
 88 conferenceA forecasting algorithm for latency compensation in indirect humancomputer interactions.Proceedings of ECCAlborg2016, 10811086back to textback to text
 89 articleA note on delay robustness for homogeneous systems with negative degree.Automatica7952017, 178184back to text