Christophe Prieur

• PhD
• Senior Researcher at CNRS

Linear fusion is a cornerstone of estimation theory. Implementing optimal linear fusion requires knowledge of the covariance of the vector of errors associated with all the estimators. In distributed or cooperative systems, the cross-covariance terms cannot be computed, and to avoid underestimating the estimation error, conservative fusions must be...

Linear fusion is a cornerstone of estimation theory. Implementing optimal linear fusion requires knowledge of the covariance of the vector of errors associated with all the estimators. In distributed or cooperative systems, the cross-covariance terms cannot be computed, and to avoid underestimating the estimation error, conservative fusions must be...

Modern vehicles have evolved from mechanical systems to complex and connected ones controlled by numerous digital computers interconnected through internal networks. While this development has improved their efficiency and safety, it also brings new potential risks, particularly cyber-attacks. Several studies have explored the security of vehicle d...

In this work, we studied the exponential stability of the nonlinear KdV equation posed on a finite star shaped network with finite number of branches. On each branch of the network we define a KdV equation posed on a finite domain [[EQUATION]] or the half-line [[EQUATION]]. We start by proving well-posedness and some regularity results. Then, we st...

This paper presents a learning-based control strategy for non-linear throttle valves with an asymmetric hysteresis, leading to a near-optimal controller without requiring any prior knowledge about the environment. We start with a carefully tuned Proportional Integrator (PI) controller and exploit the recent advances in Reinforcement Learning (RL) w...

Off-dynamics Reinforcement Learning (ODRL) seeks to transfer a policy from a source environment to a target environment characterized by distinct yet similar dynamics. In this context, traditional RL agents depend excessively on the dynamics of the source environment, resulting in the discovery of policies that excel in this environment but fail to...

This paper deals with the modelling and stabilization of a flexible clamped beam controlled with a piezoelectric actuator in the self-sensing configuration. We derive the model starting from general principles, using the general laws of piezoelectricity. The obtained model is composed by a PDE, describing the flexible deformations dynamics, interco...

Input-to-state stability (ISS) unifies the stability and robustness in one notion, and serves as a basis for broad areas of nonlinear control theory. In this contribution, we covered the most fundamental facts in the infinite-dimensional ISS theory with a stress on Lyapunov methods. We consider various applications given by different classes of inf...

A Magnetic field Aided Inertial Navigation System (MAINS) for indoor navigation is proposed in this paper. MAINS leverages an array of magnetometers to measure spatial variations in the magnetic field, which are then used to estimate the displacement and orientation changes of the system, thereby aiding the inertial navigation system (INS). Experim...

In this work, we studied the exponential stability of the nonlinear KdV equation posed in a finite star shaped network. On each branch of the network we define a KdV equation posed on a finite domain (0, ℓ j) or the half-line (0, ∞). We start by proving well-posedness and some regularity results. Then, we state the exponential stability of the line...

This paper studies state observation for a heterogeneous quasilinear traffic flow system with disturbances at the inlet of a considered road section. Based on the backstepping method, an observer is designed for the quasilinear traffic flow system with only the boundary measurements at the inlet of the considered road section. The observer is const...

A Magnetic field Aided Inertial Navigation System (MAINS) for indoor navigation is proposed in this paper. MAINS leverages an array of magnetometers to measure spatial variations in the magnetic field, which are then used to estimate the displacement and orientation changes of the system, thereby aiding the inertial navigation system (INS). Experim...

Recent advances in the use of Artificial Intelligence to control complex systems make it suitable for profile plasma control. In this work, we propose an algorithm based on Deep Reinforcement Learning to control the safety factor profile with a feedback design. For this purpose, we first derive a device-specific control-oriented model with fast sim...

To tackle the demodulation issues of wireless electromagnetic trackers, we propose a method that takes advantage of non-orthogonalities between the coils of the emitter. This method does not require an additional sensor, nor a synchronization signal, nor an initialization step. It can therefore be combined with a tracking method to make it robust t...

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Linear fusion is a cornerstone of estimation theory. Optimal linear fusion was derived by Bar-Shalom and Campo in the 1980s. It requires knowledge of the cross-covariances between the errors of the estimators. In distributed or cooperative systems, these cross-covariances are difficult to compute. To avoid an underestimation of the errors when thes...

In this work, we study the exponential stability of a system of linear Korteweg-de Vries (KdV) equations interconnected through the boundary conditions on a star-shaped network structure. On each branch of the network we define a linear KdV equation defined on a bounded domain (0, ℓj) or the half-line (0, ∞). We start by proving well-posedness usin...

Cooperative localization is a promising solution to improve the accuracy and overcome the shortcomings of GNSS. Cooperation is often achieved by measuring the distance between users. To optimally integrate a distance measurement between two users into a navigation filter, the correlation between the errors of their estimates must be known. Unfortun...

We study in this paper the one-dimensional Kuramoto-Sivashinsky equation (KS), subject to intermittent sensing. Namely, we measure the state on a sub-interval of the spatial domain during certain intervals of time, and we measure the state on the remaining sub-interval of space during the remaining intervals of time. As a result, we assign an activ...

The present paper addresses the topic of boundary output feedback stabilization of parabolic-type equations, governed by linear differential operators which can be diagonalized by the introduction of adequate weighting functions (by means of the Sturm-Liouville method), and which evolve in bounded spatial domains that are subsets of $\mathbb{R}^d,\...

This paper studies an optimal boundary control law for a heterogeneous traffic flow model with disturbances in order to remove the traffic congestion. The macroscopic first-order N-class Aw-Rascle (AR) traffic model consists of 2N hyperbolic partial differential equations (PDEs). The vehicle size and driver's behavior characterize the type of vehic...

This paper studies an optimal tuning of the boundary controller for a heterogeneous traffic flow model with disturbances in order to alleviate congested traffic. The macroscopic first-order N-class Aw-Rascle traffic model consists of 2N hyperbolic partial differential equations. The vehicle size and the driver's behavior characterize the type of ve...

Cooperative localization is a promising solution to improve the accuracy and overcome the shortcomings of GNSS. Cooperation is often achieved by measuring the distance between users. To optimally integrate a distance measurement between two users into a navigation filter, the correlation between the errors of their estimates must be known. Unfortun...

This paper focuses on the anti-windup design for saturated 1-D linear reaction-diffusion equation which admits a finite number of unstable poles. We consider a scenario in which the system is controlled via a dynamic, finite-dimensional output feedback controller ensuring closed-loop exponential stability. A method is proposed to design a dynamic a...

In many applications, attitude estimation algorithms rely mainly on magnetic and inertial measurements from MARG sensors (consisting of a magnetometer, a gyroscope, and an accelerometer). One of the main challenges facing these algorithms is that the accelerometer measures both gravity and an unknown external acceleration, while these algorithms as...

In this paper, we consider the problem of nonlinear (in particular, saturated) stabilization of the high-dimensional wave equation with Dirichlet boundary conditions. The wave dynamics are subject to a dissipative nonlinear velocity feedback and generate a strongly continuous semigroup of contractions on the optimal energy space L 2 (Ω) × H −1 (Ω)....

This paper addresses the topic of global output feedback stabilization of semilinear reaction-diffusion PDEs. The semilinearity is assumed to be confined into a sector condition. We consider two different types of actuation configurations, namely: bounded control operator and right Robin boundary control. The measurement is selected as a left Diric...

This paper addresses the derivation of generic and tractable sufficient conditions ensuring the stability of a coupled system composed of a reaction–diffusion partial differential equation (PDE) and a finite-dimensional linear time invariant ordinary differential equation (ODE). The coupling of the PDE with the ODE is located either at the boundari...

In this work, we deal with the exponential stability of the nonlinear Korteweg–de Vries equation on a finite star-shaped network in the presence of delayed internal feedback. We start by proving the well-posedness of the system and some regularity results. Then, we state an exponential stabilization result using a Lyapunov function by imposing smal...

Boundary feedback control design is studied for 1D hyperbolic systems with an in-domain disturbance and a boundary feedback controller under the effect of actuator saturation. Nonlinear semigroup theory is used to prove well-posedness of mild solution pairs to the closed-loop system. Sufficient conditions in the form of dissipation functional inequ...

This paper studies the design of a finite-dimensional output feedback controller for the stabilization of a reaction–diffusion equation in the presence of a sector nonlinearity in the boundary input. Due to the input nonlinearity, classical approaches relying on the transfer of the control from the boundary into the domain with explicit occurrence...

This paper introduces new structures called conic frameworks and their rigidity. They are composed by agents and a set of directed constraints between pairs of agents. When the structure cannot be flexed while preserving the constraints, it is said to be rigid. If only smooth deformations are considered a sufficient condition for rigidity is called...

This paper addresses the boundary output feedback stabilisation of a general class of 1-D reaction–diffusion PDEs with delayed boundary measurement. The output takes the form of either a Dirichlet or Neumann trace. The output delay can be arbitrarily large. The control strategy is composed of a finite-dimensional observer that is used to observe a...

This paper addresses the control design problem of output feedback stabilization of a reaction–diffusion PDE with a non-collocated boundary condition. More precisely, we consider a reaction–diffusion equation with a boundary condition describing a proportional relationship between the left and right Dirichlet traces. Such a boundary condition natur...

Boundary feedback control design is studied for 1D hyperbolic systems with an in-domain disturbance and a boundary feedback controller under the effect of actuator saturation. Nonlinear semigroup theory is used to prove well-posedness of mild solution pairs to the closed-loop system. Sufficient conditions in the form of dissipation functional inequ...

This paper studies state estimation for a heterogeneous quasilinear traffic flow system with disturbances at the inlet of a considered road section. On the basis of the backstepping method, a quasilinear observer is designed for the quasilinear traffic flow system with only the boundary measurements at the inlet of the considered road section. The...

This paper addresses the topic of output feedback stabilization of general one-dimensional reaction–diffusion partial differential equations (PDEs) in the presence of a saturation in the measurement. The boundary control and the second boundary condition take the form of Dirichlet/Neumann/Robin boundary conditions. The measurement is selected as a...

The attitude estimation of a rigid body by magnetic, angular rate, and gravity (MARG) sensors is a research subject for a large variety of engineering applications. A standard solution for building up the observer is usually based on the Kalman filter and its different extensions for versatility and practical implementation. However, the performanc...

In this paper, we investigate the problem of boundary stabilization for a heterogeneous quasilinear traffic flow system with disturbances in the congested regime. The H 2 integral input-to-state stability of multi-type traffic system described by first-order quasilinear hyperbolic partial differential equations is obtained in closed loop with a bou...

In this paper, two boundary controllers are proposed to stabilize the origin of the nonlinear Kuramoto-Sivashinsky equation under intermittent measurements. More precisely, the spatial domain is divided into two sub-domains. The state of the system on the first sub-domain is measured along a given interval of time, and the state on the remaining su...

This paper is concerned with the output feedback boundary stabilization of general 1-D reaction diffusion PDEs in the presence of an arbitrarily large input delay. We consider the cases of Dirichlet/Neumann/Robin boundary conditions for the both boundary control and boundary condition. The boundary measurement takes the form of an either Dirichlet...

In this letter, we study the leader-synchronization problem for a class of partial differential equations with boundary control and in-domain coupling. We describe the problem in an abstract formulation and we specialize it to a network of parabolic partial differential equations. We consider a setting in which a subset of the followers is connecte...

This chapter proposes some non-trivial extensions of the classical high-gain observer designs for finite-dimensional nonlinear systems to some classes of infinite-dimensional ones, written as triangular systems of coupled first-order hyperbolic Partial Differential Equations (PDEs), where an observation of one only coordinate of the state is consid...

This paper investigates the output feedback boundary control of reaction–diffusion equations with either distributed or boundary measurement by means of a finite-dimensional observer. A constructive method dealing with the design of finite-dimensional observers for the feedback stabilization of reaction–diffusion equations was reported in a recent...

This book, published in honor of Professor Laurent Praly on the occasion of his 65th birthday, explores the responses of some leading international authorities to new challenges in nonlinear and adaptive control. The mitigation of the effects of uncertainty and nonlinearity – ubiquitous features of real-world engineering and natural systems – on cl...

This paper is concerned with the output feedback stabilization of a reaction-diffusion equation by means of bounded control inputs in the presence of saturations. Using a finite-dimensional controller composed of an observer coupled with a finite-dimensional state-feedback, we derive a set of conditions ensuring the stability of the closed-loop pla...

This chapter tackles the output feedback stabilization of a reaction-diffusion PDE in the presence of saturations applying to the command input as well as a finite number of its time derivatives. The control strategy consists of a finite dimensional observer and a finite-dimensional state-feedback. We derive LMI-based sufficient conditions that ens...

In this letter, we study the leader-synchronization problem for a class of partial differential equations with boundary control and in-domain coupling. We describe the problem in an abstract formulation and we specialize it to a network of parabolic partial differential equations. We consider a setting in which a subset of the followers is connec...

This paper deals with a one-dimensional wave equation with a nonlinear dynamic boundary condition and a Neumann-type boundary control acting on the other extremity. We consider a class of nonlinear stabilizing feedbacks that only depend on the velocity at the controlled extremity. The uncontrolled boundary is subject to a nonlinear first-order term...

This paper investigates the output feedback setpoint regulation control of a reaction-diffusion equation by means of boundary control. The considered reaction-diffusion plant may be open-loop unstable. The proposed control strategy consists of the coupling of a finite-dimensional observer and a PI controller in order to achieve the boundary setpoin...

This paper addresses the topic of global output feedback stabilization of semilinear reaction-diffusion PDEs. The semilinearity is assumed to be confined into a sector condition. We consider two different types of actuation configurations, namely: bounded control operator and right Robin boundary control. The measurement is selected as a left Diric...

In this paper, we consider the wave equation with Dirichlet boundary control subject to a nonlinearity, the kind of which includes (but is not restricted to) pointwise saturation mappings. The case where only a subset of the boundary is actuated is allowed. Initial data is taken in the optimal energy space associated with Dirichlet boundary control...

In this paper, we consider the problem of nonlinear (in particular, saturated) stabilization of the high-dimensional wave equation in the Dirichlet boundary condition. The wave dynamics are subject to a dissipative nonlinear velocity feedback and generate a strongly continuous semigroup of contractions on the optimal energy space L 2 (Ω) × H −1 (Ω)...

This paper deals with a one-dimensional wave equation with a nonlinear dynamic boundary condition and a Neumann-type boundary control acting on the other extremity. We consider a class of nonlinear stabilizing feedbacks that only depend on the velocity at the controlled extremity. The uncontrolled boundary is subject to a nonlinear first-order term...

This paper investigates the output feedback boundary control of reaction-diffusion equations with either distributed or boundary measurement by means of a finite-dimensional observer. A constructive method dealing with the design of finite-dimensional observers for the feedback stabilization of reaction-diffusion equations was reported in a recent...

This paper is about the stabilization of a cascade system of n linear Korteweg–de Vries equations in a bounded interval. It considers an output feedback control placed at the left endpoint of the last equation, while the output involves only the solution to the first equation. The boundary control problems investigated include two cases: a classica...

This article designs an optimal observer-based output feedback control for traffic breakdown to dissolve traffic congestion using the backstepping method and optimization. The linearized Aw-Rascle-Zhang model is used to represent the congested traffic dynamics resulting from traffic breakdown. Based on the factors leading to traffic breakdown, we t...

Null controllability of nonlinear partial differential equation is a very complex challenge. The context underlying this study is to improve the behavior of the plasma in a tokamak reactor in order to lengthen the duration of the nuclear fusion process. Considering the class of a specific parabolic PDE, the well known heat equation is nonlinear if...

The boundary feedback control of networks of freeway traffic is considered in this article by means of the partial differential equation (PDE)-based techniques. The control and measurements are all located at the boundaries of each link. We have established the boundary control model for the system, a linear hyperbolic system of balance laws, which...

This paper addresses the boundary output feedback stabilization of general 1-D reaction-diffusion PDEs with delayed boundary measurement. The output takes the form of a either Dirichlet or Neumann trace. The output delay can be arbitrarily large. The control strategy is composed of a finite-dimensional observer that is used to observe a delayed ver...

This paper proposes an innovative method to estimate the velocity of a moving body. This is achieved using solely raw data from a triad of low-cost inertial sensors, i.e. accelerometer and gyroscope, as well as a determined arrangement of magnetometer array. The proposed approach combines a magnetic field gradient-based Extended Kalman Filter (EKF)...

This paper deals with synchronization of a class of infinite-dimensional systems. The considered network is described by a collection of semilinear Lipschitz boundary-actuated infinite-dimensional dynamics. For undirected connected graphs, sufficient conditions for asymptotic synchronization are established. We show that the proposed conditions whe...

This paper is concerned with the output feedback boundary stabilization of general 1-D reaction diffusion PDEs in the presence of an arbitrarily large input delay. We consider the cases of Dirichlet/Neumann/Robin boundary conditions for the both boundary control and boundary condition. The boundary measurement takes the form of a either Dirichlet o...

This paper studies the design of a finite-dimensional output feedback controller for the stabilization of a reaction-diffusion equation in the presence of a sector nonlinearity in the boundary input. Due to the input nonlinearity, classical approaches relying on the transfer of the control from the boundary into the domain with explicit occurrence...

This paper deals with synchronization of a class of infinite-dimensional nonlinear systems. The considered network is described by a collection of semilinear Lipschitz boundary-actuated infinite-dimensional dynamics. For undirected connected graphs, sufficient conditions for asymptotic synchronization are established. We show that the proposed cond...

This paper is concerned with the output feedback stabilization of a reaction-diffusion equation by means of bounded control inputs in the presence of saturations. Using a finite-dimensional controller composed of an observer coupled with a finite-dimensional state-feedback, we derive a set of conditions ensuring the stability of the closed-loop pla...

This paper addresses the derivation of sufficient linear matrix inequality conditions ensuring the stability of a coupled system composed of a reaction-diffusion partial differential equation (PDE), with possibly spatially-varying coefficients, and a finite-dimensional linear time invariant ordinary differential equation (ODE). The coupling of the...

This work addresses the problem of High-Gain Observer design for a class of quasi-linear hyperbolic systems (with one characteristic velocity), possibly including nonlocal terms, making them systems of Partial Integro-Differential Equations. The design relies on distributed measurement of a part of the state vector. The observer is presented and di...

The problem of High-Gain Observer Design is addressed for a class of 3 × 3 inhomogeneous linear hyperbolic systems with possibly distinct characteristic velocities and considering distributed measurement of part of the state. Applying an infinite-dimensional state transformation, the system is mapped into a new set of partial differential equations...

This paper is concerned with the in-domain stabilization of a class of block diagonal infinite-dimensional systems in the presence of an uncertain and time-varying delay in the distributed control input. Two actuation schemes are considered. The first one assumes a control input that is fully distributed over the domain. The second one assumes that...

Boundary feedback control design for systems of linear hyperbolic conservation laws in the presence of boundary measurements affected by disturbances is studied. The design of the controller is performed to achieve input-to-state stability (ISS) with respect to measurement disturbances with a minimal gain. The closed-loop system is analyzed as an a...

In this paper the Single Particle Model is used to describe the behavior of a Li-ion battery. The main goal is to design a feedback input current in order to regulate the State of Charge (SOC) to a prescribed reference trajectory. In order to do that, we use the boundary ion concentration as output. First, we measure it directly and then we assume...