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24 results on '"Redaud, Jeanne"'

4. Practical Output Regulation and Tracking for Linear ODE-hyperbolic PDE-ODE Systems

Author

Redaud, Jeanne, Bribiesca-Argomedo, Federico, Auriol, Jean, Niculescu, Silviu-Iulian, Editor-in-Chief, Atay, Fatihcan M., Advisory Editor, Bellen, Alfredo, Advisory Editor, Chen, Jie, Advisory Editor, Gu, Keqin, Advisory Editor, Krauskopf, Bernd, Advisory Editor, Michiels, Wim, Advisory Editor, Özbay, Hitay, Advisory Editor, Rasvan, Vladimir, Advisory Editor, Stepan, Gabor, Advisory Editor, Zerz, Eva, Advisory Editor, Zhong, Qing-Chang, Advisory Editor, Auriol, Jean, editor, Deutscher, Joachim, editor, Mazanti, Guilherme, editor, and Valmorbida, Giorgio, editor

Published
2022
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12. Numerical analysis of a chaotic coupled hyperbolic PDE system for secure image encryption

Author

Redaud, Jeanne and Sano, Hideki

Abstract

This paper focuses on the interest of using chaotic hyperbolic Partial Differential Equations (PDE) systems synchronization for secure image communication. Such systems offer a promising alternative to finite dimensional chaotic systems with enlarged key space, efficient computation, and more complex dynamics. Here, we modify the classical chaotic hyperbolic PDE system by adding integral boundary couplings and potential terms. The chaotic behaviour of the resulting system is observed in numerical simulations. Adding such couplings allows to enhance the security of the cryptosystem. The synchronization of receiver and transmitter chaotic systems is achieved by the use of a chaotic observer designed using the backstepping methodology. The initial image can then be encrypted into a chaotic signal on the transmitter side before being sent to the receiver side. Using observational data, the receiver can then reconstruct the initial image. Numerical illustrations complete the paper.

Published
2024
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19. Practical output regulation and tracking for linear ODE-hyperbolic PDE-ODE systems

Author

Redaud, Jeanne, Bribiesca-Argomedo, Federico, Auriol, Jean, Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Dynamical Interconnected Systems in COmplex Environments (DISCO), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Ampère, Département Automatique pour l'Ingénierie des Systèmes (AIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), and AURIOL, Jean

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]
Abstract

International audience; In this chapter, we consider the problem of practical output regulation and output tracking for a linear 2 × 2 hyperbolic Partial Differential Equation (PDE) system with actuation and load dynamics. Indeed, it is actuated via an Ordinary Differential Equation (ODE) at one boundary and the output to be controlled is the output of an ODE at the other boundary. The main focus is on load tracking. Here, we propose to extend existing results on approximate output regulation to a class of systems similar to that considered in [8] and to extend filtering techniques to a dynamically augmented system with finite-dimensional exosystems considering possible trajectory and disturbance inputs. Issues with respect to small delays in the state reconstruction and feedback loop are considered. Due to the nature of the disturbances, the state estimation and disturbance reconstruction problems are also considered. This scenario finds applications in many systems of engineering interest, such as drilling systems [3], pneumatic systems [17], or electric transmission lines [22].

Published
2021

21. Informatique tronc commun - ITC - PSI, MP, PC

Author

Janny Steeven, Cherrière Théodore, Redaud Jeanne, Shu-Quartier-dit-Maire Wenqi, Janny Steeven, Cherrière Théodore, Redaud Jeanne, and Shu-Quartier-dit-Maire Wenqi

Published
2022

22. Stabilizing Integral Delay Dynamics and Hyperbolic Systems using a Fredholm Transformation

Author

Jeanne Redaud, Jean Auriol, Silviu Niculescu, Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Dynamical Interconnected Systems in COmplex Environments (DISCO), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), and Redaud, Jeanne

Subjects
[SPI]Engineering Sciences [physics], [SPI] Engineering Sciences [physics], [MATH] Mathematics [math], [MATH]Mathematics [math]
Abstract

International audience; In this paper, we design a stabilizing statefeedback control law for a system represented by a general class of integral delay equations. Under an appropriate spectral controllability assumption, an implementable control law is proposed. The approach is constructive and makes use of the well-known backstepping methodology. Due to the integral terms present in the original system, the proposed problem requires a Fredholm transform, which is not always invertible. The invertibility of this transformation is proved using an operator formulation. In particular, we show that this invertibility property is a consequence of spectral controllability. The existence of the kernels defining the Fredholm transform is proved similarly by showing that they satisfy an invertible integral equation. Some test case simulations complete the paper.

Published
2021

23. Observer Design for a Class of Delay Systems Using a Fredholm Transform

Author

Jeanne Redaud, Jean Auriol, Silviu Niculescu, Redaud, Jeanne, Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Dynamical Interconnected Systems in COmplex Environments (DISCO), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire des signaux et systèmes (L2S), and CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, infinite dimensional systems, [SPI] Engineering Sciences [physics], 010102 general mathematics, 02 engineering and technology, observer design, [MATH] Mathematics [math], backstepping methodology, 01 natural sciences, [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, Control and Systems Engineering, 0101 mathematics, [MATH]Mathematics [math]
Abstract

International audience; In this paper, we design an observer for a system represented by a general class of Integral Delay Equations (IDE). This class of equations encompasses various systems, from chemical or biological processes to the propagation of electric pulses on excitable media. The available measurement corresponds to a discrete and distributed-delayed value of the state. Under an appropriate spectral observability assumption, an implementable observer is proposed. Inspired by the fact that first-order hyperbolic Partial Derivative Equations (PDE) and timedelay systems are closely related, we use a PDE formulation and the well-known backstepping methodology for the design. However, due to integral terms in the dynamics, the use of a Fredholm integral transform is required. We prove its existence and invertibility by using an operator framework. Both proofs derive from the spectral observability assumption. Some test case simulations end the paper.

Published
2021

24. Stabilization of a hyperbolic PDEs-ODE network using a recursive dynamics interconnection framework

Author

Jean Auriol, Federico Bribiesca Argomedo, Silviu Niculescu, Jeanne Redaud, Redaud, Jeanne, Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Ampère, Département Automatique pour l'Ingénierie des Systèmes (AIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Dynamical Interconnected Systems in COmplex Environments (DISCO), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire des signaux et systèmes (L2S), and CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)

Subjects
[SPI]Engineering Sciences [physics], [SPI] Engineering Sciences [physics], [MATH] Mathematics [math], [MATH]Mathematics [math]
Abstract

International audience; In this paper, we design a state-feedback law that exponentially stabilizes an underactuated network of scalar hyperbolic systems coupled at the end of the chain with a finite-dimensional system modeled by an ordinary differential equation. Our approach uses a recursive dynamics interconnection framework. More precisely, for each subsystem, we solve a stabilization problem, a tracking problem and design a statepredictor. Then, we are able to recursively design a control law that stabilizes the whole chain. Some illustrative examples complete the presentation.

Published
2021

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