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This paper considers the backstepping state feedback and observer design for hyperbolic and parabolic PDEs, which are bidirectionally interconnected in a general coupling structure. Both PDE subsystems consist of coupled scalar PDEs with…

Systems and Control · Electrical Eng. & Systems 2023-06-23 Joachim Deutscher , Nicole Gehring , Nick Jung

We establish that stabilization of a class of linear, hyperbolic partial differential equations (PDEs) with a large (nevertheless finite) number of components, can be achieved via employment of a backstepping-based control law, which is…

Optimization and Control · Mathematics 2024-11-05 Jukka-Pekka Humaloja , Nikolaos Bekiaris-Liberis

We present here the details of a backstepping transformation aiming at reformulating the dynamics of a nonlinear systems subject to unknown long input delay in a form which is suitable for Lyapunov stability analysis. The control law…

Dynamical Systems · Mathematics 2013-05-24 Delphine Bresch-Pietri , Miroslav Krstic

We consider a one-dimensional controlled reaction-diffusion equation, where the control acts on the boundary and is subject to a constant delay. Such a model is a paradigm for more general parabolic systems coupled with a transport…

Optimization and Control · Mathematics 2015-11-11 Delphine Bresch-Pietri , Christophe Prieur , Emmanuel Trélat

This paper addresses the stabilization of a chain of three coupled hyperbolic partial differential equations actuated by two control inputs applied at arbitrary nodes of the network. With the exception of configurations where one input is…

Optimization and Control · Mathematics 2026-04-24 Adam Braun , Jean Auriol , Lucas Brivadis

We solve the global asymptotic stability problem of an unstable reaction-diffusion Partial Differential Equation (PDE) subject to input delay and state quantization developing a switched predictor-feedback law. To deal with the input delay,…

Systems and Control · Electrical Eng. & Systems 2025-01-28 Florent Koudohode , Nikolaos Bekiaris-Liberis

In this paper, we design an output-feedback controller to stabilize n +m hetero-directional transport partial differential equations (PDEs) coupled on both domain boundaries to ordinary differential equations (ODEs). This class of systems…

Analysis of PDEs · Mathematics 2024-06-17 Jean Auriol , Federico Bribiesca Argomedo

This paper presents a backstepping approach for the boundary control of first-order hyperbolic equations with spatially varying coefficients posed on domains of arbitrary dimension. The method is based on a change of variables induced by…

Systems and Control · Electrical Eng. & Systems 2026-05-26 Mohamed Camil Belhadjoudja

This paper addresses the problem of robust stabilization for linear hyperbolic Partial Differential Equations (PDEs) with Markov-jumping parameter uncertainty. We consider a 2 x 2 heterogeneous hyperbolic PDE and propose a control law using…

Systems and Control · Electrical Eng. & Systems 2026-03-13 Yihuai Zhang , Jean Auriol , Huan Yu

This paper presents a control design for the one-phase Stefan problem under actuator delay via a backstepping method. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a material's…

Optimization and Control · Mathematics 2019-01-29 Shumon Koga , Delphine Bresch-Pietri , Miroslav Krstic

We consider output-feedback stabilization problems for a class of two-component linear parabolic systems with boundary actuation and measurement. The state-feedback control laws are obtained using backstepping method and require measurement…

Analysis of PDEs · Mathematics 2016-12-13 Agus Hasan

This paper deals with the problem of boundary stabilization of first-order n\times n inhomogeneous quasilinear hyperbolic systems. A backstepping method is developed. The main result supplements the previous works on how to design…

Optimization and Control · Mathematics 2015-12-14 Long Hu , Rafael Vazquez , Florent Di Meglio , Miroslav Krstic

The recently introduced DeepONet operator-learning framework for PDE control is extended from the results for basic hyperbolic and parabolic PDEs to an advanced hyperbolic class that involves delays on both the state and the system output…

Optimization and Control · Mathematics 2024-06-17 Jie Qi , Jing Zhang , Miroslav Krstic

We consider the problem of output feedback regulationfor a linear first-order hyperbolic system with collocatedinput and output in presence of a general class of disturbancesand noise. The proposed control law is designed through…

Analysis of PDEs · Mathematics 2017-10-20 Pierre-Olivier Lamare , Jean Auriol , Florent Di Meglio , Ulf Jakob F. Aarsnes

We solve the problem of stabilization of a class of linear first-order hyperbolic systems featuring n rightward convecting transport PDEs and m leftward convecting transport PDEs. Using the backstepping approach yields solutions to…

Analysis of PDEs · Mathematics 2015-12-24 Jean Auriol , Florent Di Meglio

Control of distributed parameter systems affected by delays is a challenging task, particularly when the delays depend on spatial variables. The idea of integrating analytical control theory with learning-based control within a unified…

Artificial Intelligence · Computer Science 2025-01-31 Jiaqi Hu , Jie Qi , Jing Zhang

This paper is concerned with the fault diagnosis problem for general linear heterodirectional hyperbolic ODE-PDE systems. A systematic solution is presented for additive time-varying actuator, process and sensor faults in the presence of…

Systems and Control · Electrical Eng. & Systems 2020-10-23 Ferdinand Fischer , Joachim Deutscher

In this paper an artificial delay based impedance controller is proposed for robotic manipulators with uncertainty in dynamics. The control law unites the time delayed estimation (TDE) framework with a second order switching controller of…

Robotics · Computer Science 2022-08-23 Udayan Banerjee , Bhabani Shankar Dey , Indra Narayan Kar , Subir Kumar Saha

We present a control design for semilinear and quasilinear 2x2 hyperbolic partial differential equations with the control input at one boundary and a nonlinear ordinary differential equation coupled to the other. The controller can be…

Optimization and Control · Mathematics 2021-05-20 Timm Strecker , Ole Morten Aamo , Michael Cantoni

This work studies the design problem of feedback stabilizers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping…

Optimization and Control · Mathematics 2012-12-05 Iasson Karafyllis , Miroslav Krstic