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Traditional approaches to stabilizing hyperbolic PDEs, such as PDE backstepping, often encounter challenges when dealing with high-dimensional or complex nonlinear problems. Their solutions require high computational and analytical costs.…

Analysis of PDEs · Mathematics 2024-11-08 Xianhe Zhang , Yu Xiao , Xiaodong Xu , Biao Luo

We propose an approach for the synthesis of robust and optimal feedback controllers for nonlinear PDEs. Our approach considers the approximation of infinite-dimensional control systems by a pseudospectral collocation method, leading to…

Optimization and Control · Mathematics 2019-05-16 Dante Kalise , Sudeep Kundu , Karl Kunisch

In this work, we investigate a model order reduction scheme for high-fidelity nonlinear structured parametric dynamical systems. More specifically, we consider a class of nonlinear dynamical systems whose nonlinear terms are polynomial…

Dynamical Systems · Mathematics 2023-01-24 Pawan Goyal , Igor Pontes Duff , Peter Benner

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

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 introduce a finite dimensional version of backstepping controller design for stabilizing solutions of PDEs from boundary. Our controller uses only a finite number of Fourier modes of the state of solution, as opposed to the classical…

Optimization and Control · Mathematics 2024-12-30 Varga Kalantarov , Türker Özsarı , Kemal Cem Yılmaz

In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…

Optimization and Control · Mathematics 2020-11-30 Jean-Michel Coron , Long Hu , Guillaume Olive , Peipei Shang

In this paper a solution of the data-driven robust output regulation problem for linear parabolic systems is presented. Both the system as well as the ODE, i.e., the disturbance model, describing the disturbances are unknown, but…

Systems and Control · Electrical Eng. & Systems 2025-06-10 Joachim Deutscher , Julian Zimmer

We present a methodology for stabilization of general nonlinear systems with actuator dynamics governed by general, quasilinear, first-order hyperbolic PDEs. Since for such PDE-ODE cascades the speed of propagation depends on the PDE state…

Optimization and Control · Mathematics 2017-10-23 Nikolaos Bekiaris-Liberis , Miroslav Krstic

- This paper presents the design of an output feedback control for a linear Korteweg-de Vries equation. This design is based on the backstepping method which uses a Volterra transformation. An appropriate observer is introduced and the…

Analysis of PDEs · Mathematics 2015-03-03 Swann Marx , Eduardo Cerpa

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

This paper addresses the stabilization of a chain system consisting of three hyperbolic Partial Differential Equations (PDEs). The system is reformulated into a pure transport system of equations via an invertible backstepping…

Optimization and Control · Mathematics 2025-05-01 Adam Braun , Jean Auriol , Lucas Brivadis

This paper is devoted to a simple and new proof on the optimal finite control time for general linear coupled hyperbolic system by using boundary feedback on one side. The feedback control law is designed by first using a Volterra…

Optimization and Control · Mathematics 2017-01-19 Jean-Michel Coron , Long Hu , Guillaume Olive

We develop a novel multi-layer predictor-feedback to achieve exact compensation of state-dependent input delay of general nonlinear integro-differential equations. The system of interest is an unconventional mixed Partial Differential…

Optimization and Control · Mathematics 2026-04-09 Tong Li , Peipei Shang , Mamadou Diagne

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

We present a predictive feedback control method for a class of quasilinear hyperbolic systems with one boundary control input. Assuming exact model knowledge, convergence to the origin, or tracking at the uncontrolled boundary, are achieved…

Optimization and Control · Mathematics 2022-03-18 Timm Strecker , Ole Morten Aamo , Michael Cantoni

This work is devoted to the stabilization of parabolic systems with a finite-dimensional control subjected to a constant delay. Our main result shows that the Fattorini-Hautus criterion yields the existence of such a feedback control, as in…

Optimization and Control · Mathematics 2020-04-20 Imene Aicha Djebour , Takéo Takahashi , Julie Valein

Stabilization of partial differential equations is a topic of utmost importance in mathematics as well as in engineering sciences. Concerning one dimensional problems there exists a well developed theory. Due to numerous important…

Optimization and Control · Mathematics 2025-01-24 Michael Herty , Ferdinand Thein

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

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