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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

We develop a non-collocated, observer-based output-feedback law for a class of continua of linear hyperbolic PDE systems, which are viewed as the continuum version of $n+m$, general heterodirectional hyperbolic systems as $n\to\infty$. The…

Optimization and Control · Mathematics 2025-03-12 Jukka-Pekka Humaloja , Nikolaos Bekiaris-Liberis

In this paper, a backstepping control of the one-phase Stefan Problem, which is a 1-D diffusion Partial Differential Equation (PDE) defined on a time varying spatial domain described by an ordinary differential equation (ODE), is studied. A…

Optimization and Control · Mathematics 2016-07-18 Shumon Koga , Mamadou Diagne , Shuxia Tang , Miroslav Krstic

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 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 develops an extension of infinite-dimensional backstepping method for parabolic and hyperbolic systems in one spatial dimension with two actuators. Typically, PDE backstepping is applied in 1-D domains with an actuator at one…

Optimization and Control · Mathematics 2016-03-17 Rafael Vazquez , Miroslav Krstic

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 develop a delay-adaptive controller for a class of first-order hyperbolic partial integro-differential equations (PIDEs) with an unknown input delay. By employing a transport PDE to represent delayed actuator states, the system is…

Analysis of PDEs · Mathematics 2023-07-11 Shanshan Wang , Jie Qi , Miroslav Krstic

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

In this paper, we study the indirect boundary stability and exact controllability of a one-dimensional Timoshenko system. In the first part of the paper, we consider the Timoshenko system with only one boundary fractional damping. We first…

Analysis of PDEs · Mathematics 2019-01-29 Mohammad Akil , Yacine Chitour , Mouhammad Ghader , Ali Wehbe

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

In this paper, we present output feedback boundary stabilization for a class of semilinear parabolic PDEs with a boundary measurement and an actuation located at the same place. The method uses backstepping transformations, where the state…

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

The paper is concerned with the strict-feedback form of hyperbolic distributed-parameter systems. Such a system structure is well known to be the basis for the recursive backstepping control design for nonlinear ODEs and is also reflected…

Systems and Control · Electrical Eng. & Systems 2026-03-16 Nicole Gehring

We investigate the stability of three thermoelastic beam systems with hyperbolic heat conduction. First, we study the Bresse-Gurtin-Pipkin system, providing a necessary and sufficient condition for the exponential stability and the optimal…

Analysis of PDEs · Mathematics 2021-02-11 Filippo Dell'Oro

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

A backstepping-based compensator design is developed for a system of $2\times2$ first-order linear hyperbolic partial differential equations (PDE) in the presence of an uncertain long input delay at boundary. We introduce a transport PDE to…

Optimization and Control · Mathematics 2023-07-24 Jing Zhang , Jie Qi

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 studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction-diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The…

Optimization and Control · Mathematics 2024-01-22 Dandan Guan , Jie Qi , Mamadou Diagne

This paper deals with the backstepping design of observer-based compensators for parabolic ODE-PDE-ODE systems. The latter consist of n coupled parabolic PDEs with distinct diffusion coefficients and spatially-varying coefficients, that are…

Systems and Control · Electrical Eng. & Systems 2020-08-28 Joachim Deutscher , Nicole Gehring

The paper presents an approach to flatness-based control design for hyperbolic multi-input systems, building upon the hyperbolic controller form (HCF). The transformation into HCF yields a simplified system representation that considerably…

Systems and Control · Electrical Eng. & Systems 2026-04-02 Simon Schmidt , Nicole Gehring , Abdurrahman Irscheid