Nonlinear boundary output feedback stabilization of reaction-diffusion equations

被引:6
|
作者
Lhachemi, Hugo [1 ]
Prieur, Christophe [2 ]
机构
[1] Univ Paris Saclay, CNRS, CentraleSupelec, Lab signaux & Syst, F-91190 Gif Sur Yvette, France
[2] Univ Grenoble Alpes, GIPSA lab, CNRS, Grenoble INP, F-38000 Grenoble, France
关键词
Reaction-diffusion equations; Nonlinear boundary control; Nonlinear sector condition; Output feedback; Finite-dimensional controller; DISTRIBUTED-PARAMETER-SYSTEMS; CONTROLLABILITY; STABILITY; STATE;
D O I
10.1016/j.sysconle.2022.105301
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
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 of the time-derivative of the control cannot be applied. In this context, we first demonstrate using Lyapunov direct method how a finite-dimensional observer-based controller can be designed, without using the time derivative of the boundary input as an auxiliary command, in order to achieve the boundary stabilization of general 1-D reaction-diffusion equations with Robin boundary conditions and a measurement selected as a Dirichlet trace. We extend this approach to the case of a control applying at the boundary through a sector nonlinearity. We show from the derived stability conditions the existence of a size of the sector (in which the nonlinearity is confined) so that the stability of the closed-loop system is achieved when selecting the dimension of the observer to be large enough. (C) 2022 Elsevier B.V. All rights reserved.
引用
收藏
页数:9
相关论文
共 50 条