GLOBAL STABILIZATION OF A CLASS OF NONLINEAR REACTION-DIFFUSION PARTIAL DIFFERENTIAL EQUATIONS BY BOUNDARY FEEDBACK

被引：12

作者：

Karafyllis, Iasson ^{[1
]}

Krstic, Miroslav ^{[2
]}

机构：

[1] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece

[2] Univ Calif San Diego, Dept Mech & Aerosp Engn, La Jolla, CA 92093 USA

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2019年 / 57卷 / 06期

关键词：

parabolic PDEs; semilinear reaction-diffusion PDEs; boundary feedback; global stabilization; 1-D PARABOLIC PDES; BURGERS-EQUATION; VOLTERRA NONLINEARITIES; STABILITY ENHANCEMENT; LOCAL STABILIZATION; WELL-POSEDNESS; SYSTEMS; COMPENSATION;

D O I：

10.1137/19M1252235

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 provides global exponential stabilization results by means of boundary feedback control for one dimensional nonlinear unstable reaction-diffusion partial differential equations (PDEs) with nonlinearities of superlinear growth. The class of systems studied are parabolic PDEs with nonlinear reaction terms that provide "damping" when the norm of the state is large (the class includes reaction-diffusion PDEs with polynomial nonlinearities). The case of Dirichlet actuation at one end of the domain is considered and a Control-Lypunov Functional construction is applied in conjunction with Stampacchia's truncation method. The paper also provides several important auxiliary results, among which is an extension of Wirtinger's inequality, used here for the construction of the Control-Lyapunov functional.

引用

页码：3723 / 3748

页数：26

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