Feedback Stabilization for a Scalar Conservation Law with PID Boundary Control

作     者：Jean Michel CORON Simona Oana TAMASOIU 

作者机构：Sorbonne Universités UPMC University Paris 06 NUMR 7598 Laboratoire Jacques-Louis Lions F-75005Paris France Université Paris Sud F-91405 Orsay France 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2015年第36卷第5期

页      面：763-776页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 081104[工学-模式识别与智能系统] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0701[理学-数学] 071101[理学-系统理论] 0811[工学-控制科学与工程] 071102[理学-系统分析与集成] 081103[工学-系统工程] 

基　　金：supported by the ERC Advanced Grant 266907(CPDENL)of the 7th Research Framework Programme(FP7) FIRST,Initial Training Network of the European Commission(No.238702) PITNGA-2009-238702 

主　　题：反馈镇定 边界控制 标量 守恒律 稳定性分析 比例积分微分 积分控制器 指数稳定性 

摘      要：This paper deals with a scalar conservation law in 1-D space dimension, and in particular, the focus is on the stability analysis for such an equation. The problem of feedback stabilization under proportional-integral-derivative(PID for short) boundary control is addressed. In the proportional-integral(PI for short) controller case, by spectral analysis, the authors provide a complete characterization of the set of stabilizing feedback parameters, and determine the corresponding time delay stability interval. Moreover, the stability of the equilibrium is discussed by Lyapunov function techniques, and by this approach the exponential stability when a damping term is added to the classical PI controller scheme is proved. Also, based on Pontryagin results on stability for quasipolynomials, it is shown that the closed-loop system sub ject to PID control is always unstable.