基于SLQ控制器的时滞微分系统的鲁棒镇定

数学物理学报

基于SLQ控制器的时滞微分系统的鲁棒镇定

包俊东; 邓飞其; 罗琦

内蒙古师范大学数学科学学院\quad 呼和浩特 010022

收稿日期:2005-06-08 修回日期:2006-12-01 出版日期:2007-04-25 发布日期:2007-04-25
通讯作者: 包俊东
基金资助:
国家自然科学基金(69874015, 69334030)和内蒙古自然科学基金(200308020101)资助

Robust Stabilization for Delay Differential Systems Based on SLQ Control

Bao Jundong; Deng Feiqi; Luo Qi

Institute of Mathematics, Inner Mongolia Normal University, Huhehaote 010022

Received:2005-06-08 Revised:2006-12-01 Online:2007-04-25 Published:2007-04-25

摘要/Abstract

摘要： 该文基于随机线性二次控制问题, 讨论了多时滞、且具有马尔可夫跳变参数的微分系统的最优控制的鲁棒性及可镇定问题.应用了Lyapunov-Krasovskii型的泛函、伊藤(Ito)公式、及Schur补等工具, 分析了该随机多时滞、具有马尔可夫过程的微分系统的均方指数稳定性.得到了时滞相关与时滞无关的充分性的代数判据.

关键词: 随机线性二次(SLQ)控制, 鲁棒镇定, 时滞相关, 均方指数稳定, 马尔可夫跳变过程

Abstract: This paper is based on the stochastic linear quadratic control problem. The
robustness of stabilizability of optimal controller for stochastic multi-time
delay systems with Markovian jumping parameters is investigated. Lyapunov--Krasovskii like functional, stochastic analysis, Ito formula and Schur complement are employed to analyze the exponential stability in mean square for stochastic multi-time delay differential systems with Markovian jumping parameters. The delay dependent and delay independent algebric criteria are established.

Key words: Stochastic Linear quadraic (SLQ) control, Robust stabilization, Delay dependent criteria, Exponential stability in mean square, Markov process

中图分类号:

93D21

包俊东; 邓飞其; 罗琦. 基于SLQ控制器的时滞微分系统的鲁棒镇定[J]. 数学物理学报, 2007, 27(2): 359-367.

Bao Jundong; Deng Feiqi; Luo Qi. Robust Stabilization for Delay Differential Systems Based on SLQ Control[J]. Acta mathematica scientia,Series A, 2007, 27(2): 359-367.