Optimal control of discrete-time bilinear systems with applications to switched linear stochastic systems

被引：6
|
作者：
Huang, Ran [1 ]
Zhang, Jinhui [2 ]
Lin, Zhongwei [3 ]
机构：
[1] Beijing Univ Chem Technol, Coll Informat Sci & Technol, Beijing 100029, Peoples R China
[2] Tianjin Univ, Sch Elect & Automat, Tianjin 300072, Peoples R China
[3] North China Elect Power Univ, Sch Control & Comp Engn, Beijing 102206, Peoples R China
来源：
SYSTEMS & CONTROL LETTERS | 2016年 / 94卷
基金：
中国国家自然科学基金;
关键词：
Discrete-time; Stability analysis; Optimal control; Bilinear system; Switched linear stochastic system; CONTROLLABILITY;
D O I：
10.1016/j.sysconle.2016.06.004
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 aims at characterizing the most destabilizing switching law for discrete-time switched systems governed by a set of bounded linear operators. The switched system is embedded in a special class of discrete-time bilinear control systems. This allows us to apply the variational approach to the bilinear control system associated with a Mayer-type optimal control problem, and a second-order necessary optimality condition is derived. Optimal equivalence between the bilinear system and the switched system is analyzed, which shows that any optimal control law can be equivalently expressed as a switching law. This specific switching law is most unstable for the switched system, and thus can be used to determine stability under arbitrary switching. Based on the second-order moment of the state, the proposed approach is applied to analyze uniform mean-square stability of discrete-time switched linear stochastic systems. Numerical simulations are presented to verify the usefulness of the theoretic results. (C) 2016 Elsevier B.V. All rights reserved.
引用
收藏
页码：165 / 171
页数：7
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