On the Solutions of the Matrix Equations in Optimal Stochastic Control

被引：0

作者：

Deng Feiqi

Hu Gang

Liu Yongqing Feng Zhaoshu Dept of Automation South China University of technology Guangzhou P R China ^{[510641
]}

机构：

来源：

Journal of Systems Engineering and Electronics | 1999年 / 03期

关键词：

Optimal stochastic control; Matrix algebraic equation; positive definite solution; Necessary and sufficient condition; Iterative solution;

D O I：

暂无

中图分类号：

TP13 [自动控制理论];

学科分类号：

0711 ; 071102 ; 0811 ; 081101 ; 081103 ;

摘要：

In this paperl the matrix algebraic equations involved in the optimal control problem of time-invariant linear Ito stochastic systems, named Riccati- Ito equations in the paper, are investigated. The necessary and sufficient condition for the existence of positive definite solutions of theRiccati- Ito equations is obtained and an iterative solution to the Riccati- Ito equations is also givenin the paper thus a complete solution to the basic problem of optimal control of time-invariant linearIto stochastic systems is then obtained. An example is given at the end of the paper to illustratethe application of the result of the paper.

引用

页码：38 / 43

页数：6

共 9 条

[1]

Merriam III C W.Automated Design of Control Systems. . 1974

[2]

Ladde G S.Random Differential Inequalities. . 1980

[3]

Has’minskii R Z.Stochastic Stability of Differential Equations. . 1980

[4]

Kantorovich L V,Akilov G P.Functional Analysis in Normed Space. . 1964

[5]

Socha L,Willems J L.Decentralized Stabilization of Stochastic Composite Systems. International Journal of Systems Science . 1985

[6]

Miyahara Y.Optimal Control of Ultimately Bounded Stochastic Processes. Nagoya Mathematical Journal . 1974

[7]

Willems,J L,Willems J C.Feedback Stabilizability for Stochastic Systems with State and Control Dependent Noise. Automatica . 1976

[8]

Kwackernaak H,Sivan R.The Maximally Achierable Accuracy of Linear optima1 Regulators and LinearOptimal Filters. IEEE Transactions on Aerospace and Electronic Systems . 1972

[9]

Liu Yongqing and Feng Zhaoshu.Theory and Applications of Large-Scale Dynamic Systems, Stochastic Stability and Control. . 1992

← 1 →