On the Solutions of the Matrix Equations in Optimal Stochastic Control

作     者：Deng, Feiqi Hu, Gang Liu, Yongqing Feng, Zhaoshu 

作者机构：South China Univ of Technology Guangzhou China 

出 版 物：《Journal of Systems Engineering and Electronics》 (系统工程与电子技术（英文版）)

年 卷 期：1999年第10卷第3期

页      面：38-43页

核心收录：

学科分类：0711[理学-系统科学] 0808[工学-电气工程] 0809[工学-电子科学与技术（可授工学、理学学位）] 07[理学] 08[工学] 0802[工学-机械工程] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 071102[理学-系统分析与集成] 081103[工学-系统工程] 

基　　金：广东省自然科学基金 国家自然科学基金 

主　　题：Computational methods Control system analysis Control system synthesis Iterative methods Linear control systems Matrix algebra Optimal control systems Riccati equations 

摘      要：In this paper, 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 the Riccati- Ito equations is obtained and an iterative solution to the Riccati- Ito equations is also given in the paper thus a complete solution to the basic problem of optimal control of time-invariant linear Ito stochastic systems is then obtained. An example is given at the end of the paper to illustrate the application of the result of the paper.