Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls

被引：126

作者：

Rami, MA ^{[1
]}

Chen, X

Moore, JB

Zhou, XY

机构：

[1] Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Shatin, Hong Kong, Peoples R China

[2] Australian Natl Univ, Dept Syst Engn, Canberra, ACT 0200, Australia

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2001年 / 46卷 / 03期

关键词：

asymptotic analysis; generalized Riccati equation; indefinite stochastic linear quadratic (LQ) control; linear matrix inequality; solvability;

D O I：

10.1109/9.911419

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential Riccati equation. In this paper, we provide general necessary and sufficient conditions for the solvability of this generalized differential Riccati equation. Furthermore, its asymptotic behavior is investigated along with its connection to the generalized algebraic Riccati equation associated with the linear quadratic control problem in infinite time horizon. Examples are presented to illustrate the results established.

引用

页码：428 / 440

页数：13

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