Title :
Solvability and asymptotic behavior of generalized Riccati equations arising in indefinite stochastic LQ controls
Author :
Rami, Mustapha Ait ; Chen, Xi ; Moore, John B. ; Zhou, Xun Yu
Author_Institution :
Dept. of Syst. Eng. & Eng. Manage., Chinese Univ. of Hong Kong, Shatin, China
fDate :
3/1/2001 12:00:00 AM
Abstract :
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 finite time horizon. Examples are presented to illustrate the results established
Keywords :
Riccati equations; differential equations; linear quadratic control; matrix algebra; noise; stochastic systems; asymptotic behavior; constrained matrix differential Riccati equation; finite time horizon; generalized differential Riccati equation; indefinite quadratic cost function; indefinite stochastic LQ controls; linear system; multiplicative noise; necessary and sufficient conditions; optimal control; solvability; Control systems; Cost function; Differential equations; Linear systems; Nonlinear equations; Optimal control; Riccati equations; Stochastic processes; Stochastic resonance; Stochastic systems;
Journal_Title :
Automatic Control, IEEE Transactions on
