Title :
Characterizing all optimal controls for an indefinite stochastic linear quadratic control problem
Author :
Wu, Hanzhong ; Zhou, Xun Yu
Author_Institution :
Dept. of Math., Fudan Univ., Shanghai, China
fDate :
7/1/2002 12:00:00 AM
Abstract :
This paper is concerned with a stochastic linear quadratic (LQ) control problem in the infinite-time horizon, with indefinite state and control weighting matrices in the cost function. It is shown that the solvability of this problem is equivalent to the existence of a so-called static stabilizing solution to a generalized algebraic Riccati equation. Moreover, another algebraic Riccati equation is introduced and all the possible optimal controls, including the ones in state feedback form, of the underlying LQ problem are explicitly obtained in terms of the two Riccati equations
Keywords :
Riccati equations; computability; linear quadratic control; matrix algebra; stability; state feedback; stochastic systems; algebraic Riccati equations; control weighting matrices; cost function; indefinite state; indefinite stochastic linear quadratic control problem; infinite-time horizon; optimal control characterization; solvability; state feedback; static stabilizing solution; Control systems; Cost function; Optimal control; Research and development management; Riccati equations; State feedback; Stochastic processes; Stochastic systems; Systems engineering and theory; Weight control;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2002.800650