Characterizing all optimal controls for an indefinite stochastic linear quadratic control problem

• Published in: IEEE transactions on automatic control Vol. 47; no. 7; pp. 1119 - 1122
• Main Authors: Wu, Hanzhong, Zhou, Xun Yu
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2002; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algebra; Applied sciences; Computer science; control theory; systems; Control system synthesis; Control systems; Control theory. Systems; Cost function; Equivalence; Exact sciences and technology; Linear quadratic; Mathematical analysis; Mathematics; Optimal control; Probability and statistics; Probability theory and stochastic processes; Research and development management; Riccati equation; Riccati equations; Sciences and techniques of general use; State feedback; Stochastic processes; Stochastic systems; Stochasticity; Systems engineering and theory; Weight control; State feedback; LQ control; Probabilistic approach; Optimal control; Algebraic equation; Stochastic control; Infinite horizon; Riccati equation; Linear control; Optimal control (mathematics); Solvability
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2002.800650

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.