Indefinite LQ Control for Discrete-Time Stochastic Systems via Semidefinite Programming

Abstract EN

This paper is concerned with a discrete-time indefinite stochastic LQ problem in an infinite-time horizon.

A generalized stochastic algebraic Riccati equation (GSARE) that involves the Moore-Penrose inverse of a matrix and a positive semidefinite constraint is introduced.

We mainly use a semidefinite-programming- (SDP-) based approach to study corresponding problems.

Several relations among SDP complementary duality, the GSARE, and the optimality of LQ problem are established.