Decentralized control for optimal LQ problems in stochastic systems with unknown uncertainties

In this paper, we study the optimal control problem of a linear quadratic stochastic system where the randomness results from multiplicative noises. Especially, two controllers having access to different information are involved in the system. Different from most of the existing results which are based on the condition that the information of multiplicative noise is known during the design of optimal controllers, we focus on a more general case that the statistical information of the multiplicative noise is inaccessible. Under this setting, we propose a stochastic approximation algorithm to derive the solutions to algebraic Riccati equations (AREs) and obtain the optimal and stabilizing decentralized controllers.