Decentralized Optimal Control for Linear Stochastic Systems with Control Signals subject to Unknown Noises

Decentralized strategies have been extensively applied to LQ optimal control problems, whereas, stochastic systems with unknown random parameters have not been comprehensively studied. In this paper, we consider a class of stochastic systems with a decentralized configuration consisting of multiple controllers which have access to Gaussian noises with unknown statistical information. The stabilizing and optimal control strategies are acquired by designing a novel stochastic approximation algorithm recursively evaluating the zero points of certain matrix equations, which is confirmed to be equivalent with solving the corresponding Riccati equations. The proof of convergence and boundness of the proposed algorithm is presented.