Open-Loop Decentralized LQ Control Problem With Multiplicative Noise

This article considers the decentralized linear-quadratic (LQ) optimal control problem for the multiplicative-noise stochastic systems in discrete time with asymmetric information. There exist two controllers in the system, and each controller has its own information in general structure. The adopted information structure is adapted open loop for both controllers. The main contribution is to derive the necessary and sufficient condition for the unique solvability of the LQ control problem with a general asymmetric information structure and present the explicitly optimal controllers in terms of the proposed Riccati equations. The key is to explicitly solve the forward and backward stochastic difference equations, which are derived from the maximum principle.