Optimal Control for Stochastic Systems With Multiple Controllers of Different Information Structures

In this article, we investigate the optimal linear quadratic control problem for stochastic systems with multiple controllers, where each controller has its own information structure, which differs from each other. More specifically, we consider the optimal control problem for systems with multiple controllers of different delayed state information. First, the necessary and sufficient solvability conditions are given in terms of forward and backward difference equations (FBSDEs). Further, an innovation method is proposed to decouple the FBSDEs, and the optimal control strategies are derived based on a given nonsymmetric Riccati equation. Finally, a numerical example is provided to show the effectiveness of the main results. It is stressed that the proposed methods and results can be seen as an important addition to the optimal control theory with asymmetric-information-structure controllers.