Decentralized Output-Feedback Control With Asymmetric One-Step Delayed Information

This article considers the decentralized linear-quadratic-Gaussian control problem for discrete-time decentralized system controlled by two players. In this scenario, player 1 shares a unit delayed observations and control inputs with the controller of player 2, whereas due to the limiting capacity, the controller of player 1 cannot obtain the observations and control inputs of player 2, which leads to the asymmetric one-step delay information. It should be emphasized that this structure makes the classical separation principle fail. Under the assumption of linear control strategies, we derive the optimal estimators based on asymmetric information. In virtue of the Pontryagin's maximum principle, the optimal explicit decentralized controllers are obtained by solving the forward and backward stochastic difference equations. It is noted that the control gains are coupled with the estimation gains. Moreover, the estimation gains satisfy the forward Riccati equations and the control gains follow the backward Riccati equations, which cannot be solved simultaneously. To this end, we present iterative solutions to the coupled forward and backward Riccati equations. Finally, a sufficient condition for the stabilization problem is given in terms of the coupled algebraic Riccati equations. Numerical examples are illustrated to show the effectiveness of the proposed algorithm.