Decentralized Control for Continuous‐Time Stochastic Systems With Asymmetric Information Controllers

ABSTRACT This article solves the decentralized optimal control problem for Itô stochastic systems where two controllers can access different information sets due to transmission delay. In contrast to the existing literature, the dynamics of the system involves two controllers with different information structure, which poses challenges in solving the optimal control strategy. In this paper, by adopting variational methods, the necessary and sufficient solvability conditions in terms of delayed forward and backward stochastic differential equations (D‐FBSDEs) are derived for the problem considered. Furthermore, by decoupling these D‐FBSDEs, a novel decentralized control strategy is derived. Finally, a numerical example demonstrates the effectiveness of the proposed methods and results.