Asymmetric information control for stochastic systems with different intermittent observations

Highlights：

• By adopting the convex variational method, the necessary and sufficient solvability conditions are derived under some basic assumptions, which are relied on the forward and backward di ff erence equations (FBSDEs).

• Via some non symmetric Riccati equations the feedback form control strategies are derived by decoupling the FBSDEs Furthermore, the optimal performance index is also obtained as well.

• Finally, the results are extended to investigate the general multiple controllers case. We also compare our result with single controller case which has been widely studied in some previous literature. Through the simulation result, one can see that more controllers will make the state stabler.

摘要

•The information sets available to two controllers are different and mutually exclusive (i.e., either of both is not the subset of the other one). The problem under consideration in this paper is an asymmetric information control problem. It is highlighted that previous literature on asymmetric information control mainly focused on the case when the information set is a subset of the other one. However, the case of the information set s being mutually exclusive remains less investigated to the best of our knowledge, which brings essential difficulties in finding the optimal control strategies: the structures and forms of two controllers are not clear; seeking for the solvability conditions of the optimal control problem is challenging.•By adopting the convex variational method, the necessary and sufficient solvability conditions are derived under some basic assumptions, which are relied on the forward and backward di ff erence equations (FBSDEs).•Via some non symmetric Riccati equations the feedback form control strategies are derived by decoupling the FBSDEs Furthermore, the optimal performance index is also obtained as well.•Finally, the results are extended to investigate the general multiple controllers case. We also compare our result with single controller case which has been widely studied in some previous literature. Through the simulation result, one can see that more controllers will make the state stabler.