Maximum principle for partially observed leader–follower stochastic differential game

Abstract

This paper deals with the optimal control problem for partially observed leader–follower stochastic differential game. By virtue of the classical variational method and Girsanov's theorem, the stochastic maximum principles for the follower under one type of partially observed case and for the leader under the complete information structure are derived. As applications, two partially observed cases are considered for the linear–quadratic models. Then by the stochastic filtering technique, the optimal feedback controls for the follower and the leader are represented by the new stochastic Riccati equations.

Partial information target defense game in the presence of a line segment obstacle

“…A significant benefit of using the HJI equations is that they result in detailed modeling of the system dynamics [19]. Some outstanding work based on differential games [20–22] has been published. The work [20] conducted an analysis of optimal strategies and trajectories for players in the presence of obstacles using differential games and provided a complete game solution.…”

“…The work [21] extended the classical theory of differential games to address scenarios involving multiplayer pursuit‐evasion. And the work [22] dealt with the optimal control problem for a partially observed leader‐follower stochastic differential game. However, solving the HJI equations has proven challenging due to the curse of dimensionality.…”