Exact Controllability and Duality Method for Stochastic Game-Based Systems

The dual system of general linear time-varying SGBCS is constructed, and notions of exact controllability and exact observability are introduced in this article. Further, it is proved that the exact controllability, the validity of an observability inequality for the adjoint FBSDEs, the solvability of an optimization problem, and the solvability of an norm optimal control problem are all equivalent.