Observability and Optimal Control Problems of Stochastic Switched Systems Based on Non-Cooperative Dynamic Games

This article studies the observability and optimal control problems of stochastic switched systems which is based on a non cooperative dynamic game theory involving one leader and multiple followers. Through the application of operators, duality of the system and the characteristics of the forward-backward stochastic differential equations (FBSDE), four equivalent observability criterions for the dual system of the modeled system are given. Meanwhile, it is proved that an optimization problem of the adjoint backward stochastic differential equation (BSDE) is equivalent to a norm optimal problem.