Non-zero sum differential game for stochastic Markovian jump systems with partially unknown transition probabilities

Abstract

This paper focuses on the non-zero sum differential game problem for Markovian jump systems with partially unknown transition probabilities. Firstly, a suboptimal control problem is studied by the free-connection weighting matrix method, and then the non-zero sum differential game problem is investigated on this basis. Several sufficient conditions for the existence of ε-suboptimal control strategy and ε-suboptimal Nash equilibrium strategies are provided, and their explicit expressions are designed. Moreover, the precise form for the upper bound of the cost function is also given. To facilitate the calculation, all conditions are converted into the corresponding equivalent linear matrix inequalities or bilinear matrix inequalities form. Finally, two numerical examples are utilized to demonstrate the effectiveness of the main results.