Differential games for nonlinear stochastic systems: a fuzzy approach

A fuzzy differential game theory is proposed to solve the N-person (or N-player) nonlinear differential noncooperative and cooperative (team) game problems, which are not easily tackled by the conventional methods. In this study, both noncooperative and cooperative quadratic differential game are considered. First, the nonlinear stochastic system is approximated by a stochastic fuzzy model. Based on the stochastic fuzzy model, a fuzzy observer-based controller is proposed to deal with the noncooperative differential game in the sense of Nash equilibrium strategies or cooperative (team) game in the sense of Pareto-optimal strategies. Using the suboptimal approach, the outcome of the fuzzy differential game for both noncooperative and cooperative game is parameterized in terms of the eigenvalue problem (EVP). Linear matrix inequality (LMI) techniques are employed to solve these problems from the convex optimization perspective.