Noncooperative and Cooperative Strategy Designs for Nonlinear Stochastic Jump Diffusion Systems With External Disturbance: T–S Fuzzy Approach

In this article, we consider the multiplayer <inline-formula><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> noncooperative and cooperative game strategy designs for a class of stochastic jump diffusion systems with external disturbance. To attenuate the effect from the competitive strategies of other players and unpredictable external disturbance on the desired target tracking performance of each player, a multiplayer <inline-formula><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> noncooperative game strategy design problem is proposed and formulated as an equivalent multiobjective optimization problem (MOP) with a Nash equilibrium solution. Also, the multiplayer <inline-formula><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> cooperative game strategy design problem is discussed and formulated as an equivalent single-objective optimization problem. To overcome the difficulties in solving multiple Hamilton–Jacobi–Issacs inequalities (HJIIs) for noncooperative and cooperative game strategy designs, the Takagi–Sugeno fuzzy model is introduced to approximate the nonlinear stochastic system and HJII could be transformed into a set of linear matrix inequalities (LMIs). Besides, an LMI-constrained multiobjective evolution algorithm is developed to efficiently solve the MOP of a noncooperative multiplayer <inline-formula><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> stochastic game strategy design problem. A financial market with multiple investors is provided as a simulation example to demonstrate the effectiveness of the proposed noncooperative and cooperative game investment strategies.