ε-Nash Equilibrium Model Predictive Control for Takagi–Sugeno Fuzzy Multi-Agent Systems: A Finite-Horizon Noncooperative Game Approach

This paper addresses a non-cooperative game-based model predictive control problem for constrained nonlinear multi-agent systems modeled by Takagi–Sugeno (T–S) fuzzy systems. An M-step fuzzy model predictive control (FMPC) strategy is developed within a non-cooperative game framework, where an iterative distributed algorithm is embedded to guarantee convergence to a constrained ε-Nash equilibrium (ε-NE). A novel objective function is formulated by jointly accounting for system stability, control effort, consensus performance, and inter-agent disturbance attenuation, thereby promoting recursive feasibility and convergence of the closed-loop system. To address the computational intractability induced by coupling interactions and neighboring disturbances, advanced analytical techniques, including the quadratic bounded method, the Rayleigh–Ritz theorem, and inequality relaxation, are employed to reformulate the original problem into tractable offline and online optimization programs. Furthermore, sufficient conditions are derived to ensure recursive feasibility, consensus, and convergence to an ε-NE. The effectiveness of the proposed approach is validated through theoretical analysis and simulation studies.