Nash Equilibrium Seeking in Non-Zero-Sum Games: A Prescribed-Time Fuzzy Control Approach

This paper investigates the Nash equilibrium seeking issue in
$N$
-player non-zero-sum (NZS) games. First, prescribed-time control is a priori encoded into the framework of
$N$
-player NZS games by defining a cost function that considers the interactions between multiple players and prescribed-time performance requirements. To tackle the complex challenge of solving the coupled Hamilton-Jacobi (HJ) equation, a fuzzy adaptive learning algorithm within the prescribed-time frame is proposed. An identifier is constructed to address the lack of prior knowledge about the system's nonlinear dynamics. Critic and actor-tuning laws are designed to approximate optimal value functions and Nash equilibrium strategies. The proposed algorithm achieves Nash equilibrium and ensures the system state converges to a prescribed range within a specified time. Finally, the feasibility of the proposed algorithm is substantiated through a simulation example involving three-player games.