cluster synchronization for discrete-time zero-sum graphical games with unknown constrained-input systems

This paper addresses the synchronization issue of agents with their respective leaders in each cluster for unknown discrete-time zero-sum graphical games with constrained input. to solve the coupled hamilton-jacobi-isaacs equations under the assumption of unknown dynamics, an adaptive optimal distributed technique based on value iteration heuristic dynamic programming is proposed. an actor-critic framework is employed to approximate the value functions, control policies, and worst-case disturbance policies necessary for implementing the proposed method. additionally, neural network identifiers are utilized to determine each agent's unknown dynamics. to prevent system instability, a constraint on control inputs is incorporated into the design method. by considering disturbances in the dynamics, the proposed solutions are made robust against unpredictable events, enhancing performance and stability. furthermore, the closed-loop system's stability is proven. finally, the theoretical results are validated through simulation outcomes.