Optimal synchronization control for multi-agent systems with input saturation: a nonzero-sum game

This paper presents a novel optimal synchronization control method for multi-agent systems with input saturation. The multi-agent game theory is introduced to transform the optimal synchronization control problem into a multi-agent nonzero-sum game. Then, the Nash equilibrium can be achieved by solving the coupled Hamilton—Jacobi—Bellman (HJB) equations with nonquadratic input energy terms. A novel off-policy reinforcement learning method is presented to obtain the Nash equilibrium solution without the system models, and the critic neural networks (NNs) and actor NNs are introduced to implement the presented method. Theoretical analysis is provided, which shows that the iterative control laws converge to the Nash equilibrium. Simulation results show the good performance of the presented method.