Synchronization Control of Uncertain Fractional-Order Nonlinear Multi-Agent Systems Via Fuzzy Regularization Reinforcement Learning

This study introduces a feasible reinforcement learning framework designed to address the optimal synchronization control problem in fractional-order nonlinear multi-agent systems (FONMAS) characterized by partially unknown dynamics. In order to find the optimal control, the fractional Hamilton-Jacobi-Bellman (HJB) equations containing FONMAS are firstly proposed by constructing an auxiliary system and an equivalent transformation. The optimal solution for the optimal control of the FONMAS is further obtained and the controller is induced to constitute a Nash equilibrium. Meanwhile, it is proven that the optimal cost function and optimal control strategy can be gradually approximated by policy iteration, and the regularization-based identifier-actor-critic fuzzy logic is constructed, and combined with backstepping control and reinforcement learning (RL) to approximate the unknown dynamic function to obtain the optimal control. Furthermore, the optimality error-based Lyapunov function is established, and the fractional-order update mechanism for the neural network weights is designed. This ensures the convergence of network weights to their optimal values while effectively circumventing the gradient explosion problem commonly encountered when training neural networks using gradient descent algorithms in the context of fractional calculus. Finally, the boundedness of synchronization errors is proved, and numerical simulations are conducted to validate the effectiveness of the proposed algorithm.