Reinforcement learning based predefined-time synchronization control for competitive neural networks

To optimize the comprehensive performance of competitive neural networks while strictly prescribing the transient behavior and upper bound of the synchronization error convergence time, this paper proposes a performance-guaranteed optimal synchronization control strategy based on reinforcement learning. Initially, a prescribed performance constraint function is employed to confine the synchronization tracking error within desired bounds. Balancing the minimization of synchronization errors and energy consumption, a performance-guaranteed optimal controller is formulated. To accelerate convergence, an approach law featuring predefined-time convergence characteristics is integrated into the controller framework. Furthermore, to address model uncertainties embedded in the synchronization error dynamics, a neural network approximator is utilized, thereby broadening the controller''s applicability. A reinforcement learning algorithm is then deployed to approximate the gradient function within the optimal controller, significantly reducing computational complexity. Theoretical analysis rigorously establishes the predefined-time convergence of the closed-loop system. Distinct from conventional RL methods, an adaptive law with predefined-time convergence is constructed for updating the RL network weights, thereby enhancing algorithmic efficiency. Finally, numerical simulations validate the efficacy and superior performance of the proposed control scheme.