Nesterov Accelerated Gradient-Based Fixed-Time Convergent Actor–Critic Control for Nonlinear Systems

This paper presents a novel Nesterov accelerated gradient-based fixed-time convergent actor-critic (NAG-FxT-AC) scheme for the optimal control of nonlinear systems. The proposed approach integrates the Nesterov accelerated gradient method with FxT concurrent learning to achieve rapid convergence while ensuring optimal performance. Actor-critic neural networks (NN) are employed to approximate the optimal value function and control policy, where the accelerated gradient mechanism introduces auxiliary variables to enhance learning efficiency. A FxT concurrent learning algorithm is developed to update the NN weights, guaranteeing convergence to bounded regions within fixed time independent of initial conditions. Lyapunov stability analysis proves that both the closed-loop system states and NN estimation errors are ultimately uniformly bounded with FxT NN weights convergence properties. Simulation results on a nonlinear system validate the effectiveness of the proposed control scheme. Compared to the baseline methods like FxT-ADP, the proposed NAG-FxT-AC reduces the state convergence time by up to 12% and the weight convergence time by 84%, demonstrating superior learning efficiency.