Impulsive Accelerated Reinforcement Learning for  \(H_\infty \) Control

This paper revisits reinforcement learning for \(H_\infty \) control of affine nonlinear systems with partially unknown dynamics. By incorporating an impulsive momentum-based control into the conventional critic neural network, an impulsive accelerated reinforcement learning algorithm with a restart mechanism is proposed to improve the convergence speed and transient performance compared to traditional gradient descent-based techniques or continuously accelerated gradient methods. Moreover, by utilizing the quasi-periodic Lyapunov function method, sufficient condition for input-to-state stability with respect to approximation errors of the closed-loop system is established. A numerical example with comparisons is provided to illustrate the theoretical results.