Optimal control of affine nonlinear systems: A novel actor-critic approach integrating wavelet filtering

This paper presents a wavelet filter-enhanced actor-critic (AC) algorithm for the optimal control of affine nonlinear systems. The proposed filter contracts the LaSalle invariant set by leveraging a wavelet neural network for Hamiltonian approximation and a soft threshold for error reduction. A key innovation is the use of the Morlet activation function, which separates the approximation error across time and frequency domains. This approach not only accelerates convergence by training on filtered informative components but also reduces the invariant set. Lyapunov-based analysis proves parameter convergence and uniformly ultimately bounded (UUB) stability of the closed-loop system under the designed control law. Case simulations are conducted to validate the efficacy of the proposed algorithm.