Finite-time adaptive dynamic programming control for nonlinear systems based on novel complementary terminal sliding mode surface

For a nonlinear system, a novel complementary terminal sliding mode surface-based finite-time adaptive dynamic programming optimal control scheme (FT-NCTSMS-ADP) is proposed. To begin with, with the aim to improve convergence speed and tracking precision, a novel complementary terminal sliding mode surface (NCTSMS) is developed. Then, a specific cost function related to the NCTSMS is developed, and the initial control problem is then transformed toward a series of optimal control problems. The Hamilton-Jacobi-Bellman (HJB) problem is then solved by a single critic neural network, yielding the estimated optimal controller. Finally, using the finite-time lemma, we design a Lyapunov function and verify the system’s fast finite-time convergence. Both the simulation and the real-world experiment validate the practical significance of the proposed method.