Prescribed‐Time Adaptive Dynamic Programming Control: Two Efficient Control Methods

Abstract

In the paper, the adaptive dynamic programming (ADP) control method with prescribed‐time performance is investigated. Two design methods are proposed. First, a performance function associated with the prescribed‐time sliding mode surface is constructed, and a target function incorporating a prescribed‐time varying function is designed to derive a weight update law with prescribed‐time characteristics. This approach solves the nonlinear Hamilton–Jacobi–Bellman (HJB) equation and enables the system to achieve prescribed‐time convergence. Then, by introducing a prescribed‐time varying function into the ADP neural network target function and designing a new piecewise time‐varying function for the control law, a more universal approach to realize the prescribed‐time optimal control is presented, which does not require any additional design tools and only involves pure weight updates, adhering to the general design concept in the ADP field while ensuring the system maintains prescribed‐time convergence. The stability analysis for both methods is elaborated. Finally, simulation results demonstrate the superiority of the proposed methods in terms of prescribed‐time convergence time. Comparatively, the first method benefits from the robustness of sliding mode and features a fast convergence speed, while the second method can achieve prescribed‐time stability by relying only on the weight update rate of ADP itself, without the need to superimpose other control methods.