Predefined-time nearly optimal trajectory tracking control for autonomous surface vehicles with unknown dynamics

Abstract

This paper investigates the predefined-time nearly optimal trajectory tracking control for autonomous surface vehicles (ASVs) with unknown dynamics. Unlike the existing methods, which only ensure asymptotic or finite-time stability, the proposed control method allows users to specify the settling time and convergence accuracy. Firstly, a performance index function that measures tracking error costs and control input energy costs is presented. Due to the difficulty in solving the Hamilton–Jacobi–Bellman (HJB) equation, a nearly optimal method via reinforcement learning (RL) within the identifier-actor-critic architecture is proposed. Meanwhile, an improved piecewise function including settling time and convergence accuracy is constructed. This piecewise function is embedded into the approximate optimal performance index function and control input, which avoids the chattering and singularity phenomena in the sign function. The control scheme approximates the optimal value function, control policy, and unknown dynamics without relying on the precise knowledge of system dynamics and ensures that tracking errors converge to a specific accuracy within a predefined time. Finally, simulation results demonstrate the effectiveness of the proposed control method.