Energy-efficient tracking control of unmanned surface vehicles: A fixed-time pose and velocity constrained strategy

• A tan-type nonlinear mapping function is constructed to satisfy pose and velocity constraints. • A fixed-time disturbance observer is designed to accurately estimate external disturbances. • An RL algorithm within the identifier-actor-critic framework is proposed for energy-efficient tracking control of USVs. This paper investigates the fixed-time energy-efficient tracking control for unmanned surface vehicles (USVs) with external disturbances and unknown dynamics. To guarantee the safety of USVs in constrained environments, the pose and velocity constraints are considered. Firstly, a tan-type nonlinear mapping function that incorporates the constraint set is constructed, and the original USV system with pose and velocity constraints is converted into an unconstrained one. Subsequently, a fixed-time disturbance observer is designed to estimate external disturbances. Furthermore, by employing the backstepping technique and fixed-time theory, the performance index functions that measure tracking error costs and control input costs are presented, and then the virtual and actual control signals can be derived as the optimized solutions of the corresponding subsystems. Given the inherent difficulties in solving the Hamilton-Jacobi-Bellman (HJB) equations, the reinforcement learning (RL) algorithm within an identifier-actor-critic framework is proposed, where identifiers are utilized to approximate unknown dynamics. The control scheme ensures that the tracking error converges to a small region around zero within a fixed time while minimizing the costs and meeting the constraint requirements. Finally, the simulation results verify the effectiveness of the proposed method.