Fuzzy-Based Optimal Control for an Underactuated Surface Vessel With User-Specified Performance

Accurate performance and low energy consumption are essential for trajectory tracking control of an underactuated surface vessel (USV) to satisfy marine operation requirements. This paper studies the user-specified optimal tracking control problem for the USV in the presence of modeling uncertainties. A fuzzy weights-based adaptive reinforcement learning (RL) control scheme is developed to achieve the tracking control with the predefined convergence time and steady-state accuracy while minimizing the performance index function. The constructed performance index function includes the surge velocity control law and the constrained position tracking error. Following that, an optimal backstepping design frame is proposed to derive the controllers with unknown gradient terms by constructing the error subsystems at the kinematic and kinetic levels of the USV. Then, a fuzzy reinforcement learning algorithm (FRLA) is presented to derive the optimal control solutions of corresponding error subsystems. Since the fuzzy basis function vectors derived from measured states of the USV system may be zero vectors, the persistence excitation condition may not always be satisfied. Thus, in the design of fuzzy RL updating laws of critics and actors, a positive parameter compensation technique is proposed to make the matrixes consist of fuzzy basis functions strictly positive definite. It releases the need for assumption of persistence excitation, and the convergence of the critic weight estimate and the boundedness of closed-loop systems can be guaranteed. Finally, the effectiveness of the presented method is demonstrated by numerical simulations and real-world experiments.