Disturbance observer-based adaptive reinforcement learning for perturbed uncertain surface vessels.

This article considers a problem of tracking, convergence of disturbance observer (DO) based optimal control design for uncertain surface vessels (SVs) with external disturbance. The advantage of proposed optimal control using adaptive/approximate reinforcement learning (ARL) is that consideration for whole SVs with only one dynamic equation and without conventional separation technique. Additionally, thanks to appropriate disturbance observer, the attraction region of tracking error is remarkably reduced. On the other hand, the particular case of optimal control problem is presented by directly solving for the purpose of choosing the suitable activation functions of ARL. Furthermore, the proposed ARL based optimal control also deals with non-autonomous property of closed tracking error SV model by considering the equivalent system. Based on the Lyapunov function candidate using optimal function and quadratic form of estimated error of actor/critic weight, the stability and convergence of the closed system are proven. Some examples are given to verify and demonstrate the effectiveness of the new control strategy.