Reinforcement learning-based saturated adaptive robust output-feedback funnel control of surface vessels in different weather conditions

Abstract

This article tackles the problem of saturated adaptive robust actor–critic learning PID tracking control design guaranteeing a prescribed funnel performance for ships with multiple dead bands in which the ship’s velocities/accelerations and dynamic parameters are unknown and time-variant subject to the availability of external disturbances. The controller is proposed by integrating an observer, adaptive actor–critic multi-layer neural networks, generalized saturation functions, the prescribed performance funnel control, an adaptive robust controller and multiple dead bands. The observer calculates the estimation of ship’s velocities/accelerations, in which the peaking phenomenon is prevented by limiting the observer signals. Within the structure of adaptive actor–critic design, adaptive multi-layer neural networks are exerted, which counteracts against ship’s time-variant uncertainties and the actuator saturation nonlinearity. In order to reduce the likelihood of actuator saturation well, generalized saturation functions are taken into account. To realize prespecified transient and steady-state performance of the tracking errors, the prescribed performance control is applied. With the purpose of avoiding the corner cutting to increase the trajectory tracking accuracy, curvature of the circular trajectories is calculated and the angle of arc is compensated. An adaptive robust controller is utilized to resist against external disturbances, and a scheme of multiple dead bands is devised in this paper to protect the actuator system in heavy seas.