Optimal Tracking Control of an Underactuated Container Ship Based on Direct Gauss Pseudospectral Method

In this paper, the problem of optimal tracking control for a container ship is addressed. The multi-input–multi-output nonlinear model of the S175 container ship is well established in the literature and represents a challenging problem for control design, where the design requirement is to follow a commanded maneuver at a desired speed. To satisfy the constraints on the states and the control inputs of the vessel nonlinear dynamics and minimize the heading error, a nonlinear optimal controller is formed. To solve the resulted nonlinear constrained optimal control problem, the Gauss Pseudospectral Method (GPM) is used to transcribe the optimal control problem into a Nonlinear Programming Problem (NLP) by discretization of states and controls. The resulted NLP is then solved by a well-developed algorithm known as SNOPT. The results for course-keeping and course-changing autopilots illustrate the effectiveness of the proposed approach to deal with the vessel tracking control.