Optimal Control Design For Ship Course

With the development of the control theory, more and more new controller algorithms are applied to the ship course control area, and have achieved preferable effects, but the requirement for the controllers also grows along with it, hence there is a pressing need to employ the more effective and efficient controller to the ship course control for the safety and economy of ship navigation.In this paper, aiming at designing an economically energy-saving controller, the latest achievements of the optimal control theory are introduced to design for the ship course linear and nonlinear systems, off-line and online, respectively.Firstly, an integral reinforcement learning (IRL) technique based on policy iteration (PI) is employed in this paper for partly model-free ship linear course-tracking control system, which could obtain optimal tracking controller without knowledge of the system drift dynamics, meanwhile, the convergence of the control law to optimal is ensured. Secondly, an off-line optimal control algorithm based on policy iteration is applied to the ship course nonlinear system with input saturation, by introducing a generalized nonquadratic functional to deal with rudder saturation, and neural networks (NN) to approximate cost function for solving the Hamilton-Jacobi-Bellman (HJB) equation, an optimal ship controller with good effects is achieved accordingly. In the end, based on the research aforementioned, combining the policy iteration, NN with adaptive technique, an online optimal control algorithm is studied for the ship course nonlinear system with input saturation. The algorithm is an online adaptive version implemented as an actor/critic structure which involves simultaneous adaption of both actor and critic NN, and it improved the calculation speed. The Lyapunov theory guarantees that the closed-loop system states, the critic NN error and the actor NN error are uniformly and ultimately bounded.The algorithms abovementioned in this paper can assure that the control law be convergent to the optimal and the performance of the controller meets the requirement of navigation with less use and small amplitude of the rudder. Finally, the MATLAB software illustrates the effectiveness and energy-saving performance of the algorithms.