Nearly optimal control approach to ship course-keeping system with input saturation

In this paper, an optimal control method is applied to a second-order nonlinear ship course-keeping system with input saturation. By using a nonquadratic functional as performance index the constrained control input is formulated. Neural network (NN) is employed to approximate the cost function associated with each LE. The quality of operation of the designed control algorithm is checked in simulation tests by taking a ship as an example. In order to obtain reference results for comparison, another control algorithm using the backstepping method is examined as well. The results verified the effectiveness of the nearly optimal control law with less consumption of energy.