Adaptive neural network control for course-keeping of ships with input constraints

In this paper, an adaptive neural network (NN) control method is proposed for the problem of nonlinear course control of ships with input constraints and unknown direction control gains. Specifically, dynamic surface control is used to overcome the problem of explosion of complexity inherent in the backstepping technique, and the Nussbaum function is employed to deal with the unknown signs of control gains. It is proved that the proposed adaptive NN control method, which is composed of dynamic surface control and a backstepping technique with the Nussbaum gain function, is able to guarantee uniform ultimate boundedness of all the signals in the controlled system. In addition, the tracking error between the output of the controlled system and a desired trajectory is shown to converge to a small neighbourhood of the origin. Finally, one example is introduced to illustrate the proposed theoretical results.