Trajectory tracking based on differential neural networks for a class of nonlinear systems

A very successful scheme to accomplish trajectory tracking of unknown nonlinear systems consists of identifying the unknown dynamics using differential neural networks and on the basis of the so obtained mathematical model to develop an appropriate control law. The purpose of this paper is to present some new results in this sense. In particular, for the neural identifier, a new online learning law which permits to guarantee the boundedness for both the weights and the identification error without using a dead zone function is showed. Likewise, based on this neural identifier, a new control law to guarantee the boundedness of the tracking error is developed. These results are proved using a Lyapunov like analysis. With respect to the approach based on the local optimal control theory, the new approach has a similar performance but its main advantage consists of simplifying considerably the design process. The workability of the suggested approach is illustrated by simulation.