Output trajectory tracking using dynamic neural networks

This paper deals with the development of a robust asymptotic neuro-observer (NN) for a class of unknown nonlinear systems with noise disturbances in the output. An output trajectory tracking from the estimated states is studied. The suggested asymptotic observer has three basic terms: the first one is introduced to approximate the unknown nonlinear dynamics; the second one is related with the innovation; and the last one is a time delayed term introduced especially to assure the approximation of the unmeasured states derivatives. The Lyapunov-Krasovskii technique is used to proof the robust asymptotic stability “on average” of the obtained estimation error. A special “dead-zone” multiplier is introduced into the learning procedure to guarantee the boundedness of the weight matrices of the dynamic NN