Chaos control and synchronization, with input saturation, via recurrent neural networks.

This paper deals with the adaptive tracking problem of non-linear systems in presence of unknown parameters, unmodelled dynamics and input saturation. A high order recurrent neural network is used in order to identify the unknown system and a learning law is obtained using the Lyapunov methodology. Then a stabilizing control law for the reference tracking error dynamics is developed using the Lyapunov methodology and the Sontag control law. Tracking error boundedness is established as a function of a design parameter. The new approach is illustrated by examples of complex dynamical systems: chaos control and synchronization.