Observer-based adaptive neural network control for a class of uncertain nonlinear systems

This paper deals with the problem of designing an observer-based adaptive tracking controller for a class of uncertain nonlinear systems. A neural network-based observer estimates states of the system and a neural network-based controller is designed to approximate input control signal. The estimated states by the observer are inputs of the controller and two neural networks (NNs) interact together such that the output of the system tracks the desired trajectory. Unlike most of the previous adaptive observers and controllers which employed linear in parameter neural networks (LPNNs), the proposed observer and controller are based on the nonlinear in parameter neural networks (NLPNNs). Hence, the proposed scheme supports global approximation property and is applicable to the systems with high degrees of nonlinearity. NNs learning rules are developed based on the well-known back propagation (BP) algorithm which has been proven to be the most relevant updating rule for control problems and despite most of the previous work by adding robustifying terms to the learning rules uniformly ultimately boundedness (UUB) of all signals of the closed-loop system is guaranteed by Lyapunov´s direct method. Finally, simulations performed on the “generalized pendulum” nonlinear system to demonstrate the effectiveness and performance of the proposed observer-based tracking controller scheme.