Stable direct adaptive neural network controller with a fuzzy estimator of the control error for a class of perturbed nonlinear systems

A state feedback direct adaptive control algorithm for single input single output perturbed nonlinear systems in affine form using single hidden layer neural network is introduced. The weights adaptation laws are based on an estimated control error provided by a fuzzy inference system composed of heuristically determined rules. It provides a bounded estimate of the control error, which affects only the step size of the updating laws. It is shown that under mild conditions the state variables and the control input are bounded and the tracking error and its derivatives converge to a bounded compact set. The method does not require any preliminary offline training of the network weights. All states are supposed to be measurable. Two simulation studtracking error ies are presented for testing the proposed algorithm.