Direct adaptive neural network controller for a class of nonlinear systems based on fuzzy estimator of the control error

A new approach of direct adaptive control of single input single output nonlinear systems in affine form using single-hidden layer neural network (NN) is introduced. In contrast to the algorithms in the literature, the weights adaptation laws are based on the control error and not on the tracking error or its filtered version. Since the control error is being expressed in terms of the NN controller, hence its weights updating laws are obtained via back-propagation concept. A fuzzy inference system (FIS) with heuristically defined rules is introduced to provide an estimate of this error based on the past history of the system behaviour. The stability of the closed loop is studied using Lyapunov theory. A fixed structure is then proposed for the FIS and the design parameters reduce to the parameters of the NN. The method is reproducible and does not require any pre-training of the network weights.