High-Order Fuzzy Switching Neural Networks: Application to the Tracking Control of a Class of Uncertain SISO Nonlinear Systems

Abstract

In this paper, a high-order neuro-fuzzy network (HONFN) with improved approximation capability w.r.t. the standard high-order neural network (HONN) is proposed. In order to reduce the overall approximation error, a decomposition of the neural network (NN) approximation space into overlapping sub-regions is created and different NN approximations for each sub-region are considered. To this end, the HONFN implements a fuzzy switching among different HONNs as its input vector switches along the different sub-regions of the approximation space. The HONFN is then used to design an adaptive controller for a class of uncertain single-input single-output nonlinear systems. The proposed scheme ensures the semiglobal uniform ultimate boundedness of the tracking error within a neighborhood of the origin and the boundedness of the NN weights and control law. Furthermore, a minimal HONFN, with two properly selected fuzzy rules, guarantees that the resulting ultimate bound does not depend on the unknown optimal approximation error (as is the case for classical adaptive NN control schemes) but solely from constants chosen by the designer. A simulation study is carried out to compare the proposed scheme with a classical HONN controller.