Observer-based adaptive backstepping control and the application for a class of multi-input multi-output nonlinear systems with structural uncertainties and perturbations

In this study, the adaptive backstepping control of a class of multi-input multi-output nonlinear systems with immeasurable states, structural uncertainties and periodic perturbations is researched using neural network (NN) based nonlinear observer. Firstly, a series of harmonic components obtained from Fourier series expansion (FSE) are employed to estimate the unknown periodic perturbations. Then treating the estimated perturbations as inputs, a radial basis function-based neural network (RBFNN) is constructed as a component of the observer, and the observer is proved to be uniformly ultimately bounded (UUB) in estimating the immeasurable system states with the negative-gradient adaptive laws of NN parameters. Subsequently, the adaptive backstepping control is designed to track reference signals at the outputs of system based on the FSE-RBFNN observer, and the stability of the closed-loop system is proved on a finite set of system states. Finally, the proposed methods are applied to a triangular tethered satellite formation model to test the stability of the observer and control, and the effect of FSE in estimating perturbations is comparatively tested as well.