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

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Abstract
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.
Funding Information
  • National Natural Science Foundation of China (62222313, 62173275, 91848205)

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