Robust adaptive neural networks control for a class of time-delay parabolic systems with nonlinear periodic time-varying parameter

Abstract

This paper mainly focuses on the stabilization of a class of parabolic systems with time-varying delay, external disturbance and nonlinear periodic time-varying parameter (NPTVP). Firstly, combined with Fourier series expansion (FSE) method and neural networks (NNs) approximation technology, a NNs approximator is designed to approximately describe the uncertain dynamic term with NPTVP. Then, based on adaptive control theory, NNs approximation technology and reparameterization method, two robust adaptive neural network control (RANNC) algorithms are designed to make the parabolic systems with time-varying delay, external disturbance and NPTVP achieve asymptotic stability and meet a prescribed adaptive H∞ performance of disturbance attenuation. Sufficient conditions of the asymptotical stability while satisfying the prescribed adaptive H∞ performance index for the resulting closed-loop systems are also derived. Finally, several simulations are carried out to verify the effectiveness of the designed RANNC algorithms.