Hybrid adaptive control of nonlinear systems with non-Lipschitz nonlinearities

Abstract

In this paper, a hybrid adaptive control method is proposed for a class of discrete-time multiple-inputs-multiple-outputs (MIMO) systems with non-Lipschitz nonlinearities by introducing a novel Riemann sum operator with variable step size. Firstly, for the first order approximation of the original nonlinear system, a linear adaptive controller is developed to assure essential boundedness of all the signals but with unsatisfactory performance. Secondly, an artificial neural network (ANN)-based nonlinear adaptive controller is designed for the original system to improve response performance, nevertheless, may lead to instability. Thirdly, switching mechanism between the linear adaptive controller and the nonlinear one is suitably designed to achieve stability and improved output tracking performance simultaneously. Finally, a numerical example is provided to verify the effectiveness of the proposed method.