A Chebyshev Neural Network based sliding mode controller for uncertain discrete-time-delayed nonlinear systems

Abstract

This article demonstrates a Chebyshev Neural Network (CNN) based sliding mode controller for uncertain nonlinear systems. The uncertainties in the system are classified as mismatched parametric uncertainties and unknown nonlinearities which are bounded in nature. This article, exploited the novelty of CNN that it requires a less computational time as compared to other Neural Network (NN) functions, in order to estimate the unknown non-linearities. Furthermore, the Lyapunov-Krasovskii functional (LKF) theory is used for the stability analysis of uncertain nonlinear delayed system. An adequate condition is defined to assure the asymptotic stability of the given system by linear matrix inequalities (LMI). However, the proposed CNN based controller guarantees the the error trajectory to be in close proximity of sliding surface even under unknown uncertainties and nonlineraties. The simulation results show that proposed controller outperforms other existing controller.

Subject Classification:

• 93C10

Keywords:

• Chebyshev neural network
• Linear matrix inequality
• Lyapunov-Krasovskii functional theory and Sliding mode control