Chapter

Applications of Sliding Mode Control in Science and Engineering

Volume 709 of the series Studies in Computational Intelligence pp 343-369

Date:

A Memristor-Based Hyperchaotic System with Hidden Attractor and Its Sliding Mode Control

  • Sundarapandian VaidyanathanAffiliated withResearch and Development Centre, Vel Tech University Email author 

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Abstract

Memristor-based systems and their potential applications, in which memristor is both a nonlinear element and a memory element, have been received significant attention in the control literature. In this work, we study a memristor-based hyperchaotic system with hidden attractors. First, we study the dynamic properties of the memristor-based hyperchaotic system such as equilibria, Lyapunov exponents, Kaplan-Yorke dimension, etc. We obtain the Lyapunov exponents of the memristor-based system as \(L_1 = 0.2205\), \(L_2 = 0.0305\), \(L_3 = 0\) and \(L_4 = -10.7862\). Since there are two positive Lyapunov exponents, the memristor-based system is hyperchaotic. Also, the Kaplan-Yorke fractional dimension of the memristor-based hyperchaotic system is obtained as \(D_{KY} = 3.0233\), which shows the high complexity of the system. We show that the memristor-based hyperchaotic system has no equilibrium point, which shows that the system has a hidden attractor. Control and synchronization of chaotic and hyperchaotic systems are important research problems in chaos theory. Sliding mode control is an important method used to solve various problems in control systems engineering. In robust control systems, the sliding mode control is often adopted due to its inherent advantages of easy realization, fast response and good transient performance as well as insensitivity to parameter uncertainties and disturbance. Next, using integral sliding mode control, we design adaptive control and synchronization schemes for the memristor-based hyperchaotic system. The main adaptive control and synchronization results are established using Lyapunov stability theory. MATLAB simulations are shown to illustrate all the main results of this work.

Keywords

Memristor Hidden attractor Chaos Hyperchaos Adaptive control Synchronization Sliding mode control