Control and Synchronization of a Novel Hyperchaotic Two-Disk Dynamo System via Adaptive Integral Sliding Mode Control

Abstract

Chaos and hyperchaos have important applications in physics, chemistry, biology, ecology, secure communications, cryptosystems and many scientific branches. 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. This work proposes a novel 4-D hyperchaotic two-disk dynamo system without any equilibrium point. Thus, the proposed novel hyperchaotic two-disk dynamo system exhibits hidden attractors. Also, we show that the Lyapunov exponents of the hyperchaotic two-disk dynamo system are \(L_1 = 0.0922\), \(L_2 = 0.0743\), \(L_3 = 0\) and \(L_4 = -2.1665\). The Kaplan-Yorke dimension of the hyperchaotic two-disk dynamo system is derived as \(D_{KY} = 3.0769\), which shows the high complexity of the system. Next, an adaptive integral sliding mode control scheme is proposed to globally stabilize all the trajectories of the hyperchaotic two-disk dynamo system. Furthermore, an adaptive integral sliding mode control scheme is proposed for the global hyperchaos synchronization of identical hyperchaotic two-disk dynamo systems. The adaptive control mechanism helps the control design by estimating the unknown parameters. Numerical simulations using MATLAB are shown to illustrate all the main results derived in this work.