Global Chaos Control of a Novel Nine-Term Chaotic System via Sliding Mode Control

Abstract

Chaotic systems are nonlinear dynamical systems which are very sensitive to even small changes in the initial conditions. The control of chaotic systems is to design state feedback control laws that stabilize the chaotic systems around the unstable equilibrium points. This work derives a general result for the global chaos control of novel chaotic systems using sliding mode control. The main result has been proved using Lyapunov stability theory. Sliding mode control (SMC) is well-known as a robust approach and useful for controller design in systems with parameter uncertainties. Next, a novel nine-term 3-D chaotic system has been proposed in this paper and its properties have been detailed. The Lyapunov exponents of the novel chaotic system are found as \(L_1 = 6.8548, L_2 = 0\) and \(L_3 = -32.8779\) and the Lyapunov dimension of the novel chaotic system is found as \(D_L = 2.2085\). The maximal Lyapunov exponent of the novel chaotic system is \(L_1 = 6.8548\). As an application of the general result derived in this work, a sliding mode controller is derived for the global chaos control of the identical novel chaotic systems. MATLAB simulations have been provided to illustrate the qualitative properties of the novel 3-D chaotic system and the sliding controller results for the stabilizing control developed for the novel 3-D chaotic system.