Sliding mode control based generalized technique for synchronization of identical and non-identical chaotic systems in presence of input nonlinearities

Abstract

Systems with chaotic underlying structures exhibit a high sensitivity to both initial conditions and parameter values, leading to dynamic behaviors that are challenging to predict and analyze. This paper investigates a direct way to address synchronization issues in master-slave setups, with a special emphasis on chaotic or hyperchaotic systems. The approach takes into account the effects of input nonlinearities in order to successfully address the synchronization problem. A synchronization controller which takes into account input nonlinearities is formulated by employing the sliding mode control approach. The paper introduces a generalized approach for synchronizing chaotic systems, applicable to both identical and non-identical systems, even in the presence of input nonlinearities. The Lyapunov stability principle is used to develop a nonlinear controller and to define general adequate conditions that guarantee synchronization even when input nonlinearities are present. The paper includes a detailed analysis of the systems’ dynamic behaviors, supported by Lyapunov and bifurcation diagrams. Furthermore, numerical simulations are included to confirm and reinforce the theoretical conclusions presented in the paper.