Design of novel adaptive sliding mode controller for perturbed Chameleon hidden chaotic flow

This article proposes a novel adaptive sliding mode control technique for the finite-time stabilization and transient performance improvement in perturbed Chameleon hidden chaotic flow. The Chameleon hidden chaotic flow is a unique and interesting simple chaotic flow which introduces three well-known families of hidden attractors plus self-excited attractors. In Chameleon chaotic system, based on the changes of constant parameters, the self-excited attractor and three types of hidden attractors (line of equilibria, no equilibrium, or one stable equilibrium point) can be existed. The global sliding surface provides the robust performance by the removal of the reaching phase, causes reduction in the control effort, and forms sliding around the surface right from the initial moment. The designed adaptation laws eliminate the requirement of knowledge for the bounds of disturbances and the nonlinear function ψ is employed in the sliding surface to improve the damping ratio of the system. Illustrative simulation results on perturbed Chameleon hidden chaotic flow with different values of the constant parameters, initial states and external disturbances are addressed to prove the efficiency of the proposed approach. Finally, inspired by the interest in the study of hyper-chaos, a novel Chameleon hyper-chaotic flow realized by the addition of a feedback law in the Chameleon chaotic system is presented.