Model-based robust chaotification using sliding mode control

Abstract

Chaos is a complex behavior of dynamical nonlinear systems that is undesirable in most applications and should be controlled; however, it is desirable in some situations and should be generated. In this paper, a robust chaotification scheme based on sliding mode control is proposed for model based chaotification. A continuous time single input observable system is considered such that it is subject to parameter uncertainties, nonlinearities, noises, and disturbances, which are all additive to the input and can be modeled as an unknown function but bounded by a known function. The designed dynamical state feedback control law forces the system to match a reference chaotic system in finite time irrespective of the mentioned uncertainties, noises, and disturbances, as provided by the developed sliding mode control scheme. Simulation results are provided to illustrate the robustness of the proposed scheme against parameter uncertainties and noises. The results are compared with those of other model-based methods and Lyapunov exponents are calculated to show whether the closed-loop control systems exhibit chaotic behavior or not.