Stabilization of a class of fractional-order chaotic systems using a non-smooth control methodology

This paper is devoted to demonstrate how a class of fractional-order chaotic systems can be controlled in a given finite time using just a single control input. First a novel fractional switching sliding surface is proposed with desired properties such as fast convergence to zero equilibrium and no steady state errors. At the second phase, a smooth reaching control law is derived to guarantee the occurrence of the sliding motion with a finite settling time. Owing to the integration of the control signal discontinuity, chattering oscillations are hindered from the controller. Rigorous stability analysis is performed to validate the design claims. The effects of high frequency external noises as well as modeling errors and dynamic variations are also taken into account, and the robustness of the closed-loop system is ensured. The proposed robust controller is realized for a class of chaotic fractional-order systems with one control input. In accordance, some remarks regarding the inclusion of mismatched uncertainties in the system dynamics are given. The robust functionality and quick convergence property as well as chatter-free attribute of the introduced non-smooth sliding mode technology are demonstrated using oscillation suppression of fractional-order chaotic Lorenz and financial systems.