Backstepping and Sliding Mode Control of a Fractional-Order Chaotic System

Abstract

AbstractFractional-order systems can come across in chemical processes, biological systems, viscoelastic systems, propagation of electromagnetic waves and electrochemical systems. In the literature, fractional systems are encountered in the modelling and controlling of such systems, synchronization applications, communication, modelling and controlling of power systems or chemical processes. Many methods such as PID, sliding mode control, backstepping control¸ fuzzy sliding mode control, model predictive control, reinforcement learning and adaptive sliding mode control, have been used in the control of such systems. In this study, a fractional-order chaotic system is proposed. For this fractional-order chaotic system, bifurcation, phase portraits and Lyapunov exponents have been calculated to investigate its chaotic status. Then, in order to control the chaotic system, mathematically backstepping and sliding mode method control laws are obtained and their applications are realised. Consequently, their system responses by means of backstepping and sliding mode control results are discussed and compared with each other. Nevertheless, both controllers successfully are be able to regulate the system by obtained control laws, even if the system is out of the chaotic situation for specified fractional-order.