A fractional sliding mode for finite-time control scheme with application to stabilization of electrostatic and electromechanical transducers

Abstract

Chaos suppression of non-autonomous uncertain chaotic systems is a very important and attractive topic in the field of physics and engineering. On the other hand, the use of fractional calculus in both research and practice has become as an increasing and interesting issue in recent years. In this paper, we introduce a novel fractional control method for chaos control of integer-order non-autonomous chaotic systems. It is assumed that the system is disturbed by some model uncertainties and external noises. A novel fractional nonsingular terminal sliding manifold which is appropriate for integer-order systems is proposed. Then, on the basis of fractional Lyapunov stability theorem, a suitable robust sliding mode control law is designed to force the state trajectories of the system into the sliding manifold. It is proved that both the sliding mode and reaching phase are realized in a given finite time. Finally, the proposed method is applied for stabilization of chaotic electrostatic and electromechanical transducers.