No-chatter variable structure control for fractional nonlinear complex systems

This paper concerns the problem of robust control of uncertain fractional-order nonlinear complex systems. After establishing a simple linear sliding surface, the sliding mode theory is used to derive a novel robust fractional control law for ensuring the existence of the sliding motion in finite time. We use a nonsmooth positive definitive function to prove the stability of the controlled system based on the fractional version of the Lyapunov stability theorem. In order to avoid the chattering, which is inherent in conventional sliding mode controllers, we transfer the sign function of the control input into the first derivative of the control signal. The proposed sliding mode approach is also applied for control of a class of nonlinear fractional-order systems via a single control input. Simulation results indicate that the proposed fractional variable structure controller works well for stabilization of hyperchaotic and chaotic complex fractional-order nonlinear systems. Moreover, it is revealed that the control inputs are free of chattering and practical.