Control of non‐integer‐order dynamical systems using sliding mode scheme

This article deals with the problem of control of canonical non‐integer‐order dynamical systems. We design a simple dynamical fractional‐order integral sliding manifold with desired stability and convergence properties. The main feature of the proposed dynamical sliding surface is transferring the sign function in the control input to the first derivative of the control signal. Therefore, the resulted control input is smooth and without any discontinuity. So, the harmful chattering, which is an inherent characteristic of the traditional sliding modes, is avoided. We use the fractional Lyapunov stability theory to derive a sliding control law to force the system trajectories to reach the sliding manifold and remain on it forever. A nonsmooth positive definite function is applied to prove the existence of the sliding motion in a given finite time. Some computer simulations are presented to show the efficient performance of the proposed chattering‐free fractional‐order sliding mode controller. © 2015 Wiley Periodicals, Inc. Complexity 21: 224–233, 2016