Control of non-linear non-integer-order systems using variable structure control theory

Abstract

This paper deals with the problem of robust control of uncertain non-integer-order non-linear complex systems in finite time. First, a novel fractional-order integral-type switching manifold is introduced. Then, the fractional-order stability theory is used to prove the finite time stability of the resulting sliding mode dynamics in a given finite time. Afterward, using the variable structure control theory, a novel robust non-integer control law is proposed to guarantee the convergence of the system trajectories to the prescribed sliding manifold within a given finite time. Simulation results reveal that the proposed fractional variable structure controller works well for finite-time chaos suppression of fractional-order hyperchaotic Chen and chaotic Lorenz systems with system uncertainties.