Suppressing chaos for a class of fractional-order chaotic systems by adaptive integer-order and fractional-order feedback control

This paper is devoted to studying how to more effectively suppress chaos for a class of fractional-order nonlinear systems. By means of adaptive control theory for integer-order nonlinear system, we propose two simple and novel adaptive feedback methods to control chaos. Rigorous theoretical proof is provided based on some essential properties of fractional calculus and Barbalat's Lyapunov-like stability theorem. It is discovered that both fractional-order feedback controller and integer-order one can guide chaotic trajectories to the unstable equilibrium point. To display the feasibility and validity of presented methods, some typical fractional-order chaotic systems have been chosen as numerical illustration. Furthermore, by comparing two different control techniques, one can find the fractional-order feedback control algorithm is more stable and more flexible.