Adaptive track control for fractional-order chaotic systems with or without uncertainty

Abstract

This paper focuses on an important issue in the research of fractional-order system, i.e., chaos control. Unlike previous study on chaos control for fractional-order systems, for which the control target is inherently unstable equilibrium point. In our work, any desired state embedded in the chaotic attractor is the control target. For deterministic fractional-order chaotic system, a simple and general controller is designed to achieve track control. For fractional-order chaotic system with uncertain parameter and external perturbation, a novel adaptive control technique is presented to achieve tracking control. Furthermore, the new control method is extended to track the desired bounded trajectories. All the above methods have been proved rigorously according to the stability theory of fractional-order system. Numerical simulation results for fractional-order unified chaotic system are also provided to illustrate the effectiveness of proposed schemes.