分数阶Brussel系统混沌同步的三种控制方案

基于分数阶微积分理论,提出三种同步控制方案使分数阶Brussel系统的误差系统收敛到平衡点。第一种控制方案通过设计适当的控制器,利用Mittag-Leffler函数得到误差系统的收敛性。第二种控制方案引入了分数阶的滑模面,利用分数阶Lyapunov 稳定性理论和滑模控制方法,得到分数阶Brussel主从系统的混沌同步。第三种控制方案充分考虑系统的不确定性和外部扰动,设计一个新型趋近律,利用分数阶终端滑模控制方法使误差系统快速收敛到平衡点。研究表明,选取适当的控制器,分数阶主从Brussel系统可以达到混沌同步。通过数值算例说明所提出的三种控制策略的有效性和适用性,并验证了本研究的理论结果。

Three control schemes of chaos synchronization for fractional-order Brussel system

Based on the fractional calculus theory, three synchronous control schemes were proposed to make the error system of the fractional Brussel system converge the error system states to the equilibrium point. An appropriate controller was designed in the first control scheme and the convergence of the error system was obtained by using Mittag-Leffler function. In the second control scheme, the fractional sliding mode surface was introduced, and the chaos synchronization of the fractional order Brussel master-slave systems was achieved based on the fractional version of the Lyapunov stability and the sliding mode control method. The effects of model uncertainties and external disturbances were fully taken into account in the third control scheme. A new sliding mode reaching law was designed and the fast convergence of the error system to the equilibrium point was obtained based on fractional order terminal sliding mode control. It was proved that master-slave systems were chaos synchronization under proper controllers. Numerical simulations were presented to illustrate the effectiveness and applicability of the proposed schemes and to validate the theoretical results of the paper.