控制方向未知分数阶混沌系统的 Nussbaum增益同步 吴梅 1,程继红2,余名哲 4,张友安3

Nussbaum Gain Synchronization for Fractional-Order Chaotic Systemswith Unknown Control Direction

摘要:

文章将 Nussbaum增益控制引入分数阶混沌系统,解决了分数阶混沌系统在存在控制方向未知情况下的同步控制问题。首先,选取了一类稳定的分数阶积分滑模面。然后,结合整数阶 Nussbaum增益控制方法与滑模变结构控制理论,设计了一种 Nussbaum增益同步控制器。最后,作为例子,实现了分数阶 Chen系统和分数阶 R.ssler系统在控制系数未知时的混沌同步控制,数值仿真验证了文中方法的正确性和有效性。

Abstract:

The Nussbaum gain control method was introduced to solve the synchronization control problem for fractionalorder chaotic systems with unknown control direction. Firstly, a fractional-order sliding motion was selected. Then, a Nuss baum gain controller was designed by combining the Nussbaum gain control method for integer-order systems and sliding mode variable structure control theory. Finally, an example was given, which realized the synchronization control between fractional-order Chen systems and fractional-order R?ssler systems with unknown control direction. Simulation results demonstrated the correctness and effectiveness of the presented method.