物理学报Issue(7)：1-10,10.DOI:10.7498/aps.64.070503
带有未知非对称控制增益的不确定分数阶混沌系统自适应模糊同步控制
Adaptive fuzzy synchronization for uncertain fractional-order chaotic systems with unknown non-symmetrical control gain
摘要
Abstract
In this paper the synchronization problem for the uncertain fractional-order chaotic systems with unknown non-symmetrical control gain matrices is investigated by means of adaptive fuzzy control. Fuzzy logic systems are employed to approximate the unknown nonlinear functions. We decompose the control gain matrix into a positive definite matrix, a unity upper triangular matrix, and a diagonal matrix with diagonal entries +1 or −1. The positive matrix is used to construct the Lyapunov function;the diagonal matrix is employed to design the controller. Based on the fractional Lya-punov stability theorem, an adaptive fuzzy controller, which is accompanied by fractional adaptation laws, is established. The proposed methods can guarantee the boundedness of the involved signals as well as the asymptotical convergence of the synchronization errors. It should be pointed out that the methods for using quadratic Lyapunov function in the stability analysis of the fractional-order chaotic systems are developed in this paper. Based on the results of this paper, many control methods which are valid for integer-order nonlinear systems can be extended to control fractional-order nonlinear systems. Finally, the effectiveness of the proposed methods is shown by simulation studies.关键词
分数阶混沌系统/自适应模糊控制/分数阶自适应律Key words
fractional chaotic system/adaptive fuzzy control/fractional adaptation law引用本文复制引用
刘恒,李生刚,孙业国,王宏兴..带有未知非对称控制增益的不确定分数阶混沌系统自适应模糊同步控制[J].物理学报,2015,(7):1-10,10.基金项目
国家自然科学基金(批准号:11401243,61403157)和中央高校基本科研业务费专项资金(批准号：GK201504002)资助的课题 （批准号:11401243,61403157）
