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

作　　者：刘恒[1,2] 李生刚[1] 孙业国[2] 王宏兴[2] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710119 [2]淮南师范学院数学与计算科学系,淮南232038

出　　处：《物理学报》2015年第7期120-128,共9页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11401243;61403157);中央高校基本科研业务费专项资金(批准号:GK201504002)资助的课题~~

摘　　要：针对带有非对称控制增益的不确定分数阶混沌系统的同步问题设计了模糊自适应控制器.模糊逻辑系统用来逼近未知的非线性函数,非对称的控制增益矩阵被分解为一个未知的正定矩阵、一个对角线上元素为+1或-1的已知对角矩阵和一个未知的上三角矩阵的乘积.基于分数阶Lyapunov稳定性理论构造了模糊控制器以及分数阶的参数自适应律,在保证所有变量有界的情况下实现驱动系统和响应系统的同步.在分数阶系统稳定性分析中给出了一种平方Lyapunov函数的使用方法,根据此方法很多针对整数阶系统的控制方法可以推广到分数阶系统中.最后数值仿真结果验证了所提控制方法的可行性.In this paper the synchronization problem for the uncertain fractional-order chaotic systems with unknown nonsymmetrical 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 Lyapunov 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 

分 类 号：O159[理学—数学] O231[理学—基础数学]