分数阶线性时滞切换系统PDα型迭代学习控制  

PD-type Iterative Learning Control for a Class of Fractional-order Linear Switched Systems with Time-delay

作　　者：张克军[1,2] 彭国华[2] ZHANG Ke-jun;PENG Guo-hua(School of Mathematics and Statistics,Xuzhou University of Technology,Xuzhou 221018,China;School of Mathematics and Statistics,Northwestern Polytechnical University,Xi'an 710129,China)

机构地区：[1]徐州工程学院数学与统计学院,江苏徐州221018 [2]西北工业大学数学与统计学院,陕西西安710129

出　　处：《控制工程》2021年第6期1179-1186,共8页Control Engineering of China

基　　金：国家自然科学基金青年项目(61201323);徐州市科技项目(KC18013)。

摘　　要：针对一类具有任意切换规则的分数阶线性时滞切换系统,利用λ范数研究了PDα型分数阶迭代学习控制算法(FOILC)的收敛性,分析了在其控制下系统的跟踪性能,并对算法收敛的充分条件进行了严格的数学证明。理论分析表明,对于有限时间域内可任意切换的分数阶线性时滞切换系统,如果选取适当的学习增益矩阵和系统参数矩阵,随着迭代次数的增加,利用该算法可以实现切换系统的实际输出对期望输出的完全跟踪。数值仿真进一步验证了该算法的可行性和有效性。For a class of fractional-order linear time-delay switched systems with an arbitrary switching rule, the convergence of PDα-type fractional-order iterative learning control(FOILC) algorithm is firstly discussed by taking advantage of λ norm, the tracking performance of the systems under its control is analyzed, and the sufficient condition for the convergence of the algorithm is deduced. The theoretical analysis manifests that, for fractional-order linear time-delay switched systems with an arbitrary switching rule in finite time domain, if proper learning gains and systems matrices are given, the algorithm can realize the complete tracking of the desired output for the actual output of the systems as the iteration number increases. The succedent simulations support the feasibility and effectiveness of the proposed algorithm.

关 键 词：迭代学习控制 分数阶 切换系统 收敛性 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]