PDα-型分数阶迭代学习控制在Lp范数意义下的收敛性分析

摘要

针对一类分数阶线性系统,讨论了PDα-型分数阶迭代学习控制算法的单调收敛性.首先,在Lebesgue-p(Lp)范数意义下,对一、二阶PDα-型控制算法的单调收敛性进行理论分析,推导出其单调收敛的充分条件,并推广到N阶控制算法的情形;然后,对二者的收敛快慢进行了详细说明.结论表明,控制算法的收敛条件由学习增益和系统自身属性共同决定.仿真实验验证了理论的正确性和控制算法的可行性.%The monotone convergence of PDα-type fractional-order iterative learning control is discussed for a class of fractional-order linear system.First,the convergences of first and second-order PDα-type control algorithms are analyzed and the sufficient conditions for the monotone convergence are deduced in the sense of Lebesgue-p (Lp) norm,and extended to the convergence condition of the N-order control algorithm.Then,the convergence speeds of both control algorithms are described in detail.The analysis indicates that the sufficient condition of the control algorithm is determined by the learning gains and the attributes of the system itself.The simulation experiment validates the correctness of the theory and the feasibility of this algorithm.