PD^α-type iterative learning control with initial state learning for fractional-order systems

基于分数阶线性系统初态学习的PD^α-型迭代学习控制

¹ School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China
² College of Mathematics and Computer Science, Yan'an University, Yan'an 716000, China
³ School of Mathematics and Physical Sciences, Xuzhou Institute of Technology, Xuzhou 221111, China

Received: 28 April 2020

Abstract

In order to eliminate the influence of the arbitrary initial state on the systems, open-loop and open-close-loop PD^α-type fractional-order iterative learning control (FOILC) algorithms with initial state learning are proposed for a class of fractional-order linear continuous-time systems with an arbitrary initial state. In the sense of Lebesgue-p norm, the sufficient conditions for the convergence of PD^α-type algorithms are disturbed in the iteration domain by taking advantage of the generalized Young inequality of convolution integral. The results demonstrate that under these novel algorithms, the convergences of the tracking error are can be guaranteed. Numerical simulations support the effectiveness and correctness of the proposed algorithms.

摘要

为了消除任意初始状态对系统的影响，针对一类具有任意初始状态的分数阶线性连续系统，提出了一种具有初始状态学习的开环和开闭环PD^α-型分数阶迭代学习控制算法。在Lebesgue-p范数的意义下，利用卷积积分的广义Young不等式在迭代域中给出具有抗干扰的PD^α-型算法收敛的充分条件。实验结果表明，该算法能够保证跟踪误差的收敛性。数值仿真验证了所提算法的有效性和正确性。