反馈辅助学习算法在Lebesgue-p范数意义下的单调收敛性
Monotonic convergence of feedback-aided iterative learning control algorithms in the sense of Lebesgue-p norm

针对一类线性时不变系统, 讨论存在固定初始偏移时的学习控制问题, 提出带有反馈辅助项的比例微分 (proportion differentiation, PD)型学习控制算法, 分析所提算法在Lebesgue-p范数意义下的单调收敛性, 获得对期望 轨迹的渐近跟踪结果. 进一步地, 为获得系统输出对期望轨迹的完全跟踪, 给出带有初始修正策略的比例–积分–微 分(proportion multiple integration differentiation, PMID)型学习律, 并给出了所提学习算法的单调收敛性能分析结果. 最后, 通过数值结果, 验证了所提学习算法的跟踪性能和单调收敛性能.
Feedback-aided proportion differentiation (PD)-type iterative learning control is proposed for a class of linear time invariant systems in the presence of a fixed initial shift. Based on Lebesgue-p norm, the monotonic convergence analysis result is obtained, and the output trajectory asymptotically convergence to the desired one. Furthermore, a kind of PID-–proportion multiple integration differentiation (PMID)-type learning algorithm with initial rectifying strategy is addressed to realize completely tracking result, and the monotonic convergence analysis processes are stated. Finally, numerical results are presented to demonstrate the tracking performance and the monotonic convergence property of the proposed learning algorithms.