Learning-Ability of Discrete-Time Iterative Learning Control Systems with Feedforward
Jian Liu, Xiaoe Ruan, Yuanshi Zheng, Yingmin Yi, Congsi Wang
Abstract
.This paper considers the learning-ability for discrete-time iterative learning control (ILC) systems with feedforward. More specifically, the relation between the output realizability and the feedforward matrix is first established. Then, the learning-ability of four ILC systems is considered. It is shown that the proportional type (P-type) update law can only ensure the fully asymptotic learning-ability. By only using the feedforward matrix, a more efficient point-wise P-type update law is developed, which can ensure the fully \((T+2)\)-step learning-ability, where \(T\) is the trial length. In the case that the state is measurable and controllable, it is proven that the update law with current state feedback can ensure the fully monotone learning-ability and the fully 2-step learning-ability, respectively. In addition, by only using the output data at the previous trial, a full output feedback update law is proposed, which can respectively ensure the fully 2-step learning-ability and the fully monotonic learning-ability.Keywordsiterative learning controloutput realizabilitydiscrete-time systemslearning-abilityconvergence performanceMSC codes93C5593B5093B52