Current Iteration Tracking Error Assisted High - orderIterative Learning Control of Discrete - time

A P-type iterative learning controller (ILC) which includes a current iteration tracking error (CITE) in its high-order updating law is proposed for the tracking control of repetitive uncertain discrete-time non-linear systems. It is shown that, under relaxed conditions , the tracking error bounds are class-K functions of the bounds of uncertainty, disturbance and the ini-tialization error. The tracking error bound and the ILC convergence rate are tunable by the CITE learning gain. Moreover, the tracking error bound is shown to be a class-K function of the bounds of the diier-ences of initialization errors, uncertainties, and disturbances between two successive ILC repetitions. The eeectiveness of the proposed ILC scheme is illustrated by simulation results of a single-link manipulator. 1. Motivations Iterative Learning Control (ILC) 1] is a simple algorithm to improve the system performance iteratively when the system performs a given task repeatedly. For implementation of ILC algorithms, a discrete-time form of the algorithm as well as the theoretical analysis are more important. The existing robust ILC convergence analysis for continuous and discrete time uncertain systems only show the boundedness of the nal tracking errors with the bounded uncertainty, disturbance and initialization error 2, 3, 4]. Nevertheless, how to adjust the tracking error bound is more interesting. An easy way is to include the current iteration tracking error (CITE) in the ILC updating law. This was discussed under the feedback connguration 4] but the tuning of the tracking error bound was not discussed. For continuous-time nonlinear system, the ILC using CITE was shown that the tracking error bound and the ILC convergence rate can be tuned by the learning gain of CITE 5]. A discrete-time case was considered in 6] for the rst-order ILC updating law. However, it is observed that a high-order ILC scheme is essentially a PI or a PID controller in the iteration number i-axis while the conventional rst-order scheme is only a pure integrator. Following 6], in this paper, a high-order ILC scheme assisted by CITE is addressed. This provides the capacity for (i) improving ILC performance along i-axis; (ii) tuning of convergence rate and (iii) adjusting the tracking error bound. Some simulation results are presented to illustrate the eeectiveness of the proposed scheme. 2. Problem Settings Consider a class of repetitive discrete-time uncertain nonlinear time-varying systems as follows: x i (t + 1) = f(x i (t); t) + B(x i (t); t)u i (t) + …