2-D H∞ based iterative learning control design for linear discrete-time uncertain systems with multiple high order internal models

Abstract

In this work we focus on the iterative learning control (ILC) design problem for linear discrete-time uncertain systems with iteration-varying factors, including reference trajectories, initial states, and exogenous disturbances. First, multiple high-order internal models (HOIMs) are given for various iteration-varying factors. Second, a new ILC scheme is constructed according to an augmented HOIM that is the aggregation of all HOIMs. Third, the HOIM-based ILC is transformed into a controller design problem of 2-D Roesser model. Fourth, H∞ the performance of 2-D Roesser model is studied under a non-zero boundary condition. Then, a HOIM-based ILC design criterion is presented to achieve perfect tracking and 2-D H∞ tracking performance which yields a high-order ILC (HO-ILC). Utilizing information provided by multiple HOIMs, it is shown that HO-ILC laws outperform low-order ILC (LO-ILC) laws in presence of iteration-varying factors. In addition, a composite HOIM-based law is proposed to improve the initial phase tracking performance. Finally, a numerical example is given to illustrate the efficiency of the proposed HOIM-based ILC design method.