Finite-Horizon Tracking Control for Repetitive Systems with Uncertain Initial Conditions

Authors: Sung Wook Yun, Yun Jong Choi, Kyong-min Lee, Poogyeon Park*

Abstract:

Repetitive systems stand for a kind of systems that perform a simple task on a fixed pattern repetitively, which are widely spread in industrial fields. Hence, many researchers have been interested in those systems, especially in the field of iterative learning control (ILC). In this paper, we propose a finite-horizon tracking control scheme for linear time-varying repetitive systems with uncertain initial conditions. The scheme is derived both analytically and numerically for state-feedback systems and only numerically for output-feedback systems. Then, it is extended to stable systems with input constraints. All numerical schemes are developed in the forms of linear matrix inequalities (LMIs). A distinguished feature of the proposed scheme from the existing iterative learning control is that the scheme guarantees the tracking performance exactly even under uncertain initial conditions. The simulation results demonstrate the good performance of the proposed scheme.

Keywords: Finite time horizon, linear matrix inequality (LMI), repetitive system, uncertain initial condition.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1327845

References:

[1] Tae-Jeong Chang, Chong-Ho Choi, Hyun-Sik Ahn, "Iterative Learning Control in Feedback Systems", Automatica, Vol. 31, No. 2, 1995.
[2] Tommy W. S. Chow, Yong Fang, "An Interative Learning Control Method for Continuous-Time Systems Based on 2-D System Theory", IEEE Trans. on Autom. Cont., Vol. 45, No. 4, 1998
[3] Yong Fang, Tommy W. S. Chow, "Iterative Learning Control of Linear Discrete-Time Multivariable Systems", Automatica, Vol. 34, No. 11, 1998.
[4] Yong Fang, Tommy W. S. Chow, "2-D Analysis for Iterative Learning Controller for Discrete-Time Systems With Variable Initial Conditions", IEEE Trans. on Circuits Syst. I: Fundamental Theory and Applica.t., Vol. 50, No. 5, pp. 722-727, 2003.
[5] Jerzy E. Kurek, Marek B. Zaremba, "Iterative Learning Control Synthesis Based on 2-D System Theory", IEEE Trans. on Autom. Cont., Vol. 38, No. 1, 1993.
[6] Samer S. Saab, "A Discrete-Time Learning Control Algorithm for a Class of Linear Time-Invariant Systems", IEEE Trans. on Atuom. Cont., Vol. 40, No. 6, 2002.
[7] Luis G. Sison, Edwin K. P. Chong, "Design of Repetitive Learning Control.", Proceedings of the 36th Conference on Decision & Control, San Diego, California, USA, 1997.