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Mathematical Problems in Engineering
Volume 2015, Article ID 808903, 10 pages
http://dx.doi.org/10.1155/2015/808903
Research Article

Optimal Control for a Linear System Subject to a General ARIMA Disturbance

1School of Economics, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, China
2School of Finance, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, China

Received 28 November 2014; Revised 24 January 2015; Accepted 16 February 2015

Academic Editor: Alain Vande Wouwer

Copyright © 2015 Hongyan Xie and Fangyi He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A novel run-to-run (R2R) control algorithm based on Kalman filter approach is proposed to deal with a linear system with a general ARIMA() process, in the presence of measurement error and adjustment error together with a random initial bias. We mathematically prove its optimality. The performance of the newly proposed controller and the proportional-integral () controller is evaluated and compared under multiple scenarios through Monte Carlo simulations. Almost all the results reflect the new controller’s superiority.