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

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(p,d,q) 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 (PI) controller is evaluated and compared under multiple scenarios through Monte Carlo simulations. Almost all the results reflect the new controller’s superiority.