Optimal control for a linear system subject to a general ARIMA disturbance (Q1666616)

Summary: A novel run-to-run (R2R) control algorithm based on Kalman filter approach is proposed to deal with a linear system with a general \(\mathrm{ARIMA}(p,d,q)\) 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.