An optimal control algorithm based on Kalman filter for ARMA disturbances

Harmonic rule is popularly used in machine setup adjustment problems introduced by Grubbs (1954). The algorithm is optimal when the disturbance process is white noise and the initial process bias is an unknown value. When the initial process bias is assumed to be a random variable with a priori distribution, Grubbs' extended rule is optimal when the disturbance process is white noise. This paper considers the case that the initial process bias is a random variable and the disturbance process is a general ARMA(p, q) process. Under the framework of state-space model and based on Bayesian rule, an optimal control algorithm is derived. Several illustrative numerical examples are given through Monte Carlo simulations.