A Technical Note on “Sample Size Determination for Achieving Stability of Double Multivariate Exponentially Weighted Moving Average Controller”

Abstract

Recently, Tseng, Tang, and Lin (2007) presented an explicit formula for determining a minimum sample size (which is needed to construct the input–output predicted model) in such a way that the asymptotic stability of double multivariate exponentially weighted moving average (dMEWMA) controller can be achieved with a guaranteed probability. This formula indicates that two key components on the sample size determination are: the canonical correlation of input–output (I–O) variables and the condition number of the covariance matrix of input variables. Since this condition number is a nuisance parameter, the problem on how to minimize its effect on the sample size determination is of great practical importance. This note proposes a stable dMEWMA controller with which the sample size (required at the off-line stage) only depends on the canonical correlation of I–O variables. Hence, the sample size can be reduced significantly.

Keywords:  :

• Drifted MIMO systems
• Double multivariate EWMA (dMEWMA) controller
• Sample size determination