A Multivariate Adaptive Control Model

by John D.C. Little

Excerpt from A Multivariate Adaptive Control Model
A specialized multivariate adaptive control model is developed. Each of r control variables is to be set in each of a sequence of time periods. The process being controlled has a response (profit) function that is the sum of a constant plus linear and quadratic forms in the control variables. The coefficients of the quadratic form are assumed to be known constants, those of the linear form to change with time as first order, autoregressive processes. Information about the changing coefficients is collected by performing a 2r factorial experiment on a subportion of the process being controlled. Provision is also made for adding further information from unspecified sources. Bayesian methods are used to update distributions of the unknown coefficients. The values of the control variables are set to maximize the sum of discounted future profits, as arc the experimental design parameters. The probabilistic assumptions of the model are chosen so that all distributions are normal with known variances and, for the most part, zero covariances between variables. Partly as a result of this, optimal control turns out to involve rather simple exponential smoothing rules.

59 pages, Paperback

First published August 5, 2015

About the author

John Dutton Conant Little was an Institute Professor at the Massachusetts Institute of Technology best known for his result in operations research, Little's law.