#### Degree Type

Dissertation

#### Date of Award

1994

#### Degree Name

Doctor of Philosophy

#### Department

Statistics

#### First Advisor

Stephen B. Vardeman

#### Second Advisor

Herbert T. David

#### Abstract

Sampling and adjustment strategies for a standard optimal control problem incorporating a non-random drift per time period are considered;The cost associated with an l-period problem in which a fixed nonzero, potentially non-integer sample size is used at each time period and the adjustment made at each time period is the sum of a fixed proportion, [alpha], 0 < [alpha] ≤ 1, of the perceived deviation from target and a fixed proportion, [beta], 0 < [beta] ≤ 1, of the non-random drift is derived. The optimal sample size to use in the "infinite horizon" case is defined to be the sample size which minimizes the limiting average cost function. The optimal adjustment strategy is defined similarly in terms of the values of [alpha] and [beta] which minimize this function;Dynamic programming is used to determine the potentially non-integer sample sizes and adjustments which will minimize the cost function associated with the l-period problem. The limiting behavior of these sample sizes and adjustments is used to define the optimal sampling and adjustment strategies for the "infinite horizon" case;The penalty associated with a restriction to integer sample sizes is discussed, and alternative sampling strategies using integer sample sizes are proposed for several cases where the penalty is high.

#### Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

#### Copyright Owner

Gerri M. Dunnigan

#### Copyright Date

1994

#### Language

en

#### Proquest ID

AAI9503548

#### File Format

application/pdf

#### File Size

84 pages

#### Recommended Citation

Dunnigan, Gerri M., "Sampling strategies for an optimal control problem " (1994). *Retrospective Theses and Dissertations*. 10695.

https://lib.dr.iastate.edu/rtd/10695