Optimal Control for Linear System with Colored Noise and Its Application to Periodical Ordering System

Abstract

The objective of this paper is to formulate the optimal control system for the linear system with colored noise and to apply to the periodical ordering system for the push-type production and inventory systems, which provides the possible procedure to control both the variances of order quantity and inventory. This system realizes the optimization of the criterion of the weighted sum of the variances of production and inventory. For the extension to the solution of multi-stage process and of the case the demand is not stationary, it is necessary to formulate the control system by the optimal control theory. However, the optimal regulator control which is the conventional optimal control theory can be applied directly to the system with colored noise. In this paper, we propose the new formulation of this problem and the application to the production and inventory control system.