On the uncertainties of decentralized controllers in a transfer production line

In this paper, an information theoretic approach is applied to analyze the performance of a decentralized control system. The control system plays the role of a correcting device which decreases the uncertainties associated with state variables of a production line by applying an appropriate ‘correcting signal’ for each deviation from the target. In particular, a distributed feedback control policy is considered to govern a transfer production line, which consists of machines and buffers and processes a single part type in response to a stochastic demand. It is shown how the uncertainty of the demand propagates dynamically into the production system, causing uncertainties associated with buffer levels and machine production rates. The paper proposes upper estimates for these uncertainties as functions of the demand variance, parameters of the distributed controllers and some physical properties of the production line. The bounds are based on dynamic entropy measures of the system state and the control variables. Some practical implications into the area of decentralized controller design are proposed, an information-economical analysis is presented and a numerical study is performed.