Average flow constraints and stabilizability in uncertain production-distribution systems
type: Item
instance of: scholarly article
title: Average flow constraints and stabilizability in uncertain production-distribution systems
zbMATH Open document ID: 1185.90006
author: Dario Bauso
author: Raffaele Pesenti
author: Franco Blanchini
published in: Journal of Optimization Theory and Applications
publication date: 2010-03-05T00:00:00Z
full work available at URL: JOTA-afcwcs-accepted.pdf
review text: This paper considers a continuous time multi-inventory system with controlled flows and uncertain demands. Flows and demands are bounded within assigned polytopic sets. The authors focus on stabilizing control strategies meeting alternatively one of the two following requirements: Average Flow Constraints (AFS), where the control strategy must return an average control that balances the average disturbance, or Worst Case Stability (WCS), where the control strategy must drive the state to a hyperbox in finite time and keep the state within it for the rest of the time under any disturbance realization. Necessary and sufficient conditions for achieving both objectives have been presented by the same authors in a previous paper from 2006. In this new paper, only one of the two basic requirements is imposed. It is shown that, if WCS is relaxed, one can always define a control strategy that satisfies AFC and achieves stochastic stability provided that the demand and the buffer levels are not correlated and that there exists an average control internal to the bounding polytopic set that satisfy the average demand. Moreover, it is proven that, if AFC is relaxed, one can find a control strategy that satisfies WCS while optimizing a linear cost of the average control. A numerical example is presented to illustrate the proposed investigation method.
Mathematics Subject Classification ID: 90B05
Mathematics Subject Classification ID: 90B30
Mathematics Subject Classification ID: 90C31
zbMATH DE Number: 5677806
zbMATH Keywords: inventory control
zbMATH Keywords: stochastic stability
zbMATH Keywords: robust control
Wikidata QID: Q59341797
reviewed by: Frank Werner
MaRDI profile type: Publication
OpenAlex ID: W2065593498
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DOI: 10.1007/S10957-009-9593-5
description: scientific article; zbMATH DE number 5677806