Average flow constraints and stabilizability in uncertain production-distribution systems
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.
scientific article; zbMATH DE number 5677806
scientific article