Optimization of Long-Run Average-Flow Cost in Networks With Time-Varying Unknown Demand

Bauso, D., Blanchini, F. & Pesenti, R., Jan-2010, In : IEEE Transactions on Automatic Control. 55, 1, p. 20-31 12 p.

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We consider continuous-time robust network flows with capacity constraints and unknown but bounded time-varying demand. The problem of interest is to design a control strategy off-line with no knowledge of the demand realization. Such a control strategy regulates the flow on-line as a function of the realized demand.

We address both the case of systems without and with buffers. The main novelty in this work is that we consider a convex cost which is a function of the long-run average-flow and average-demand. We distinguish a worst-case scenario where the demand is the worst-one from a deterministic scenario where the demand has a neutral behavior. The resulting strategies are called min-max or deterministically optimal respectively. The main contribution are constructive methods to design either min-max or deterministically optimal strategies. We prove that while the min-max optimal strategy is memoryless, i.e., it is a piece-wise affine function of the current demand, deterministically optimal strategy must keep memory of the average flow up to the current time.

Original languageEnglish
Pages (from-to)20-31
Number of pages12
JournalIEEE Transactions on Automatic Control
Issue number1
Publication statusPublished - Jan-2010
Externally publishedYes


  • Average flow cost, flow control, gradient-based control, min-max optimality, uncertain demand, MULTI-INVENTORY SYSTEMS, ROBUST OPTIMIZATION, DESIGN, INPUTS

ID: 72168543