No Switching Policy Is Optimal for a Positive Linear System with a Bottleneck Entrance

Mahdiar Sadeghi, M. Ali Al-Radhawi*, Michael Margaliot, Eduardo D. Sontag

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a nonlinear SISO system that is a cascade of a scalar 'bottleneck entrance' and an arbitrary Hurwitz positive linear system. This system entrains, i.e., in response to a $T$-periodic inflow every solution converges to a unique $T$-periodic solution of the system. We study the problem of maximizing the averaged throughput via controlled switching. The objective is to choose a periodic inflow rate with a given mean value that maximizes the averaged outflow rate of the system. We compare two strategies: 1) switching between a high and low value and 2) using a constant inflow equal to the prescribed mean value. We show that no switching policy can outperform a constant inflow rate, though it can approach it asymptotically. We describe several potential applications of this problem in traffic systems, ribosome flow models, and scheduling at security checks.

Original languageEnglish
Article number8721170
Pages (from-to)889-894
Number of pages6
JournalIEEE Control Systems Letters
Volume3
Issue number4
DOIs
StatePublished - Oct 2019

Keywords

  • Entrainment
  • airport security
  • ribosome flow model
  • switched systems
  • traffic systems

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