@article{994aba5768a242e9af2b7dfb2c1c2ed1,
title = "No Switching Policy Is Optimal for a Positive Linear System with a Bottleneck Entrance",
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.",
keywords = "Entrainment, airport security, ribosome flow model, switched systems, traffic systems",
author = "Mahdiar Sadeghi and {Ali Al-Radhawi}, M. and Michael Margaliot and Sontag, {Eduardo D.}",
note = "Publisher Copyright: {\textcopyright} 2017 IEEE.",
year = "2019",
month = oct,
doi = "10.1109/LCSYS.2019.2918757",
language = "אנגלית",
volume = "3",
pages = "889--894",
journal = "IEEE Control Systems Letters",
issn = "2475-1456",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "4",
}