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Robust and Structural Ergodicity Analysis and Antithetic Integral Control of a Class of Stochastic Reaction Networks

View ORCID ProfileCorentin Briat, View ORCID ProfileMustafa Khammash
doi: https://doi.org/10.1101/481051
Corentin Briat
D-BSSE, ETH-Zürich, Switzerland
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Mustafa Khammash
D-BSSE, ETH-Zürich, Switzerland
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Abstract

Controlling stochastic reactions networks is a challenging problem with important implications in various fields such as systems and synthetic biology. Various regulation motifs have been discovered or posited over the recent years, a very recent one being the so-called Antithetic Integral Control (AIC) motif [3]. Several appealing properties for the AIC motif have been demonstrated for classes of reaction networks that satisfy certain irreducibility, ergodicity and output controllability conditions. Here we address the problem of verifying these conditions for large sets of reaction networks with time-invariant topologies, either from a robust or a structural viewpoint, using three different approaches. The first one adopts a robust viewpoint and relies on the notion of interval matrices. The second one adopts a structural viewpoint and is based on sign properties of matrices. The last one is a direct approach where the parameter dependence is exactly taken into account and can be used to obtain both robust and structural conditions. The obtained results lie in the same spirit as those obtained in [3] where properties of reaction networks are independently characterized in terms of control theoretic concepts, linear programs, and graph-theoretic/algebraic conditions. Alternatively, those conditions can be cast as convex optimization problems that can be checked efficiently using modern optimization methods. Several examples are given for illustration.

Footnotes

  • * This paper is the combined version of the following conference papers [1, 2]. Some results are new and complete proofs are now given.

  • ↵† email: corentin{at}briat.info, mustafa.khammash{at}bsse.ethz.ch; url: www.briat.info, https://www.bsse.ethz.ch/ctsb.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
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Posted December 08, 2018.
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Robust and Structural Ergodicity Analysis and Antithetic Integral Control of a Class of Stochastic Reaction Networks
Corentin Briat, Mustafa Khammash
bioRxiv 481051; doi: https://doi.org/10.1101/481051
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Robust and Structural Ergodicity Analysis and Antithetic Integral Control of a Class of Stochastic Reaction Networks
Corentin Briat, Mustafa Khammash
bioRxiv 481051; doi: https://doi.org/10.1101/481051

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