Feedback stabilization of positive nonlinear systems with applications to biological systems

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Abstract

Various feedback stabilizers based on Sontag's 'universal' formula for stabilizing control laws are presented, incorporating restrictions inspired by models from systems biology. The main contribution is an extension of Sontag's 'universal' formula for positive nonlinear control systems. More specifically, an auxiliary function is introduced in the feedback interconnection, such that invariance of the positive orthant is retained for the system in closed loop with the 'universal' stabilizer. We further state a 'universal' event-based stabilizer with bounded controls for positive systems. Two examples inspired by systems biology are presented for illustration and demonstration of the effectiveness of the proposed stabilizers. One example considers the problem of regulating the cortisol level, where the methodology is shown to provide clinically realistic control inputs, suitable for treatment in real life.

Original languageEnglish
Title of host publication2018 European Control Conference, ECC 2018
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages1619-1624
Number of pages6
ISBN (Electronic)9783952426982
DOIs
Publication statusPublished - 27 Nov 2018
Event16th European Control Conference, ECC 2018 - Limassol, Cyprus
Duration: 12 Jun 201815 Jun 2018

Conference

Conference16th European Control Conference, ECC 2018
CountryCyprus
CityLimassol
Period12/06/1815/06/18

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  • Cite this

    Steentjes, T. R. V., Doban, A. I., & Lazar, M. (2018). Feedback stabilization of positive nonlinear systems with applications to biological systems. In 2018 European Control Conference, ECC 2018 (pp. 1619-1624). [8550371] Piscataway: Institute of Electrical and Electronics Engineers. https://doi.org/10.23919/ECC.2018.8550371