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Modelling and finite-time stability analysis of psoriasis pathogenesis

Oza, HB; Pandey, R; Roper, D; Al-Nuaimi, Y; Spurgeon, SK; Goodfellow, M; (2016) Modelling and finite-time stability analysis of psoriasis pathogenesis. International Journal of Control , 90 (8) pp. 1664-1677. 10.1080/00207179.2016.1217566. Green open access

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Abstract

A new systems model of psoriasis is presented and analysed from the perspective of control theory. Cytokines are treated as actuators to the plant model that govern the cell population under the reasonable assumption that cytokine dynamics are faster than the cell population dynamics. The analysis of various equilibria is undertaken based on singular perturbation theory. Finite-time stability and stabilisation have been studied in various engineering applications where the principal paradigm uses non-Lipschitz functions of the states. A comprehensive study of the finite-time stability properties of the proposed psoriasis dynamics is carried out. It is demonstrated that the dynamics are finite-time convergent to certain equilibrium points rather than asymptotically or exponentially convergent. This feature of finite-time convergence motivates the development of a modified version of the Michaelis–Menten function, frequently used in biology. This framework is used to model cytokines as fast finite-time actuators.

Type: Article
Title: Modelling and finite-time stability analysis of psoriasis pathogenesis
Open access status: An open access version is available from UCL Discovery
DOI: 10.1080/00207179.2016.1217566
Publisher version: http://dx.doi.org/10.1080/00207179.2016.1217566
Language: English
Additional information: Copyright © 2016 Informa UK Limited, trading as Taylor & Francis Group. This is an Accepted Manuscript of an article published by Taylor & Francis in the International Journal of Control on 8 September 2016, available online: http://www.tandfonline.com/doi/full/10.1080/00207179.2016.1217566
Keywords: Biological modelling, psoriasis, finite-time stability, singular perturbation analysis
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Electronic and Electrical Eng
URI: https://discovery.ucl.ac.uk/id/eprint/1514540
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