Modelling and finite time stability analysis of psoriasis pathogenesis
Goodfellow, M; Oza, HB; Pandey, R; et al.Roper, D; Al-Nuaimi, Y; Spurgeon, SK
Date: 9 August 2016
Journal
International Journal of Control
Publisher
Taylor & Francis
Publisher DOI
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 ...
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
has 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.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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