Modelling and finite-time stability analysis of psoriasis pathogenesis
Modelling and finite-time stability analysis of psoriasis pathogenesis
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DOI：
10.1080/00207179.2016.1217566
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发表时间：
2017-01-01
影响因子：
2.1
通讯作者：
Goodfellow, Marc
中科院分区：
文献类型：
--
作者：
Oza, Harshal B.;Pandey, Rakesh;Goodfellow, Marc
从控制理论的角度提出并分析了一种新的银屑病系统模型。细胞因子被视为植物模型的执行器，在细胞因子动力学比细胞群动力学更快的合理假设下控制细胞群。各种平衡的分析是基于奇异微扰理论进行的。有限时间稳定性和稳定性已在各种工程应用中进行了研究，其中主要范式使用状态的非 Lipschitz 函数。对所提出的银屑病动力学的有限时间稳定性特性进行了全面研究。证明了动力学是有限时间收敛到某些平衡点的，而不是渐近或指数收敛的。有限时间收敛的这一特征激发了生物学中常用的 Michaelis-Menten 函数的修改版本的开发。该框架用于将细胞因子建模为快速有限时间执行器。
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.