Non-Lipschitz Growth Functions as a Natural Way of Modelling Finite Time Behaviour in Auto-immune Dynamics
Non-Lipschitz Growth Functions as a Natural Way of Modelling Finite Time Behaviour in Auto-immune Dynamics
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DOI：
10.3182/20140824-6-za-1003.01032
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Harshal B. Oza;S. Spurgeon;N. Valeyev
中科院分区：
文献类型：
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作者：
Harshal B. Oza;S. Spurgeon;N. Valeyev
摘要本文从有限时间稳定性的角度分析了健康免疫系统的动力学行为。有限时间稳定性和稳定化在各种工程应用中得到了很好的研究。主要范例使用非Lipschitz函数的状态。近年来对闭环非Lipschitz动力系统鲁棒性的研究是基于李雅普诺夫函数的，并表明有限时间稳定性既是系统渐近稳定性的一个特例，也是系统渐近稳定性的上级.这种有限时间收敛性质在生物系统领域还没有得到广泛的研究，在生物系统中，很明显，动力学是有限时间收敛到某些平衡点，而不是渐近或指数收敛。此外，还有一些例子，如健康的免疫系统反应，其中发现了对自身免疫疾病状态的鲁棒性。这些固有的功能，鲁棒性和有限时间收敛激励的Michaelis-Menten函数，这是经常使用的生物学，基于有限时间稳定性范例的修改版本的发展。该论文假设了有限时间稳定性和健康免疫系统的动态之间的潜在联系。
Abstract This paper presents an analysis of healthy immune system dynamics from the perspective of finite time stability. Finite time stability and stabilisation have been well-studied in various engineering applications. The principal paradigm uses non-Lipschitz functions of the states. Recent studies on robustness of closed-loop non-Lipschitz dynamical systems are based on Lyapunov functions and show that finite time stability is both a special case of and superior to the asymptotic stability of the system. Such a finite time convergence property has not been studied extensively in the area of biological systems where it is evident that the dynamics are finite time convergent to certain equilibrium points rather than asymptotically or exponentially convergent. Furthermore, there are examples such as a healthy immune system response where robustness is found to the state of auto-immune disease. These inherent features of robustness and finite time convergence motivate the development of a modified version of the Michaelis-Menten function, which is frequently used in biology, based on the finite time stability paradigm. The paper hypothesizes a potential connection between finite time stability and the dynamics of a healthy immune system.