Finite time orbitally stabilizing synthesis of complex dynamic systems with bifurcations with application to biological systems

具有分岔的复杂动态系统的有限时间轨道稳定合成及其在生物系统中的应用

基本信息

批准号：
EP/J018295/1
负责人：
Sarah Spurgeon
金额：
$ 41.98万
依托单位：
University of Kent
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2012
资助国家：
英国
起止时间：
2012 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FJ018295%2F1
关键词：
Finite time orbitally stabilizing synthesis

项目摘要

Stabilization, in finite time rather than asymptotically, of linear and non-linear dynamical systems is an active current area of research internationally. In much of the existing work finite time convergence of a Lyapunov function to the origin of the state space is achieved using an increasing condition on that Lyapunov function given by a differential inequality which is dependent upon the decay rate and both known and uncertain system parameters. The proof of finite time stability on the basis of such a strong Lyapunov function satisfying a differential inequality poses a challenge when compared to proofs of Lyapunov theorems relating to asymptotic stability considerations. The task can be further complicated when the paradigm requires not only a settling time estimate but also seeks to achieve parameter selections for a control strategy to ensure an apriori chosen settling time is achieved. Recent work by the investigators in the domain of mechanical systems has obtained corresponding results using a homogeneity approach where the methodology is founded on a quasihomogeneity principle of possibly discontinuous systems, and thus a broader range of uncertainty is permitted than in the existing literature. Finite time stability which is uniform in the initial data and in the uncertainty is possible, a feature that cannot be guaranteed using existing methods. A finite upper bound on the settling time is determined without the need to find a Lyapunov function satisfying a differential inequality. Work has developed a single Lyapunov function for uncertain, discontinuous mechanical systems to provide global finite time stability to the origin of the system in the presence of velocity jumps without having to analyze the Lyapunov function at the jump instants and has developed parameterisations of sliding mode controllers that ensure finite time stabilisation where the designer specifies a convergence time and controller parameters are explicitly computed as a function of the required convergence time. The current proof of concept demonstrates that finite time stability characteristics can be imposed in possibly discontinuous systems and provides an exciting platform to explore more complex practical scenarios of current interest. It is clear that current methods which analyse systems based upon an assumption of an infinite time horizon are frequently flawed. For example, individual clonal immune cell populations are required to expand and become activated for limited time. Further in the natural world, discontinuity is frequently found as a result of evolution. This project seeks to broaden the system class to which the developed theoretical framework can be applied to encompass such biological dynamics. One specific driver is to parameterise and assess the bifurcations present in the immune system, where a key paradigm is to investigate how a triggering event may move the immune system from the healthy to the autoimmune state and also how control paradigms can be used to postulate treatment to move the system back to the healthy state. Autoimmune disease affects 50 million people in the USA where it is one of the top ten causes of death in women under 65, is the second highest cause of chronic illness, and is the top cause of morbidity in women. The number of cases of autoimmune disease are rising across the world. This rise in the number of people affected and the absence of robust treatment regimes results in the incidence of autoimmune disease contributing significantly to the rise in healthcare spending as well as loss of productivity in the workforce and of course poor quality of life for those affected. There is currently no mechanism-based, conceptual understanding of autoimmune disease. This project seeks to develop and apply emerging methods from finite time stabilisation of uncertain possibly discontinuous dynamic systems to this problem.

在有限的时间内而不是渐近地，线性和非线性动力学系统是国际研究的活动领域。在现有的工作中，Lyapunov函数与状态空间的起源的许多现有工作有限时间收敛是使用差异不平等给出的lyapunov函数的增加来实现的，该功能取决于衰减率以及已知和不确定的系统参数。与与渐近稳定性注意事项有关的Lyapunov定理的证明相比，根据如此强大的Lyapunov功能，有限的时间稳定性证明构成了挑战。当范式不仅需要定居时间估算，而且还试图实现控制策略的参数选择以确保实现APRIORI选择的结算时间时，该任务可能会更加复杂。研究人员在机械系统领域的最新工作已使用均匀性方法获得了相应的结果，在这种方法中，该方法是基于可能不连续系统的准原理原理建立的，因此允许在现有文献中更广泛的不确定性范围。有限的时间稳定性在初始数据和不确定性中都是统一的，这种功能无法使用现有方法来保证。确定定居时间的有限上限，而无需找到满足差异不平等的Lyapunov函数。 Work has developed a single Lyapunov function for uncertain, discontinuous mechanical systems to provide global finite time stability to the origin of the system in the presence of velocity jumps without having to analyze the Lyapunov function at the jump instants and has developed parameterisations of sliding mode controllers that ensure finite time stabilisation where the designer specifies a convergence time and controller parameters are explicitly computed as a function of the required convergence time.当前的概念证明表明，有限的时间稳定性特征可以在可能不连续的系统中强加，并提供了一个令人兴奋的平台，以探索更复杂的当前兴趣实践场景。显然，当前的方法基于无限时间范围的假设分析系统经常存在缺陷。例如，需要单个克隆免疫细胞群来扩展和激活有限的时间。在自然世界中，由于进化而经常发现不连续性。该项目旨在扩大可以将开发的理论框架应用于涵盖这种生物学动态的系统类别。一个特定的驱动因素是参数化和评估免疫系统中存在的分叉，其中关键范式是研究触发事件如何将免疫系统从健康状态转移到自身免疫性状态，以及如何使用控制范式来假设治疗以将系统移至健康状态。自身免疫性疾病在美国影响5,000万人，这是65岁以下女性死亡原因之一，是慢性疾病的第二高原因，并且是女性发病率的主要原因。全球自身免疫性疾病的病例数量正在增加。受影响的人数的增加和缺乏强大的治疗方案导致自身免疫性疾病的发生率显着导致医疗保健支出的上升以及劳动力的生产率降低，当然，受影响者的生活质量差。目前尚无基于机制的自身免疫性疾病的概念理解。该项目旨在开发和应用新兴方法，从不确定可能不连续的动态系统的有限时间稳定到此问题。