Abrupt changes in the behaviour of hybrid systems in discontinuity induced multiple attractors bifurcations

混合系统在不连续性中行为的突然变化引起了多个吸引子分岔

基本信息

批准号：
EP/K001353/1
负责人：
Piotr, Sebastian Kowalczyk
金额：
$ 12.6万
依托单位：
Manchester Metropolitan University
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2013
资助国家：
英国
起止时间：
2013 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FK001353%2F1
关键词：
Abrupt changes behaviour hybrid systems

项目摘要

The fundamental question we address is: How can the study of hybrid dynamical systems inform our understanding of human balance? To answer this question we have to know what are hybrid systems, and how they can be used in the context of human balance. In simple terms, systems characterised by an interaction of continuous and discrete evolution are termed as hybrid systems. To give an example from everyday life: consider an aircraft whose position during the flight evolves continuously in time. The aircraft is controlled by microprocessors which operate on discrete inputs, and hence the whole system is a hybrid system. Another example, from outside of the field of engineering, is growth and division of biological cells. Growth is a continuous time process but division is a discrete transition. Actually, it is virtually impossible to think of any complex system, that is, a system built from a number of interacting subsystems, that does not have a hybrid characteristic in the sense of a heuristic definition given here. An invaluable and a highly successful tool used for dynamical systems investigation is bifurcation analysis. In simple terms, bifurcations give information on stability boundaries of steady states (equilibrium points or periodic motions) as functions of system parameters that may vary; these parameters could be a temperature, pressure or other physical quantity. It turns out that hybrid systems, due to the presence of switches, may exhibit bifurcations (loss of stability) which are solely caused by these switches. An important feature of bifurcations (transitions) which are induced by the presence of switches is that they may lead to an abrupt change of system's behaviour. For instance, an abrupt transition from a stable oscillatory motion to a chaotic motion. It has also been shown that in hybrid systems many stable states, say oscillatory states, may originate from a single one, again due to the presence of switches. Any system operates in continuously changing environmental conditions, and if there is a possibility of different stable motions originating from a single one there are certain parameter values at which the system is highly susceptible to changing its evolution by jumping between its stable states. And if one of these stable states is undesirable, for instance from the point of view of system's performance, this may lead to a catastrophic failure of a system. Clearly, understanding this type of behaviour, that is birth of multiple attractors, is of critical importance for system designers. What is the link between hybrid systems and human balance and how the research on hybrid systems will be used to understand human balance? In recent years, mathematical models have been used to gain insight into the problem of maintaining balance in humans during quiet standing. It is usually assumed that, as a first approximation, a human body can be modelled as a single link inverted pendulum where different control feedback laws model neuromuscular response to change in posture which then ensures the upright stance. Recently, it has been pointed out that it is impulsive like muscle movements that control upright stance, and hence it is switch like behaviour that seems to play a crucial role in balance control. By understanding the dynamics of systems with switches, routes to possible failures in their behaviour, we may then use this knowledge, for instance, to understand the mechanisms behind falling in humans.

我们解决的基本问题是：混合动力学系统的研究如何为我们对人类平衡的理解提供信息？要回答这个问题，我们必须知道什么是混合系统，以及如何在人类平衡的背景下使用它们。简而言之，以连续和离散进化的相互作用为特征的系统称为混合系统。从日常生活中举一个例子：考虑一架飞机在飞行过程中持续不断发展的飞机。该飞机由以离散输入操作的微处理器控制，因此整个系统是混合系统。在工程领域之外的另一个例子是生物细胞的生长和分裂。增长是一个连续的时间过程，但分裂是一个离散的过渡。实际上，几乎不可能想到任何复杂的系统，即是由许多交互子系统构建的系统，它在此处给出的启发式定义的意义上没有混合特征。分叉分析是一种宝贵的和非常成功的工具。简而言之，分叉提供了有关稳态稳定边界（平衡点或周期性动作）的信息，作为可能变化的系统参数的函数；这些参数可能是温度，压力或其他物理量。事实证明，由于开关的存在，混合系统可能表现出分叉（稳定性的损失），这完全是由这些开关引起的。由开关的存在引起的分叉（过渡）的一个重要特征是它们可能导致系统行为的突然改变。例如，从稳定的振荡运动到混乱的运动突然过渡。还已经显示，在混合系统中，由于开关的存在，许多稳定状态（例如振荡状态）可能源自单个状态。任何系统都在不断变化的环境条件下运行，如果有不同稳定的动作来自单个系统，则有一定的参数值，该系统非常容易通过在其稳定状态之间跳跃来改变其演变。如果这些稳定状态之一是不希望的，例如，从系统性能的角度来看，这可能会导致系统的灾难性故障。显然，了解这种行为，即多种吸引子的诞生，对于系统设计师来说至关重要。混合系统与人类平衡之间的联系是什么，以及如何使用有关混合系统的研究来了解人类的平衡？近年来，数学模型已被用来深入了解在安静地位期间保持人类平衡的问题。通常假定，作为第一个近似，可以将人体建模为单个链接倒置，其中不同的控制反馈定律模型神经肌肉对姿势变化的反应，从而确保直立的立场。最近，有人指出，像肌肉运动一样冲动，可以控制直立的立场，因此，就像行为一样，切换似乎在平衡控制中起着至关重要的作用。通过了解带开关的系统的动态，即其行为可能发生故障的路线，我们可以使用这些知识来理解人类落入人类的机制。