弹性的数学框架：动力、策略、冲击和可接受的路径
A Mathematical Framework for Resilience: Dynamics, Strategies, Shocks and Acceptable Paths
摘要：
弹性是自然灾害管理中的一个抽象概念-城市对地震，洪水，火灾等的弹性，一句话，如果存在一种策略，可以在冲击后将系统状态恢复到“正常”（可接受的状态），则系统被称为弹性。我们能给这种可塑性的观念赋予什么样的形式肉体呢？我们建议在不确定性条件下，以控制理论的数学外衣来构建弹性的概念。我们的设置包括动力系统在离散或连续时间，确定性或不确定性。我们对韧性的定义延伸了其他人，无论他们是“一个la Holling”还是植根于可行性理论。事实上，我们要求，在冲击后，系统返回到一个可接受的“制度”，也就是说，状态控制路径作为一个整体必须返回到一组可接受的路径（不仅状态值必须属于一个可接受的状态集的子集）。更一般地说，由于状态和控制路径是偶然的不确定性，我们要求它们的尾部过程必须位于可接受的随机过程的域。最后，我们指出如何这些领域可以划定感谢所谓的风险措施。
英文摘要：
Resilience is a rehashed concept in natural hazard management - resilience of cities to earthquakes, to floods, to fire, etc. In a word, a system is said to be resilient if there exists a strategy that can drive the system state back to "normal" (acceptable states) after a shock. What formal flesh can we put on such malleable notion? We propose to frame the concept of resilience in the mathematical garbs of control theory under uncertainty. Our setting covers dynamical systems both in discrete or continuous time, deterministic or subject to uncertainties. Our definition of resilience extends others, be they "a la Holling" or rooted in viability theory. Indeed, we require that, after a shock, the system returns to an acceptable "regime" , that is, that the state-control path as a whole must return to a set of acceptable paths (and not only the state values must belong to an acceptable subset of the state set). More generally, as state and control paths are contingent on uncertainties, we require that their tails processes must lay within acceptable domains of stochastic processes. We end by pointing out how such domains can be delineated thanks to so called risk measures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
