复原力的数学框架：动态、不确定性、策略和恢复机制
A Mathematical Framework for Resilience: Dynamics, Uncertainties, Strategies and Recovery Regimes
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。简而言之，如果存在一种策略，可以在任何扰动后将系统状态恢复到“正常”状态，则称系统具有弹性。我们能给这样一个可塑的概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。我们将说，系统状态是弹性的，如果存在一个自适应策略，使所产生的状态和控制路径，偶然的不确定性，躺在一个可接受的域的随机过程，称为恢复制度。我们指出，这种复苏制度可以划定由于所谓的风险措施，使连接与弹性指标。我们对韧性的定义延伸了其他人，无论他们是“一个拉霍林”或植根于可行性理论。事实上，我们的弹性的定义是一种形式的可控性的整个随机过程（政权），而其他要求的状态值必须属于一个可接受的子集的状态集。
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" after any perturbation. What formal flesh can we put on such a 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. We will say that a system state is resilient if there exists an adaptive strategy such that the generated state and control paths, contingent on uncertainties, lay within an acceptable domain of random processes, called recovery regimes. We point out how such recovery regimes can be delineated thanks to so called risk measures, making the connection with resilience indicators. Our definition of resilience extends others, be they "` a la Holling" or rooted in viability theory. Indeed, our definition of resilience is a form of controlability for whole random processes (regimes), whereas others require that the state values must belong to an acceptable subset of the state set.
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。
