In natural resource management, or more generally in the study of sustainability issues, the objective often consists of maintaining the state of a given system within a desirable configuration, typically established in terms of standards or thresholds. For instance, in fisheries management, the procedure for designing policies may include maintaining the spawning stock biomass over a precautionary threshold and ensuring minimal catches. With the evolution of some natural resources, under the action of controls and uncertainties, being represented by a dynamical system in discrete time, the aim of this paper is to characterize the set of robust sustainable thresholds. That is, the thresholds for which there exists a trajectory satisfying, for all possible uncertainty scenarios, prescribed constraints parametrized by such thresholds. This set provides useful information to users and decision-makers, illustrating the tradeoffs between constraints. Using optimal control, maximin and level-set approaches, we characterize the weak Pareto front of the set of robust sustainable thresholds and derive a numerical method for computing the entire set, as we show with a numerical example relying on renewable resource management.

中文翻译：

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关于稳健的可持续阈值集

在自然资源管理中，或更一般地在可持续性问题的研究中，目标通常包括将给定系统的状态维持在理想的配置内，通常根据标准或阈值建立。例如，在渔业管理中，设计政策的程序可能包括将产卵种群生物量维持在一个预防阈值之上并确保最小捕获量。随着一些自然资源的演变，在控制和不确定性的作用下，以离散时间的动力系统为代表，本文的目的是表征一组稳健的可持续阈值。也就是说，存在轨迹满足的阈值，对于所有可能的不确定性场景，由这些阈值参数化的规定约束条件。该集合为用户和决策者提供了有用的信息，说明了约束之间的权衡。使用最优控制、最大值和水平集方法，我们表征了一组稳健的可持续阈值的弱帕累托前沿，并推导出一种用于计算整个集合的数值方法，正如我们通过一个依赖可再生资源管理的数值示例所展示的那样。