论文标题
通过圆锥预订的可行性内核比较定理
Comparison Theorem for Viability Kernels via Conic Preorders
论文作者
论文摘要
在自然资源管理中，决策者通常旨在维持在所有时间的理想设置中的系统。当初始状态属于所谓的VialbilityKernel时，所有时间都有理想的集合。我们介绍了圆锥准综合性降低性的概念。在此属性的情况下，我们通过在两个VialbilityKernels之间包含在无限地平线中的两个控制系统中提供了比较定理。 Wealso得出平等条件。我们用一种模型来说明该方法的载体传播流行病。
In natural resource management, decision-makers often aim at maintaining thestate of the system within a desirable set for all times.For instance, fisheries management procedures include keeping thespawning stock biomass over a critical threshold.Another example is given by the peak control of an epidemic outbreakthat encompasses maintaining thenumber of infected individuals below medical treatment capacities.In mathematical terms, one controls a dynamical system.Then, keeping the state of the system within a desirable set for all times is possible when the initial state belongs to the so-called viabilitykernel. We introduce the notion of conic quasimonotonicity reducibility.With this property, we provide a comparison theorem by inclusion between two viabilitykernels, corresponding to two control systems in the infinite horizon case. Wealso derive conditions for equality. We illustrate the method with a model for thebiocontrol of a vector-transmitted epidemic.
