Comparison Theorem for Viability Kernels via Conic Preorders
Abstract
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.
Keywords
Cite
@article{arxiv.2004.04473,
title = {Comparison Theorem for Viability Kernels via Conic Preorders},
author = {Michel de Lara and Pedro Gajardo and Diego Vicencio},
journal= {arXiv preprint arXiv:2004.04473},
year = {2020}
}