Robust control of predator-prey-hunter systems

Abstract

We explore the use of robust control techniques to manage conflicting economic and ecological goals and constraints that naturally arise in many predator-prey-hunter systems. In particular, we focus on a general predator-prey-hunter system in which both the predator and prey may be harvested. Our goal is to design and test a controller that can maintain populations at prescribed target levels in the presence of uncertainty in the system dynamics and noisy measurements, while rejecting external disturbances. The dynamic equations of the model are based upon Brown et al. (2005, Marine Resource Economics), suitably modified for control systems design. Given this specification, we define a robust control problem and simulate its properties using the set of parameters for which performance of the closed-loop system is worst. One of the main advantages of using a robust control approach is that it provides deterministic tools for analysis of sensitivities and robustness to multiple uncertain parameters and affords the designer a framework to balance competing objectives. Simulations of the controlled system show promising results, with policy implications not only for managing existing predator-prey-hunter systems, but also for the planning of sustainable reintroduction efforts involving large, mammalian carnivores.