15th Triennial World Congress of the International Federation of Automatic Control
  Barcelona, 21–26 July 2002 
THRESHOLD POLICIES IN THE CONTROL OF PREDATOR-PREY MODELS
Magno E. M. Meza* Michel I. S. Costa**
Amit Bhaya and Eugenius Kaszkurewicz*
* Dept. of Electrical Engineering, COPPE, Federal
University of Rio de Janeiro, P.O. Box 68504, RJ
21945-970, BRAZIL
E-mail: magno@pee.coppe.ufrj.br,
amit@nacad.ufrj.br, eugenius@coep.ufrj.br
** Lab. Nacional de Computação Cientifica, Av. Getúlio
Vargas, 333 - Quitandinha Petrópolis-RJ 25651-070,
BRAZIL
E-mail: michel@lncc.br

Threshold policies are defined and analysed for different types of one species and predator-prey type models. It is shown that such policies can be designed by suitable choice of so called virtual equilibrium points. The simplest threshold policies are discontinuous, which leads to some drawbacks. It is also shown how to design continuous threshold policies that retain most of the advantages of their discontinuous versions but do not have the major drawback of chatter in the control. Threshold policies are also seen to be robust to uncertainty of the model parameters, and the initial conditions, as well as to delays between stock assessment and policy enactment. The models studied are the Noy-Meir herbivore-vegetation model, subject to linear consumption curves, the two species Rosenzweig-MacArthur model, and a three-dimensional chemostat model.
Keywords: Virtual equilibrium point, variable structure, Rosenzweig-MacArthur model, robustness, chemostat model
Session slot T-Tu-E21: Posters of Agricultural, Biological and Environmental Systems/Area code 4d : Modelling and Control of Environmental Systems