Abstract of Thesis presented at COPPE/UFRJ as a partial fulfillment of the requirements for the degree of Doctor of Science (D.Sc.)

Nonlinear Systems of the Predator-Prey Type: Design of Control Using Liapunov Functions

Magno Enrique Mendonza Meza

April/2004

Advisors:

Amit Bhaya Eugenius Kaszkurewicz

Department:

Eletrical Engineering

      A large class of predator-prey models can be written as a nonlinear dynamical system in one or two species. In many contexts, it is necessary to introduce a control into these dynamics. Without loss of generality, we assume that the control corresponds to a proportional removal of the prey population, in one species models. In the context of two species of fish, which gave rise to the classical predator-prey models, this control action corresponds to harvesting of the predator.
      This thesis develops a systematic design method of a simple on-off control, also referred to as a threshold policy, so that the controlled system has a globally stable equilibrium. The method is based on the application of control Liapunov functions, exploiting the structure of the predator-prey system, applying the idea of backstepping, and using the concepts of real and virtual equilibria that arises in variable structure control.
      This combination of elements - CLFs, backstepping with variable structure and consequent introduction of a unique globally asymptotically stable equilibrium through a simple on-off control - for the systematic design of control for predator-prey systems constitutes the main contribution of this thesis.