Optimum control applied to prey-predator models for the Holling II model: Application in the biological control of the mite Panonychus ulmi

  • Angelo M. Tusset
  • Mauricio A. Ribeiro
  • José M. Balthazar


In this paper, the coefficients were obtained for the prey-predator models Lotka-Volterra with competition and prey-predator of the Holling II type considering the mite system \textit{P. ulmi} and its predator \textit{N. californicus}. Using the SDRE control for both the control and a state observer, it was possible to solve the optimal control problem for quadratic functional non-linear systems. The computational simulations demonstrate the efficiency of both the control strategy and stabilize the system at the desired level below that considered critical as the state observer proposal.