A NOTE ON SDRE CONTROL APPLIED IN PREDATOR–PREY MODEL: BIOLOGICAL CONTROL OF SPIDER MITE PANONYCHUS ULMI

Abstract

The spider mite Panonychus ulmi (P. ulmi) is one of the most important pests of apple plantations. Studies suggested that spider mite Neoseiulus californicus (N. californicus) is able to control spider mite P. Ulmi, minimizing the risk of having leaves with high index of injury, therefore avoiding economic damage. In this work, we consider a predator–prey system, where the prey is the mite P. ulmi and its predator is the spider mite N. californicus. The coefficients for the Lotka–Volterra model with competition between predators are obtained. Here, we will use the state-dependent riccati equation (SDRE) control technique to design a state feedback control, and to determine a state observer. In both cases, it is necessary to solve the quadratic optimal control problem for nonlinear systems. Numerical simulations shown that both approaches are efficient to stabilize the system in a desired point below the critical concentration, allowing us to minimize the level of economic damage.