On impulse control problems arising in automatization of pests control in greenhouses

The paper proposes a mathematical model based on a continuous dynamic system that formalizes the interaction of populations of a greenhouse agricultural insect pest and an entomophage acting as an agent of environmental control of the pest population in the framework of the concept of integrated pest management paradigm. The model parameters are identified based on experimental data obtained in laboratory conditions for the greenhouse system “cucumber — spider mite — acariphage mite”. For the proposed system, an impulse control problem that corresponds to the implementation of the pest population control using an entomophage is formulated, and the issues of the existence of solutions and their continuous dependence on control are investigated. Based on the studied control system, the issues of constructing cost-effective control strategies that allow implementing the mathematical software for automated pest control systems in greenhouses are discussed.