Application Of Singular Space-Time Transformation To Impulsive Pest Management
The journal version of this paper is published in Cybernetics And Physics, Vol.4, Is.2, 2015
We consider three versions of a problem of impulsive pest control by its natural enemies. The model is of a prey-predator type. The control system is described by a measure differential equation and hence admits discontinuous solutions. The cost functional of the first problem represents a balance between a negative profit provided by a pest (prey) and a price for applying an additional population of its natural enemies (predators). The problem of keeping the pest quantity below a practically admissible threshold leads to a state-constrained model, while the most complicated version is due to the presence of a mixed constraint relating impulsive action (measure) and the left one-sided limit of a trajectory. We employ a conceptual approach for optimal impulsive pest control based on a certain singular space-time transformation and share our experience in its numerical implementation.