Discrete time optimal control applied to pest control problems

We apply discrete time optimal control theory to the mathematical modeling of pest control. Two scenarios: biological control and the combination of pesticide and biological control are considered. The goal is maximizing the “valuable” population, minimizing the pest population and the cost to apply the control strategies. Using the extension of Pontryagin’s maximum principle to discrete system, the adjoint systems and the characterization of the optimal pest controls are derived. Numerical simulations of various cases are provided to show the effectiveness of our methods.