Optimal impulsive harvesting policies for single-species populations

In this paper, we address an optimal impulsive control problem with the aim of optimizing the harvesting rate for a non-autonomous logistic model. In addressing this problem, we combine bang–bang and singular controls for an impulsive optimization problem in which the singular controls are blocked at certain harvesting times. In our approach, we first obtain the singular controls by applying a Pontryagin optimal control framework for impulsive systems. Second, we investigate and derive a number of relationships characterizing the optimal harvesting rates and present an optimization principle: the optimal path lies as close as possible to the singular path. Finally, based on this optimization principle, we obtain analytical expressions for the optimal harvesting policy for our problem and use numerical simulations to demonstrate the effectiveness of our method. This study develops concepts and theory related to continuous control problems and applies them to impulsive control problems, and extends the related work of Xiao et al. (2006) and Braverman and Mamdani (2008).