Optimal Control of Renewable Resources Based on the Effective Utilization Rate

Abstract

The effective utilization rate of exploited renewable resources affects the final total revenue and the further exploitation of renewable resources. Considering the effective utilization rate, we propose an optimal control model for the exploitation of the renewable resources in this study. Firstly, we can prove that the novel model is nonsingular compared with the singular basic model. Secondly, we solve the novel model and obtain the optimal solution by Bang-Bang theory. Furthermore, we can determine the optimal total resources and the maximal total revenue. Finally, a numerical example is provided to verify the obtained theoretical results.