Optimizing Algal Bloom Through Bioenzyme and Harvesting Control for Bioenergy Purposes in Eutrophic Water Bodies

This article discusses the optimization of algae growth for bioenergy purposes in eutrophic water bodies through bioenzyme control and harvesting. The study explores innovative approaches to manage algae growth in such water bodies. A mathematical model based on dynamical systems, specifically the NASC (Nutrients, Algae, Detritus, and Dissolved Oxygen) algae growth model, was used for the analysis. The results indicate that the system used is unstable, given the needs of algae growth over time. To optimize algae growth, this study proposes controlling the bioenzyme (u1) feeding to decompose detritus into nutrients and harvesting algae using (u2). The Pontryagin Maximum Principle (PMP) method was used to obtain optimization with control parameters u1=0.093 and u2=0.32. The results show that the optimal time to harvest algae is every 84 days or 2.8 months, with an estimated harvestable amount of 16.3667 . This discovery enhances our understanding of controlling algae growth in the context of renewable energy and reinforces the mathematical approach to managing eutrophic aquatic ecosystems.