Mathematical methods in solving environmental problems

This document explores the utilization of mathematical formulations and superior control methodologies to lessen adverse environmental effects and encourage the intelligent utilization of energy resources. The central aim revolves around managing the rate at which different power production plants generate electricity, all while concurrently seeking reductions in the amount of fuel consumed and setting limits on the release of detrimental airborne pollutants. This undertaking is conceptualized as an optimization problem where overall performance must be maximized across several, frequently divergent, metrics, thereby demanding a careful balancing act between economic prudence and environmental stewardship. To ascertain the optimal control regime, a structured, repetitive procedure, derived from Pontryagin's maximum principle, is employed. Random fluctuations and constraints are taken into account in the model to approximate real processes. The obtained numerical results demonstrate optimal distribution of generator powers, reduction of total fuel consumption, and controlled levels of environmental emissions. The research results confirm the effectiveness of mathematical methods in ensuring environmental safety and creating sustainable energy systems.

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