Abstract
Abstract The authors consider a continuous dynamic approximating model of a gas fields group and, on its basis, set maximum and minimum issues. The tasks proposed for research are optimal control problems with mixed constraints with free-final-time and moving right end. We analytically solve the rapid-action problem. The central mathematical apparatus is Pontryagin maximum principle in Arrow form, using Lagrange multipliers. The theoretically obtained results of the analysis are of particular interest.
Highlights
The authors consider a continuous dynamic approximating model of a gas fields group and, on its basis, set maximum and minimum issues
The tasks proposed for research are optimal control problems with mixed constraints with free-final-time and moving right end
The theoretically obtained results of the analysis are of particular interest
Summary
Natural gas refers to non-renewable minerals located under the surface of the earth at high pressure and temperature. It is located in the earth’s layer in a gaseous state in the form of separate accumulations (gas deposits). It is necessary to solve two optimal control problems with a mixed restriction on the maximum and minimum. We can analytically solve these problems and obtain theoretically substantiated estimates of the gas fields shelf length. The 1972 Nobel Prize winner in economics, published an article [3], where he, taking Pontryagin maximum principle [4] as a basis, modifies it and formulates propositions that allow solving problems optimal control with mixed constraints.
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