Abstract
We consider a nonlinear optimal control problem with an infinite planning horizon, which extends a dynamic gas field development model by taking into account a gas price forecast. (The prices varies in time.) The solution is constructed on the basis of the Pontryagin maximum principle. To prove the optimality of the extremal solution, we use the theorem on sufficient optimality conditions in terms of constructions of the Pontryaginmaximum principle. We discuss the problem of constructing an optimal solution by dynamic programming.
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Kiselev, Yu.N., Sufficient Optimality Conditions in Terms of Constructions of the Pontryagin Maximum Principle, Mater. nauch. sem. “Matematicheskie modeli v ekonomike i biologii” (Proc. Sci. Sem. “Math, Models in Economics and Biology”), Moscow, 2003, pp. 57–67.
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Original Russian Text © Yu.N. Kiselev, M.V. Orlov, 2011, published in Differentsial’nye Uravneniya, 2011, Vol. 47, No. 11, pp. 1583–1591.
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Kiselev, Y.N., Orlov, M.V. Analysis of a gas field development model with an infinite planning horizon. Diff Equat 47, 1603–1611 (2011). https://doi.org/10.1134/S0012266111110073
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DOI: https://doi.org/10.1134/S0012266111110073