Formulation and study of dynamic problems in the gas field development model

We consider continuous aggregated dynamic model for gas field algorithm development. Two mathematical problems are posed, solved and investigated. One of them is a direct fixed time optimal control problem with a free right end. The other one is the inverse problem. For a fixed optimal control, planning horizons are searched. We propose an algorithm for the numerical search of all planning horizons.The problems are subjected to comprehensive analysis. The main mathematical apparatus is the Pontryagin maximum principle. The implicit function existence and differentiability theorem is used.