Resolution of the optimal control problem within the framework of the gas product realization model

A linear state-based optimal control problem with a finite planning horizon associated with a dynamic model of gas field development is considered. The construction of extreme control is carried out on the basis of the maximum principle. The global solution of the problem is realized with the help of a sufficient optimality condition in the terminology of highly extreme controls. For a more complete solution of the problem, in addition to the maximum principle, sufficient optimality conditions are used. The optimal process is described by simple integral relations depending on the price function. A special variant of the problem is singled out separately when the price of raw materials is constant