Maximising discounted accumulated income for two gas fields

A gas production model based on two gas fields is being built. The model has the following characteristic properties: it is dynamic, continuous, and aggregated. It takes into account the depth of the deposits. The controls in the model are the drilling rates at each of the two fields. The model is based on the assumption of proportionality between changes in the average well flow rate and current natural gas production. The task of maximising discounted accumulated income for two gas fields is formulated. The problem considered in the article belongs to a well-known class of optimal control problems. It is assumed that the planning period is fixed. The right end of the trajectory is not fixed. To solve the formulated problem, the Pontryagin maximum principle is used. Various options for the implementation of optimal control are being investigated.