Algorithm to determine the optimal solution of a boundary control problem

Consideration was given to the problem of optimal control where the initial condition (boundary control) was assumed to be the control action, the object motion obeyed the nonlinear ordinary differential equation having a discontinuity within the interval of definition of the phase coordinates, and the optimized quadratic functional consisted also of the sum of squares of the initial and final conditions with corresponding negative and positive weight matrices. An algorithm to solve this problem of optimization with boundary control action based on the corresponding Euler–Lagrange equations was given. On the basis of a specific example from the petroleum industry, a computational algorithm was proposed to provide the maximal yield of the gaslift borehole cavities with the minimal supply of gas to the mouths of the borehole cavity. This approach enables a maximal delivery of the geological horizon with a sufficiently high speed. A computer-based experiment corroborating the adequacy of the proposed mathematical model was described.