This paper considers an optimal control problem of large-scale gas supply systems. Solving this problem, we must take into account line packing in systems modeling. For unsteady-state gas flow modeling, a lumped-parameter model is proposed. On the base of this model the paper elaborates a system of ordinary differential equations to imitate unsteady-state gas flow in pipeline system of selectable configuration and provides the integration algorithm using the global gradient method. Adduced an example of calculating a circuitous gas supply system demonstrates the adequacy of the proposed model. The paper includes the mathematical formulation of a technical diagnostics problem of large pipeline system equipment in case of unsteady-state gas flow. The estimation of technical state is reduced to the constrained optimization problem. On the base of the lumped parameters model, we propose an algorithm of the solution of this problem and use it for identification of the gas supply system of selectable configuration. The numerical experiments demonstrate that the algorithm converges with good speed. The paper contains a description of an optimal control concept of large-scale pipeline system. Stated ideas can be applied in case of the system collapse. (C) 2018 Elsevier Ltd. All rights reserved.