Abstract
A partially periodic control problem is considered, where the control parameter enters the initial condition. We study the formalization related to the calculus of variations. The necessary conditions are written out in the form of Euler–Lagrange equations, with the help of which an algorithm for finding the optimal program trajectories is developed. The results are illustrated by an example when the motion is described by a time-averaged hyperbolic equation at a sufficiently large well depth during a gas lift.
Similar content being viewed by others
REFERENCES
I. M. Gel’fand and S. V. Fomin, Variation Calculus (Fizmatlit, Moscow, 1961) [in Russian].
F. A. Aliev, M. Kh. Il’yasov, and M. A. Dzhamalbekov, “Simulation of the operation of gaslift wells,” Dokl. Nats. Akad. Nauk Azerb., No. 4, 30–41 (2008).
F. A. Aliev, M. Kh. Il’yasov, and N. B. Nuriev, “Problems of modeling and optimal stabilization of the gas-lift process,” Int. Appl. Mech. 46 (6), 709–717 (2010).
F. A. Aliev and N. A. Ismailov, “Algorithm for calculating the coefficient of hydraulic resistance in the gaslift process,” Proc. IAM 2 (1), 3–10 (2013).
F. A. Aliev and M. M. Mutallimov, “Algorithm for constructing software trajectories and control in gaslift oil production,” Dokl. Nats. Akad. Nauk Azerb. 65 (5), 9–18 (2009).
F. A. Aliev and N. A. Ismailov, “Optimization problems with periodic boundary condition and boundary control in gaslift wells,” Nelineinye Kolebaniya 17 (2), 151–160 (2014).
A. Bryson and Yu-Chi Ho, Applied Optimal Control (Blaisdell, Waltham, Mass., 1969; Mir, Moscow, 1972).
F. A. Aliev, Methods for Solving Applied Problems of Optimization of Dynamical Systems (Elm, Baku, 1989) [in Russian].
R. Bellman and R. Kalaba, Quasilinearization and Nonlinear Boundary-Value Problems (Elsevier, New York, 1965; Mir, Moscow, 1968).
N. S. Hajiyeva, “An asymptotical method for determining the coefficient of hydraulic resistance in gas-lift process by the lines method,” Proc. IAM 8 (2), 187–195 (2019).
F. A. Aliev, N. A. Ismailov, and A. A. Namazov, “Asymptotic method for finding the coefficient of hydraulic resistance in lifting of fluid on tubing,” J. Inverse Ill-Posed Probl. 23 (5), 511–518 (2015).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors declare that they have no conflicts of interest.
Additional information
Publisher’s Note.
Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Aliev, F.A., Magerramov, I.A., Mutallimov, M.M. et al. Optimal Control of the Initial Condition in the Problem of Gas Lifting. J. Comput. Syst. Sci. Int. 62, 296–303 (2023). https://doi.org/10.1134/S1064230723020028
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064230723020028