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Algorithm to determine the optimal solution of a boundary control problem

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Abstract

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.

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References

  1. Aliev, F.A., Il’yasov, M.Kh., and Dzhamalbekov, M.A., Modeling of Operation of the Gaslift Borehole Cavity, Dokl. NANA, 2008, no. 4, pp. 107–116.

    Google Scholar 

  2. Mirzadzhanzade, A.Kh., Ametov, I.M., and Khasaev, A.M., Tekhnologiya i tekhnika dobychi nefti (Technology and Machinery of Oil Extraction), Moscow: Nauka, 1986.

    Google Scholar 

  3. Charnyi, I.A., Neustanovivsheesya dvizhenie real’noi zhidkosti v trubakh (Unsteady Motion of Real Liquid in Pipes), Moscow: Gostekhizdat, 1951.

    Google Scholar 

  4. Aliev, F.A., Ismailov, N.A., and Temirbekova, L.N., Methods of Solving the Choice of Extremal Modes for the Gas-lift Process, Appl. Comput. Math., 2012, vol. 11, no. 3, pp. 348–357.

    MATH  MathSciNet  Google Scholar 

  5. Aliev, F.A., Il’yasov, M.Kh., and Nuriev, N.B., Problems of Modeling and Optimal Stabilization of the Gaslift Process, Prikl. Mekhan., NAN Ukrainy, 2010, vol. 46, no. 6, pp. 113–122.

    Google Scholar 

  6. Bryson, A.E., Jr. and Yu-Chi Ho, Applied Optimal Control (Optimization, Estimation and Control), Waltham: Blaisdell, 1969. Translated under the title Prikladnaya teoriya optimal’nogo upravleniya, Moscow: Mir, 1972.

    Google Scholar 

  7. Aliev, F.A., Metody resheniya prikladnykh zadach optimizatsii dinamicheskikh sistem (Methods to Solve the Applied Problems of Dynamic System Optimization), Baku: Elm, 1989.

    MATH  Google Scholar 

  8. Slavov, T., Mollov, L., and Petkov, P., Real-time Linear Quadratic Control Using Digital Signal Processor, TWMS J. Pure Appl. Math., 2012, vol. 3, no. 2, pp. 145–157.

    MATH  MathSciNet  Google Scholar 

  9. Himmelblau, D.M., Applied Nonlinear Programming, New York: McGraw-Hill, 1972. Translated under the title Prikladnoe nelineinoe programmirovanie, Moscow: Mir, 1975.

    MATH  Google Scholar 

  10. Andreev, Yu.I., Upravlenie konechnomernymi lineinymi ob”ektami (Control of Finite-dimensional Linear Plants), Moscow: Nauka, 1976.

    Google Scholar 

  11. Aliev, F.A. and Ismailov, N.A., Inverse Problem to Determine the Hydraulic Resistance Coefficient in the Gas Lift Process, Appl. Comput. Math., 2013, vol. 12, no. 3, pp. 306–313.

    MATH  MathSciNet  Google Scholar 

  12. Aliev, F.A., Mutallimov, M.M., Ismailov, N.A., et al., Algorithms for Constructing Optimal Controllers for Gaslift Operation, Autom. Remote Control, 2012, vol. 73, no. 8, pp. 1279–1289.

    Article  MATH  MathSciNet  Google Scholar 

  13. Bellman, R.E. and Kalaba, R.E., Quasilinearization and Nonlinear Boundary-Value Problems, NewYork: Elsevier, 1965. Translated under the title Kvazilinearizatsiya i nelineinye kraevye zadachi, Moscow: Mir, 1968.

    MATH  Google Scholar 

  14. Gurbanov, R.S., Nuriyev, N.B., and Gurbanov, R.S., Technological Control and Optimization Problems in Oil Production: Theory and Practice, Appl. Comput. Math., 2013, vol. 12, no. 3, pp. 314–324.

    MATH  Google Scholar 

  15. Okosun, K.O. and Makinde, O.D., Optimal Control Analysis of Malaria in the Presence of Non-Linear Incidence Rate, Appl. Comput. Math., 2013, vol. 12, no. 1, pp. 20–32.

    MATH  MathSciNet  Google Scholar 

  16. Gabasov, R., Dmitruk, N.M, Kirillova, F.M., On Optimal Control of an Object at Its Approaching to Moving Target under Uncertainty, Appl. Comput. Math., 2013, vol. 12, no. 2, pp. 152–167.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan

    F. A. Aliev & N. A. Ismailov

  2. Institute of Cybernetics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan

    N. S. Mukhtarova

Authors
  1. F. A. Aliev
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  2. N. A. Ismailov
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  3. N. S. Mukhtarova
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Correspondence to F. A. Aliev.

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Original Russian Text © F.A. Aliev, N.A. Ismailov, N.S. Mukhtarova, 2015, published in Avtomatika i Telemekhanika, 2015, No. 4, pp. 97–104.

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Aliev, F.A., Ismailov, N.A. & Mukhtarova, N.S. Algorithm to determine the optimal solution of a boundary control problem. Autom Remote Control 76, 627–633 (2015). https://doi.org/10.1134/S0005117915040074

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  • DOI: https://doi.org/10.1134/S0005117915040074

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