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Feedback Control of the Plate Heating Process with Optimization of the Locations of Sources and Control

  • Control in Technical Systems
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Abstract

We consider the synthesis problem for concentrated controls of the plate heating process, where the locations of heat sources and state control are both optimized. For its numerical solution, we obtain formulas for the gradient of the objective functional using efficient first-order optimization methods. We present the results of computer experiments. The proposed approach can be used in the design of automatic control systems for many other processes and objects with distributed parameters.

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References

  1. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., The Mathematical Theory of Optimal Processes, New York: Wiley, 1965.

    MATH  Google Scholar 

  2. Bellman, R., Gliksberg, I., and Gross, O.A., Some Aspects of the Mathematical Theory of Control Processes, Santa Monica, California: Rand Corporation, 1958. Translated under the title Nekotorye voprosy matematicheskoi teorii upravleniya, Moscow: Inostrannaya Literatura, 1962.

    Google Scholar 

  3. Letov, A.M., Analytical Controller Design. I–IV, Autom. Remote Control, 1960, vol. 21, no. 4, pp. 303–307; no. 5, pp. 389–394; no. 6, pp. 458–462; 1961, vol. 22, no. 4, pp. 363-373.

    MATH  Google Scholar 

  4. Krasovskii, N.N., Teoriya upravleniya dvizheniem (Theory of Motion Control), Moscow: Nauka, 1968.

    Google Scholar 

  5. Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.

    Google Scholar 

  6. Butkovskii, A.G., Metody upravleniya sistemami s raspredelennymi parametrami (Control Methods for Systems with Distributed Parameters), Moscow: Nauka, 1984.

    Google Scholar 

  7. Sirazetdinov, T.K., Optimizatsiya sistem s raspredelennymi parametrami (Optimization of Systems with Distributed Parameters), Moscow: Nauka, 1977.

    Google Scholar 

  8. Egorov, A.I., Optimal Stabilization of the Distributed Parameter Systems, Berlin: Springer-Verlag, 1975.

    MATH  Google Scholar 

  9. Butkovskii, A.G. and Pustyl’nikov, L.M., Teoriya podvizhnogo upravleniya sistemami s raspredelennymi parametrami (Theory of Movable Control for Systems with Distributed Parameters) Moscow: Nauka, 1980.

    MATH  Google Scholar 

  10. Ray, W.H., Advanced Process Control, New York: McGraw-Hill, 1981.

    Google Scholar 

  11. Vasil’ev, F.P., Metody optimizatsii (Methods of Optimization), Moscow: Faktorial Press, 2002.

    Google Scholar 

  12. Aida-zade, K.R. and Abdullaev, V.M., Optimizing Placement of the Control Points at Synthesis of the Heating Process Control, Autom. Remote Control, 2017, vol. 78, no. 9, pp. 1585–1599.

    Article  MathSciNet  Google Scholar 

  13. Akhmetzyanov, A.V., Computational Aspects in Controlling Filtration of Fluids and Gases in Porous Media, Autom. Remote Control, 2008, vol. 69, no. 1, pp. 1–12.

    Article  MathSciNet  Google Scholar 

  14. Akhmetzyanov, A.V. and Kulibanov, V.N., Problems of Optimal Control of Percolation of Subterranean Water, Autom. Remote Control, 1999, vol. 60, no. 8, part 1, pp. 1097–1105.

    MATH  Google Scholar 

  15. Polyak, B.T., Khlebnikov, M.V., and Rapoport, L.B., Matematicheskaya teoriya avtomaticheskogo up-ravleniya (Mathematical Theory of Automatic Control), Moscow: LENAND, 2019.

    Google Scholar 

  16. Lions, J.-L. and Magenes E., Problemes aux limites non homogenes at application, Paris, 1968, vol. 1. Translated under the title Neodnorodnye granichnye zadachi i ikh prilozheniya, Moscow: Mir, 1971.

  17. Lions, J.-L., Control optimal de sistemes gouvernes par des equations aux derivees partielles, Paris: Dunod Ganthier-Villars, 1969. Translated under the title Optimal’noe upravlenie sistemami, opisyvae-mymi uravneniyami s chastnymi proizvodnymi, Moscow: Mir, 1972.

    Google Scholar 

  18. Engl, H.W., Hanke, M., and Neubauer, A., Regularization of Inverse Problems, Netherlands: Kluwer, 1996.

    Book  Google Scholar 

  19. Nakhushev, A.M., Nagruzhennye uravneniya i ikh prilozheniya (Loaded Equations and Their Applications), Moscow: Nauka, 2012.

    Google Scholar 

  20. Alikhanov, A.A., Berezgov, A.M., and Shkhanukov-Lafishev, M.X., Boundary Value Problems for Certain Classes of Loaded Differential Equations and Solving Them by Finite Difference Methods, Comp. Math. Math. Phys., 2008, vol. 48, no. 9, pp. 1581–1590.

    Article  Google Scholar 

  21. Abdullayev, V.M. and Aida-zade, K.R., Finite-Difference Methods for Solving Loaded Parabolic Equations, Comp. Math. Math. Phys., 2016, vol. 56, no. 1, pp. 93–105.

    Article  MathSciNet  Google Scholar 

  22. Aida-zade, K.R. and Abdullaev, V.M., On the Solution of Boundary Value Problems with Non Separated Multipoint and Integral Conditions, Differ. Equat., 2013, vol. 49, no. 9, pp. 1114–1125.

    Article  Google Scholar 

  23. Aida-zade, K.R. and Handzel, A.V., An Apprach to Lumped Control Synthesis in Distributed Systems, Int. J. Appl. Comput. Math., 2007, no. 1, pp. 69–79.

    Google Scholar 

  24. Samarskii, A.A., The Theory of Difference Schemes, Bosa Roca: CRC Press, 2001.

    Book  Google Scholar 

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Correspondence to K. R. Aida-zade or V. A. Hashimov.

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This paper was recommended for publication by A.G. Kushner, a member of the Editorial Board

Russian Text © The Author(s), 2020, published in Avtomatika i Telemekhanika, 2020, No. 4, pp. 120–139.

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Aida-zade, K.R., Hashimov, V.A. Feedback Control of the Plate Heating Process with Optimization of the Locations of Sources and Control. Autom Remote Control 81, 670–685 (2020). https://doi.org/10.1134/S0005117920040098

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  • DOI: https://doi.org/10.1134/S0005117920040098

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