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Synthesis of Motion Control of Rod Heating Sources with Optimization of Places for Measuring States

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Mathematical Optimization Theory and Operations Research: Recent Trends (MOTOR 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1661))

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Abstract

The problem of control synthesis for the heating process of a rod by lumped sources moving along the rod is studied. The problem of feedback control of moving heat sources during rod heating is considered. The speed of point-wise sources are assigned depending on the state of the processes at the measurement points. The formulas for the gradient components of the objective functional allowing for the numerical solution of the problem using of the first-order optimization methods are obtained.

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References

  1. Butkovskiy, A.G.: Methods of control of systems with distributed parameters. Nauka, Moscow (1984) (in Russian)

    Google Scholar 

  2. Utkin, V.I.: Sliding Modes in Control and Optimization. Springer, Berlin (1992). https://doi.org/10.1007/978-3-642-84379-2

  3. Ray W.H.: Advanced Process Control. McGraw-Hill Book Company (2002)

    Google Scholar 

  4. Yegorov, A.I.: Bases of the control theory. Fizmatlit, Moscow (2004) (in Russian)

    Google Scholar 

  5. Butkovskiy, A.G., Pustylnikov, L.M.: The theory of mobile control of systems with distributed parameters. Nauka, Moscow (1980) (in Russian)

    Google Scholar 

  6. Sirazetdinov, T.K.: Optimization of systems with distributed parameters. Nauka, Moscow (1977) (in Russian)

    Google Scholar 

  7. Sergienko, I.V., Deineka, V.S.: Optimal control of distributed systems with conjugation conditions. Kluwer Acad. Publ., New York (2005)

    MATH  Google Scholar 

  8. Polyak, B.T., Khlebnikov, M.V., Rapoport, L.B.: Mathematical theory of automatic control. LENAND, Moscow (2019) (in Russian)

    Google Scholar 

  9. Vasilyev, F.P.: Optimization methods, 824. Faktorial Press, Moscow (2002) (in Russian)

    Google Scholar 

  10. Guliyev, S.Z.: Synthesis of zonal controls for a problem of heating with delay under non-separated boundary conditions. Cybern. Syst. Analysis. 54(1), 110–121 (2018)

    Article  Google Scholar 

  11. Aida-zade, K.R., Abdullaev, V.M.: On an approach to designing control of the distributed-parameter processes. Autom. Remote. Control. 73(9), 1443–1455 (2012)

    Article  MathSciNet  Google Scholar 

  12. Aida-zade, K.R., Hashimov, V.A., Bagirov, A.H.: On a problem of synthesis of control of power of the moving sources on heating of a rod. Proc. Inst. Math. Mech. ANAS 47(1), 183–196 (2021)

    MathSciNet  MATH  Google Scholar 

  13. Nakhushev, A.M.: Loaded equations and their application. Nauka, Moscow (2012) (in Russian)

    Google Scholar 

  14. Abdullaev, V.M., Aida-Zade, K.R.: Numerical method of solution to loaded nonlocal boundary value problems for ordinary differential equations. Comput. Math. Math. Phys. 54(7), 1096–1109 (2014). https://doi.org/10.1134/S0965542514070021

    Article  MathSciNet  MATH  Google Scholar 

  15. Abdullayev, V.M., Aida-zade, K.R.: Finite-Difference Methods for Solving Loaded Parabolic Equations. Comp. Math. Math. Phys. 56(1), 93–105 (2016)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Control Systems of ANAS, B. Vahabzade 9, AZ1141, Baku, Azerbaijan

    Kamil R. Aida-Zade & Vugar A. Hashimov

Authors
  1. Kamil R. Aida-Zade
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  2. Vugar A. Hashimov
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Corresponding author

Correspondence to Kamil R. Aida-Zade .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Yury Kochetov

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Anton Eremeev

  3. Melentiev Energy Systems Institute, Irkutsk, Russia

    Oleg Khamisov

  4. Institute of Applied Mathematical Research, Petrozavodsk, Russia

    Anna Rettieva

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Aida-Zade, K.R., Hashimov, V.A. (2022). Synthesis of Motion Control of Rod Heating Sources with Optimization of Places for Measuring States. In: Kochetov, Y., Eremeev, A., Khamisov, O., Rettieva, A. (eds) Mathematical Optimization Theory and Operations Research: Recent Trends. MOTOR 2022. Communications in Computer and Information Science, vol 1661. Springer, Cham. https://doi.org/10.1007/978-3-031-16224-4_16

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  • DOI: https://doi.org/10.1007/978-3-031-16224-4_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-16223-7

  • Online ISBN: 978-3-031-16224-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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