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An optimality criterion in a linear-quadratic optimal control problem for a descriptor system

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References

  1. Brenan, K.E., Campell, S.L., and Petzold, L.R.,Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, New York, 1989.

  2. Petzold, L.,SIAM J. Sci. and Statist. Comp., 1982 no. 3, pp. 367–384.

  3. Boyarintsev, Yu.E.,Metody resheniya vyrozhdennykh sistem obyknovennykh differentsial’nykh uravnenii (Methods for Degenerate Systems of Ordinary Differential Equations), Novosibirsk, 1988.

  4. Griepentrog, E. and März, R.,Differential-Algebraic Eguations and Their Numerical Treatment. Teubner-Texte zur Mathematik; 88, Teubner, Leipzig. 1986.

  5. Müller, P.C.,Appl. Mech. Rev., 1993, vol. 46, no. 11, part 2, pp. S16-S164.

    Google Scholar 

  6. Kučera, V.,Kybernetika, 1986, vol. 22, no. 1, pp. 1–18.

    MathSciNet  Google Scholar 

  7. Yamada, I. and Luenberge, D.G.,IEEE Trans., on Automatic Control, 1985, vol. AC-30, no. 2, pp. 144–152.

    Article  Google Scholar 

  8. Kunkel, P. and Mehrmann, V.,Math. Control Signals Systems, 1997, vol. 10, no. 3, pp. 247–264.

    Article  MATH  MathSciNet  Google Scholar 

  9. Kalachev, L.V. and O’Malley, R.E.,Numer. Funct. Anal. and Optimiz., 1995, vol. 16, no. 3–4, pp. 363–378.

    Article  MATH  MathSciNet  Google Scholar 

  10. Gritsis, D.M., Pantelides, C.C., and Sardent, R.W.N.,SIAM J. Sci. Comput., 1995, vol. 16, no. 6, pp. 1349–1366.

    Article  MATH  MathSciNet  Google Scholar 

  11. Ascher, U. and Spiteri, R.,SIAM J. Sci. Comput., 1994, vol. 15, no. 4, pp. 938–952.

    Article  MATH  MathSciNet  Google Scholar 

  12. Müller. P.C.,Proc. Int. Symp. “Analysis and Synthesis of Nonlinear Dynamical Systems in Mechanics,” Riga, 1996, pp 102–113.

  13. Müller, P.C.,Appl. Math., and Comp. Sci., 1998, vol. 8, no. 2, pp. 269–286.

    MATH  Google Scholar 

  14. Jonckheere, E.,IEEE Trans., on Automatic Control, 1988, vol. AC-33, no. 5, pp. 491–495.

    Article  MathSciNet  Google Scholar 

  15. Lin Jing-Yue and Yang Zi-Hou,Int. J. Contr., 1988, vol. 47, no. 6, pp. 1915–1924.

    Article  MATH  MathSciNet  Google Scholar 

  16. Kurina, G.A.,Izv. RAN. Tekhnicheskaya kibernetika, 1992, no. 4, pp. 20–48.

  17. Krasovskii, N.N. and Letov, A.M.,Avtomat. Telemekh., 1962, vol. 23, no. 6, pp. 713–720.

    MathSciNet  Google Scholar 

  18. Krasovskii, N.N.,Teoriya upravleniya dvizheniem (Control Theory of Motion), Moscow, 1968.

  19. Lee, E.B. and Markus, L.,Foundations of Optimal Control Theory, New York: John Wiley, 1967. Translated under the titleOsnovy teorii optimal’nogo upravleniya, Moscow: Nauka, 1972.

    MATH  Google Scholar 

  20. Gol’shtein, E.G.,Teoriya dvoistvennosti v matematicheskom programmirovanii i ee prilozheniya (Duality Theory in Mathematical Programming and Its Applications), Moscow, 1971.

  21. Gantmakher, F.R.,Teoriya matrits (Theory of Matrices), Moscow, 1988.

  22. Afanas’ev, A.P., Dikusar, V.V., Milyutin, A.A., and Chukanov, S.A.,Neobkhodimye usloviya v optimal’nom upravlenii (Necessary Conditions in Optimal Control), Moscow, 1990.

  23. Robbins, H.,JOTA, 1980, vol. 31, no. 1, pp. 85–99.

    Article  MATH  MathSciNet  Google Scholar 

  24. Fuller, A.T.,Trudy I kongressa IFAK (Proc. of the First Congress of IFAC), Moscow, 1961, pp. 584–607.

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  1. Institute for Mathematics, National Academy of Sciences, Belarus

    O. I. Kostyukova

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  1. O. I. Kostyukova
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Kostyukova, O.I. An optimality criterion in a linear-quadratic optimal control problem for a descriptor system. Diff Equat 36, 1621–1627 (2000). https://doi.org/10.1007/BF02757362

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  • DOI: https://doi.org/10.1007/BF02757362

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