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On the continuity of the Bellman function in an optimal control problem with monotone dynamics

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References

  1. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes), Moscow: Nauka, 1969.

    Google Scholar 

  2. Lee, E.B. and Markus, L., Foundations of Optimal Control Theory, New York: John Wily & Sons, 1967. Translated under the title Osnovy teorii optimal’nogo upravleniya, Moscow: Nauka, 1972.

    MATH  Google Scholar 

  3. Filippov, A.F., Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1959, vol. 2, no. 1, pp. 25–32.

    Google Scholar 

  4. Matrosov, V.M., Anapol’skii, L.Yu., and Vasil’ev, S.N., Metod sravneniya v matematicheskoi teorii sistem (The Comparison Method in Mathematical Theory of Systems), Novosibirsk: Nauka, 1980.

    Google Scholar 

  5. Matrosov, V.M., Metod funktsii Lyapunova: analiz dinamicheskikh svoistv nelineinykh sistem (The Method of Lyapunov Functions in Analysis of Dynamics of Nonlinear Systems), Moscow: Fizmatlit, 2001.

    Google Scholar 

  6. Cesari, L., Optimization Theory and Applications. Problems with Ordinary Differential Equations, New York, 1983.

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

    Google Scholar 

  8. Kolmogorov, A.N. and Fomin, S.V., Elementy teorii funktsii i funktsional’nogo analiza (Elements of the Theory of Functions and Functional Analysis), Moscow: Nauka, 1989.

    Google Scholar 

  9. Ashmanov, S.A., Vvedenie v matematicheskuyu ekonomiku (Introduction to Mathematical Economics), Moscow: Nauka, 1984.

    Google Scholar 

  10. Intriligator, M.D., Mathematical Optimization and Economic Theory, Prentice Hall, Englewood Cliffs, 1971. Translated under the title Matematicheskie metody optimizatsii i ekonomicheskaya teoriya, Moscow: Airis, 2002.

    Google Scholar 

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Original Russian Text © M.S. Nikol’skii, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 11, pp. 1491–1496.

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Nikol’skii, M.S. On the continuity of the Bellman function in an optimal control problem with monotone dynamics. Diff Equat 43, 1529–1535 (2007). https://doi.org/10.1134/S0012266107110080

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  • DOI: https://doi.org/10.1134/S0012266107110080

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