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Differential equations in control synthesis problems: I. Ordinary systems

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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, 1961.

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

  3. Bellman, R. and Kalaba, R., Dynamic Programming and Modern Control Theory, New York: Academic, 1965. Translated under the title Dinamicheskoe programmirovanie i sovremennaya teoriya upravleniya, Moscow, 1968.

    Google Scholar 

  4. Isaacs, R., Differential Games, New York, 1965.

  5. Kolmogorov, A.N., Izv. Akad. Nauk SSSR. Ser. Mat., 1941, vol. 5, pp. 3–14.

    Google Scholar 

  6. Wiener, N., Extrapolation, Interpolation and Smoothing of Stationary Time Series, Cambridge, 1949.

  7. Kalman, R.E., Trans. ASME, 1960, ser. D, vol. 82, pp. 35–45.

    Google Scholar 

  8. Krasovskii, N.N., Igrovye zadachi o vstreche dvizhenii (Game Problems on the Encounter of Motions), Moscow, 1970.

  9. Lee, E.B. and Markus, L., Foundations of Optimal Control Theory, New York, 1967.

  10. Leitmann, G., in Dynamical Systems and Microphysics: Control Theory and Mechanics, Blaquiere, A. and Leitmann, G., Eds., Orlando, 1984, pp. 119–141.

  11. Kurzhanskii, A.B., Upravlenie i nablyudenie v usloviyakh neopredelennosti (Control and Observation Under Conditions of Indeterminacy), Moscow, 1977.

  12. Pontryagin, L.S., Obyknovennye differentsial’nye uravneniya (Ordinary Differential Equations), Moscow, 1970.

  13. Fleming, W.H. and Soner, H.M., Controlled Markov Processes and Viscosity Solutions, New York, 1993.

  14. Bertsekas, D.P., Dynamic Programming and Stochastic Control, New York, 1975.

  15. Crandall, M.G., Evans, L.C., and Lions, P-L., Trans. Amer. Math. Soc., 1984, vol. 282, no.2, pp. 487–502.

    Google Scholar 

  16. Bardi, M. and Capuzzo-Dolcetta, I., Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Boston, 1997.

  17. Subbotin, A.I., Generalized Solutions of First-Order PDE’s. The Dynamical Optimization Perspective, Boston, 1995.

  18. Subbotina, N.N., Dokl. RAN, 2003, vol. 389, no.2, pp. 169–172.

    Google Scholar 

  19. Filippov, A.F., Differential Equations with Discontinuous Right-Hand Sides, Dordrecht, 1988.

  20. Panasyuk, A.I. and Panasyuk, V.I., Mat. Zametki, 1980, vol. 27, no.3, pp. 213–218.

    Google Scholar 

  21. Kurzhanski, A.B. and Fillippova, T.F., Advances in Nonlinear Dynamics and Control Ser. PSCT. 17, Boston, 1993, pp. 122–188.

  22. Krasovski, N.N. and Subbotin, A.N., Game-Theoretical Control Problems, New York, 1988.

  23. Zelikin, M.I. and Borisov, V.F., Theory of Chattering Control with Applications to Astronautics, Robotics, Economics and Engineering, 1994.

  24. Kurzhanski, A.B. and Varaiya, P., J. of Opt. Theory and Appl., 2001, no. 2, pp. 227–251.

  25. Kurzhanski, A.B. and Varaiya, P., Opt. Methods and Software. Taylor and Francis, 2002, vol. 17, pp. 177–237.

    Google Scholar 

  26. Gurman, V.I., Printsip rasshireniya v zadachakh upravleniya (The Extension Principle in Control Problems), Moscow, 1997.

  27. Kurzhanski, A.B. and Varaiya, P., in Variational Methods and Applications, Giannessi, F. and Maugeri, A., Eds., New York, 2004, pp. 613–627.

  28. Rockafellar, R.T. and Wets, R.J., Variational Analysis, New York, 1997.

  29. Clarke, F.H., Ledyaev, Yu.S., Stern, R.J., and Wolenski, P.R., Nonsmooth Analysis and Control Theory. Ser. GTM, 1998, vol. 178.

  30. Sethian, J.A., Level Set Methods and Fast Marching Methods, 2nd ed., Cambridge, 1999.

  31. Osher, S. and Fedkiw, R., Level Set Methods and Dynamic Implicit Surfaces. Ser. AMS, 2003, vol. 153.

  32. Guseinov, Kh.I., Moiseev, A.N., and Ushakov, V.N., Prikl. Mat. Mekh., 1998, no. 2, pp. 179–186.

  33. Patsko, V.S., Pyatko, S.G., and Fedotov, A.A., J. of Computer and Syst. Sc. Intl., 2003, vol. 42, no.3, pp. 320–328.

    Google Scholar 

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. B. Kurzhanskii

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  1. A. B. Kurzhanskii
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Translated from Differentsial’nye Uravneniya, Vol. 41, No. 1, 2005, pp. 12–22.

Original Russian Text Copyright © 2005 by Kurzhanskii.

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Kurzhanskii, A.B. Differential equations in control synthesis problems: I. Ordinary systems. Diff Equat 41, 10–21 (2005). https://doi.org/10.1007/s10625-005-0130-5

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  • DOI: https://doi.org/10.1007/s10625-005-0130-5

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