Abstract
A theorem published earlier by the author is strengthened and a more informative necessary condition for an extremum in optimal control problems is obtained. The result is illustrated by a simple optimal control problem.
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References
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko,The Mathematical Theory of Optimal Processes [in Russian], Nauka, Moscow (1976).
M. F. Sukhinin, “On an analog of Bellman’s equation,”Mat. Zametki, [Math. Notes],38, No. 2, 267–271 (1985).
M. F. Sukhinin,Selected Topics in Nonlinear Analysis [in Russian], Izd. Russian Peoples’ Frindship Univ., Moscow (1992).
V. G. Boltyanskii, “Sufficient conditions for optimality and the justification of the dynamical programming approach,”Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv],28, No. 3, 481–514 (1964).
M. G. Crandall and P.-L. Lions, “Viscosity solutions of Hamilton-Jacobi equations,”Trans. Amer. Math. Soc.,277, 1–42 (1983).
A. I. Subbotin,Minimax Inequalities and Hamilton-Jacobi Equations [in Russian], Nauka, Moscow (1991).
A. D. Ioffe and V. M. Tikhomirov,The Theory of Extremum Problems [in Russian], Nauka, Moscow (1974).
E. B. Lee and L. Marcus,Foundations of Optimal Control Theory. J. Wiley, New York-London (1969).
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Translated fromMatematicheskie Zametki, Vol. 66, No. 5, pp. 770–776, November, 1999.
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Sukhinin, M.F. On Bellman’s approach to optimal control theory. Math Notes 66, 636–641 (1999). https://doi.org/10.1007/BF02674205
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DOI: https://doi.org/10.1007/BF02674205