Abstract:
A new numerical method is suggested for constructing the value function in optimal control problems of prescribed duration with positional running cost along motions of controlled dynamical systems. The algorithm is based on a backward procedure involving characteristics of the Bellman equation. Estimations of the approximation are provided. Results of simulations for a model example are exposed.
Citation:
N. N. Subbotina, T. B. Tokmantsev, “A numerical method for the minimax solution of the Bellman equation in the Cauchy problem with additional restrictions”, Dynamical systems: modeling, optimization, and control, Trudy Inst. Mat. i Mekh. UrO RAN, 12, no. 1, 2006, 208–215; Proc. Steklov Inst. Math. (Suppl.), 253, suppl. 1 (2006), S221–S228
\Bibitem{SubTok06}
\by N.~N.~Subbotina, T.~B.~Tokmantsev
\paper A~numerical method for the minimax solution of the Bellman equation in the Cauchy problem with additional restrictions
\inbook Dynamical systems: modeling, optimization, and control
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2006
\vol 12
\issue 1
\pages 208--215
\mathnet{http://mi.mathnet.ru/timm144}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2247237}
\zmath{https://zbmath.org/?q=an:1122.49026}
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2006
\vol 253
\issue , suppl. 1
\pages S221--S228
\crossref{https://doi.org/10.1134/S0081543806050166}
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https://www.mathnet.ru/eng/timm144
https://www.mathnet.ru/eng/timm/v12/i1/p208
This publication is cited in the following 4 articles:
Subbotina N.N., Tokmantsev T.B., “On Grid Optimal Feedbacks to Control Problems of Prescribed Duration on the Plane”, Advances in Dynamic Games: Theory, Applications, and Numerical Methods for Differential and Stochastic Games: Dedicated to the Memory of Arik a. Melikyan, Annals of the International Society of Dynamic Games, 11, eds. Breton M., Szajowski K., Birkhauser Boston, 2011, 133–147
N. N. Subbotina, T. B. Tokmantsev, “Estimating error of the optimal grid design in the problems of nonlinear optimal control of prescribed duration”, Autom. Remote Control, 70:9 (2009), 1565–1578
N. N. Subbotina, T. B. Tokmantsev, “Optimal Synthesis in a Control Problem with Lipschitz Input Data”, Proc. Steklov Inst. Math., 262 (2008), 231–243
Alexander M. Tarasyev, Vladimir N. Ushakov, Nina N. Subbotina, “Positional procedures for solving dynamical optimization problems of prescribed duration”, IFAC Proceedings Volumes, 41:2 (2008), 11334
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