Geodesic
A numerical method for approximate calculation of the value function in the optimal control problem with a terminal functional
Numerical methods and programming, Tome 5 (2004) no. 1, pp. 240-251

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The optimal control problem with a terminal functional is considered. A numerical method for calculation of the value function is proposed. This method is based on Pontryagin' principle. The convergence of the method is proved. Some error estimates are given, depending on the method' parameters. A method is proposed for constructing a program optimal control ensuring the near-optimal functional value.
Keywords: optimal control, value function, Bellman function, Pontryagin maximum principle. 
@article{VMP_2004_5_1_a22,
     author = {D. V. Kamzolkin},
     title = {A numerical method for approximate calculation of the value function in the optimal control problem with a terminal functional},
     journal = {Numerical methods and programming},
     pages = {240--251},
     publisher = {mathdoc},
     volume = {5},
     number = {1},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2004_5_1_a22/}
}
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D. V. Kamzolkin. A numerical method for approximate calculation of the value function in the optimal control problem with a terminal functional. Numerical methods and programming, Tome 5 (2004) no. 1, pp. 240-251. http://geodesic.mathdoc.fr/item/VMP_2004_5_1_a22/