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The geometry of maximum principle. (English. Russian original) Zbl 1227.49026

Proc. Steklov Inst. Math. 273, 1-22 (2011); translation from Tr. Mat. Inst. Steklova 273, 5-27 (2011).
Summary: An invariant formulation of the maximum principle in optimal control is presented, and some second-order invariants are discussed.

MSC:

49K15 Optimality conditions for problems involving ordinary differential equations
34H05 Control problems involving ordinary differential equations
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References:

[1] A. A. Agrachev and R. V. Gamkrelidze, ”The Pontryagin Maximum Principle 50 Years Later,” Tr. Inst. Mat. Mekh., Ural. Otd. Ross. Akad. Nauk 12(1), 6–14 (2006) [Proc. Steklov Inst. Math., Suppl. 1, S4–S12 (2006)]. · Zbl 1122.49001
[2] R. V. Gamkrelidze, ”The Pontryagin Derivative in Optimal Control,” Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 268, 94–99 (2010) [Proc. Steklov Inst. Math. 268, 87–92 (2010)]. · Zbl 1208.49021
[3] A. A. Agrachev and Yu. L. Sachkov, Geometric Control Theory (Fizmatlit, Moscow, 2004); Engl. transl.: Control Theory from the Geometric Viewpoint (Springer, Berlin, 2004).
[4] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Fizmatgiz, Moscow, 1961; J. Wiley & Sons, New York, 1962).
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