×
Agrachev, A. A.; Gamkrelidze, R. V.

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.

Cited in 3 Documents

MSC:

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

Keywords:

differential-geometric method; invariant formulation of maximum principle; optimal control; second-order invariants
PDF BibTeX XML Cite
\textit{A. A. Agrachev} and \textit{R. V. Gamkrelidze}, Proc. Steklov Inst. Math. 273, 1--22 (2011; Zbl 1227.49026); translation from Tr. Mat. Inst. Steklova 273, 5--27 (2011)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

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).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.