On curvature and feedback classification of two-dimensional optimal control systems

Abstract : The goal of this paper is to extend the classical notion of Gaussian curvature of a two-dimensional Riemannian surface to two-dimensional optimal control systems with scalar input using Cartan's moving frame method. This notion was already introduced by A. A. Agrachev and R. V. Gamkrelidze for more general control systems using a purely variational approach. Further, we will see that the "control" analogue of Gaussian curvature reflects similar intrinsic properties of the extremal flow. In particular, if the curvature is negative, arbitrarily long segments of extremals are locally optimal. Finally, we will define and characterize flat control systems.
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Journal of Mathematical Sciences, Springer Verlag (Germany), 2007, 144 (1), http://dx.doi.org/10.1007/s10958-007-0237-8. 〈10.1007/s10958-007-0237-8〉
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https://hal.archives-ouvertes.fr/hal-00706056
Contributeur : Ulysse Serres <>
Soumis le : vendredi 8 juin 2012 - 18:00:39
Dernière modification le : jeudi 19 avril 2018 - 14:34:08

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Ulysse Serres. On curvature and feedback classification of two-dimensional optimal control systems. Journal of Mathematical Sciences, Springer Verlag (Germany), 2007, 144 (1), http://dx.doi.org/10.1007/s10958-007-0237-8. 〈10.1007/s10958-007-0237-8〉. 〈hal-00706056〉

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