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On the curvature of two-dimensional optimal control systems and Zermelo's navigation problem

Abstract : The goal of this paper is to extend the notion of Gaussian curvature of two-dimensional surfaces to nonlinear time-optimal control systems in the plane by applying the moving frame method. This notion of curvature was introduced earlier by A. A. Agrachev and R. V. Gamkrelidze by means of Jacobi curves. Here we give a self-contained presentation of its two-dimensional version and apply the results to the well-known Zermelo navigation problem.
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https://hal.archives-ouvertes.fr/hal-00706054
Contributor : Ulysse Serres <>
Submitted on : Friday, June 8, 2012 - 5:54:42 PM
Last modification on : Thursday, November 21, 2019 - 2:08:57 AM

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Ulysse Serres. On the curvature of two-dimensional optimal control systems and Zermelo's navigation problem. Journal of Mathematical Sciences, Springer Verlag (Germany), 2006, 135 (4), http://dx.doi.org/10.1007/s10958-006-0153-3. ⟨10.1007/s10958-006-0153-3⟩. ⟨hal-00706054⟩

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