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Journal of Mathematical Sciences

, Volume 135, Issue 4, pp 3224–3243 | Cite as

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

  • U. Serres
Article

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.

Keywords

Control System Gaussian Curvature Navigation Problem Optimal Control System Frame Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • U. Serres

There are no affiliations available

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