On curvature and feedback classification of two-dimensional optimal control systems - Archive ouverte HAL Access content directly
Journal Articles Journal of Mathematical Sciences Year : 2007

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.

Dates and versions

hal-00706056 , version 1 (08-06-2012)

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Ulysse Serres. On curvature and feedback classification of two-dimensional optimal control systems. Journal of Mathematical Sciences, 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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