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Geometry and feedback classification of low-dimensional non-linear control systems

Abstract : The purpose of this thesis is the study of the local and global differential geometry of fully nonlinear smooth control systems on two-dimensional smooth manifolds. We are particularly interested in the feedback-invariants of such systems.

In a first part we will use the Cartan's moving frame method in order to determine these invariants and we will see that one of the most important feedback-invariants is the control analogue to the Gaussian curvature of a surface. As we will explain it, the control curvature reveals very precious information on the optimal synthesis of time optimal problems.

In a second part we will construct some microlocal normal forms for time optimal control systems and we will characterize in an intrinsic manner the flat systems. Finally, we will deal with global features; in particular we will see how to generalize the Gauss-Bonnet theorem for control systems on surfaces without boundary.
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https://tel.archives-ouvertes.fr/tel-00172902
Contributor : Ulysse Serres <>
Submitted on : Tuesday, September 18, 2007 - 2:17:00 PM
Last modification on : Friday, July 17, 2020 - 2:54:04 PM
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  • HAL Id : tel-00172902, version 1

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Ulysse Serres. Geometry and feedback classification of low-dimensional non-linear control systems. Mathematics [math]. Université de Bourgogne, 2006. English. ⟨tel-00172902⟩

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