# Geometry and analysis of control-affine systems: motion planning, heat and Schrödinger evolution

3 GECO - Geometric Control Design
Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR7641
Abstract : This thesis is dedicated to two problems arising from geometric control theory, regarding control-affine systems $\dot q= f_0(q)+\sum_{j=1}^m u_j f_j(q)$, where $f_0$ is called the drift. In the first part we extend the concept of complexity of non-admissible trajectories, well understood for sub-Riemannian systems, to this more general case, and find asymptotic estimates. Then, in the second part of the thesis, we consider a family of 2-dimensional driftless control systems. For these, we study how the set where the control vector fields become collinear affects the evolution of the heat and of a quantum particle with respect to the associated Laplace-Beltrami operator.
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Document type :
Theses

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Contributor : Dario Prandi <>
Submitted on : Wednesday, October 30, 2013 - 12:10:47 PM
Last modification on : Wednesday, March 27, 2019 - 4:08:31 PM
Long-term archiving on : Friday, April 7, 2017 - 7:12:17 PM

### Identifiers

• HAL Id : pastel-00878567, version 1

### Citation

Dario Prandi. Geometry and analysis of control-affine systems: motion planning, heat and Schrödinger evolution. Optimization and Control [math.OC]. Ecole Polytechnique X, 2013. English. ⟨pastel-00878567⟩

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