Obstructions to small time local controllability | Vidéo | Carmin.tv

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Obstructions to small time local controllability

By Karine Beauchard

Appears in collection : Inverse Problems and Control for PDEs and the Hamilton-Jacobi Equation / Problèmes inverses et contrôle des EDP, et équation de Hamilton-Jacobi

We study the small-time local controllability (STLC) for scalar input control affine systems, in finite dimension. It is known that the entire information about STLC is contained in the evaluation at zero of the Lie brackets of the vector fields. In the 80's, several authors formulated necessary conditions for controllability (obstructions), relying on particular 'bad' brackets. In this talk, I will present a unified approach to determine and prove obstructions to STLC, that allows to recover known obstructions and prove new ones, in a relatively systematic way. This approach relies on a recent Magnus-type representation of the state, a new Hall basis of the free Lie algebra over 2 generators and interpolation inequalities. This is a joint work with Frédéric Marbach and Jérémy Leborgne.

Information about the video

Date of recording 14/06/2022
Date of publication 11/07/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19933403
Cite this video Beauchard, Karine (14/06/2022). Obstructions to small time local controllability. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19933403
URL https://dx.doi.org/10.24350/CIRM.V.19933403

Domain(s)

Optimization and Control

Bibliography

BEAUCHARD, Karine et MARBACH, Frédéric. A unified approach of obstructions to small-time local controllability for scalar-input systems. arXiv preprint arXiv:2205.14114, 2022. - https://arxiv.org/abs/2205.14114

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