INNER AND OUTER CAPTURE BASIN APPROXIMATION WITH SUPPORT VECTOR MACHINES

Laetitia Chapel, Guillaume Deffuant

2011

Abstract

We propose a new approach to solve target hitting problems, that iteratively approximates capture basins at successive times, using a machine learning algorithm trained on points of a grid with boolean labels. We consider two variants of the approximation (from inside and from outside), and we state the conditions on the machine learning procedure that guarantee the convergence of the approximations towards the actual capture basin when the resolution of the grid decreases to 0. Moreover, we define a control procedure which uses the set of capture basin approximations to drive a point into the target. When using the inner approximation, the procedure guarantees to hit the target, and when the resolution of the grid tends to 0, the controller tends to the optimal one (minimizing time to hit the target). We use Support Vector Machines as a particular learning method, because they provide parsimonious approximations, from which one can derive fast and efficient controllers. We illustrate the method on two simple examples, Zermelo and car on the hill problems.

Paper Citation

in Harvard Style

Chapel L. and Deffuant G. (2011). INNER AND OUTER CAPTURE BASIN APPROXIMATION WITH SUPPORT VECTOR MACHINES . In Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-8425-74-4, pages 34-40. DOI: 10.5220/0003536000340040

in Bibtex Style

@conference{icinco11,
author={Laetitia Chapel and Guillaume Deffuant},
title={INNER AND OUTER CAPTURE BASIN APPROXIMATION WITH SUPPORT VECTOR MACHINES},
booktitle={Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2011},
pages={34-40},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003536000340040},
isbn={978-989-8425-74-4},
}

in EndNote Style

TY - CONF
JO - Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - INNER AND OUTER CAPTURE BASIN APPROXIMATION WITH SUPPORT VECTOR MACHINES
SN - 978-989-8425-74-4
AU - Chapel L.
AU - Deffuant G.
PY - 2011
SP - 34
EP - 40
DO - 10.5220/0003536000340040