Butcher series and control theory
Optimization and Control
2007-05-23 v1 Classical Analysis and ODEs
Abstract
We show how solutions of a non--linear differential equation can be written as sum indexed by planar trees: the Butcher series. Then we use that property in order to control non--linear differential equation. We show that if the linearized system is controllable then the system itself is controllable if the nonlinear term is small enough and we express explicitly the control as a sum indexed by planar tree which each terms is obtained by minimization of a functional.
Keywords
Cite
@article{arxiv.math/0603133,
title = {Butcher series and control theory},
author = {Dikanaina Harrivel},
journal= {arXiv preprint arXiv:math/0603133},
year = {2007}
}
Comments
14 pages, 3 figures