Characterization of gradient control systems
Optimization and Control
2007-05-23 v1 Differential Geometry
Abstract
We investigate necessary and sufficient conditions under which a general nonlinear affine control system with outputs can be written as a gradient control system corresponding to some pseudo-Riemannian metric defined on the state space. The results rely on a suitable notion of compatibility of the system with respect to a given affine connection, and on the output behavior of the prolonged system and the gradient extension. The symmetric product associated with an affine connection plays a key role in the discussion.
Cite
@article{arxiv.math/0303371,
title = {Characterization of gradient control systems},
author = {Jorge Cortes and Arjan van der Schaft and Peter E. Crouch},
journal= {arXiv preprint arXiv:math/0303371},
year = {2007}
}
Comments
21 pages, no figures