Control Sets for Affine Systems, Spectral Properties and Projective Spaces
Optimization and Control
2023-05-23 v2
Abstract
For affine control systems with bounded control range the control sets, i.e., the maximal subsets of complete approximate controllability, are studied using spectral properties. For hyperbolic systems there is a unique control set with nonvoid interior and it is bounded. For nonhyperbolic systems, these control sets are unbounded. In an appropriate compactification of the state space there is a unique chain control set and the relations to the homogenous part of the control system are worked out.
Cite
@article{arxiv.2201.05014,
title = {Control Sets for Affine Systems, Spectral Properties and Projective Spaces},
author = {Fritz Colonius and Alexandre J. Santana and Juliana Setti},
journal= {arXiv preprint arXiv:2201.05014},
year = {2023}
}
Comments
corrected version 27 pages