Parametrization of the regular equivalences of the canonical controller and its applications
Abstract
We study control problems for linear systems in the behavioral framework. Our focus is a class of regular controllers that are equivalent to the canonical controller. The canonical controller is a particular controller that is guaranteed to be a solution whenever a solution exists. However, it has been shown that in most cases, the canonical controller is not regular. The main result of the paper is a parametrization of all regular controllers that are equivalent to the canonical controller. The parametrization is then used to solve two control problems. The first problem is related to designing a regular controller that uses as few control channels as possible. The second problem is to design a regular controller that satisfies a predefined input-output partitioning constraint. In both problems, based on the parametrization, we present algorithms that does the controller design.
Keywords
Cite
@article{arxiv.0708.1309,
title = {Parametrization of the regular equivalences of the canonical controller and its applications},
author = {A. A. Julius and J. W. Polderman and A. J. van der Schaft},
journal= {arXiv preprint arXiv:0708.1309},
year = {2007}
}
Comments
submitted to IEEE Trans. Automatic Control. The title has been changed from the previous arXiv version to avoid confusion with the submitted version