Optimization of the $H_\infty$-norm of Dynamic Flow Networks
Optimization and Control
2017-10-10 v1
Abstract
In this paper, we study the -norm of linear systems over graphs, which is used to model distribution networks. In particular, we aim to minimize the -norm subject to allocation of the weights on the edges. The optimization problem is formulated with LMI (Linear-Matrix-Inequality) constraints. For distribution networks with one port, i.e., SISO systems, we show that the -norm coincides with the effective resistance between the nodes in the port. Moreover, we derive an upper bound of the -norm, which is in terms of the algebraic connectivity of the graph on which the distribution network is defined.
Keywords
Cite
@article{arxiv.1710.03154,
title = {Optimization of the $H_\infty$-norm of Dynamic Flow Networks},
author = {Alexander Johansson and Jieqiang Wei and Henrik Sandberg and Karl H. Johansson and Jie Chen},
journal= {arXiv preprint arXiv:1710.03154},
year = {2017}
}