Complexity reduction of large-scale stochastic systems using linear quadratic Gaussian balancing
Abstract
In this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic systems are identified exploiting these Gramians. An associated balancing related scheme is proposed that removes unimportant information from the stochastic dynamics in order to obtain a reduced system. We show that this reduced model preserves important features like stabilizability and detectability. Additionally, a comprehensive error analysis based on eigenvalues of the Gramian pair product is conducted. This provides an a-priori criterion for the reduction quality which we illustrate in numerical experiments.
Cite
@article{arxiv.2303.13460,
title = {Complexity reduction of large-scale stochastic systems using linear quadratic Gaussian balancing},
author = {Tobias Damm and Martin Redmann},
journal= {arXiv preprint arXiv:2303.13460},
year = {2023}
}