Error bounds for model reduction of feedback-controlled linear stochastic dynamics on Hilbert spaces
Optimization and Control
2022-03-18 v2 Numerical Analysis
Dynamical Systems
Numerical Analysis
Abstract
We analyze structure-preserving model order reduction methods for Ornstein-Uhlenbeck processes and linear S(P)DEs with multiplicative noise based on balanced truncation. For the first time, we include in this study the analysis of non-zero initial conditions. We moreover allow for feedback-controlled dynamics for solving stochastic optimal control problems with reduced-order models and prove novel error bounds for a class of linear quadratic regulator problems. We provide numerical evidence for the bounds and discuss the application of our approach to enhanced sampling methods from non-equilibrium statistical mechanics.
Cite
@article{arxiv.1912.06113,
title = {Error bounds for model reduction of feedback-controlled linear stochastic dynamics on Hilbert spaces},
author = {Simon Becker and Carsten Hartmann and Martin Redmann and Lorenz Richter},
journal= {arXiv preprint arXiv:1912.06113},
year = {2022}
}
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