Error bounds for model reduction of feedback-controlled linear stochastic dynamics on Hilbert spaces

TL;DR

This paper develops and analyzes error bounds for structure-preserving model reduction techniques applied to feedback-controlled linear stochastic dynamics, including initial conditions and stochastic optimal control, with numerical validation.

Contribution

It introduces novel error bounds for model reduction of feedback-controlled stochastic systems with initial conditions and applies these to stochastic optimal control problems.

Findings

Derived new error bounds for reduced-order models with feedback control.

Validated bounds through numerical experiments.

Discussed applications to non-equilibrium statistical mechanics.

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.