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

Understand

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.