Balanced truncation and singular perturbation approximation model order reduction for stochastically controlled linear systems
For researchers in stochastic systems and model order reduction, this paper provides a theoretical foundation and error bounds for reducing the complexity of stochastically controlled linear systems.
This work extends balanced truncation and singular perturbation approximation model order reduction techniques to linear stochastic differential equations with additive Lévy noise, providing theoretical tools and error bounds, with numerical results supporting the theory.
When solving linear stochastic differential equations numerically, usually a high order spatial discretisation is used. Balanced truncation (BT) and singular perturbation approximation (SPA) are well-known projection techniques in the deterministic framework which reduce the order of a control system and hence reduce computational complexity. This work considers both methods when the control is replaced by a noise term. We provide theoretical tools such as stochastic concepts for reachability and observability, which are necessary for balancing related model order reduction of linear stochastic differential equations with additive Lévy noise. Moreover, we derive error bounds for both BT and SPA and provide numerical results for a specific example which support the theory.