Stability preservation in Galerkin-type projection-based model order reduction
For engineers and scientists using model order reduction, this work offers a method to preserve stability, a known issue, but the approach is incremental.
This paper addresses instability in Galerkin-type projection-based model order reduction for linear and nonlinear dynamical systems. It proposes a transformation that guarantees asymptotic stability of the reduced system, requiring a high-dimensional Lyapunov equation, and provides an efficient iterative approximation. Numerical results demonstrate computational feasibility.
We consider linear dynamical systems consisting of ordinary differential equations with high dimensionality. The aim of model order reduction is to construct an approximating system of a much lower dimension. Therein, the reduced system may be unstable, even though the original system is asymptotically stable. We focus on projection-based model order reduction of Galerkin-type. A transformation of the original system guarantees an asymptotically stable reduced system. This transformation requires the numerical solution of a high-dimensional Lyapunov equation. We specify an approximation of the solution, which allows for an efficient iterative treatment of the Lyapunov equation under a certain assumption. Furthermore, we generalise this strategy to preserve the asymptotic stability of stationary solutions in model order reduction of nonlinear dynamical systems. Numerical results for high-dimensional examples confirm the computational feasibility of the stability-preserving approach.