Balanced Truncation Model Reduction for Systems with Inhomogeneous Initial Conditions
M. Heinkenschloss
Department of Computational and Applied Mathematics
Rice University
T. Reis
Institut für Mathematik
Technische Universität Berlin
A. C. Antoulas
Department of Electrical and Computer Engineering
Rice University
Automatica, 2011, Vol. 47, No. 3, pp. 559-564.
Abstract
We present a rigorous approach to extend balanced truncation model reduction (BTMR)
to systems with inhomogeneous initial conditions, we provide
estimates for the error between the input-output maps of the original and of the reduced initial value system, and
we illustrate numerically the superiority of our approach over the naive application of BTMR.
When BTMR is applied to linear time-invariant systems with inhomogeneous
initial conditions, it is crucial that the initial data are well represented by the subspaces generated by BTMR.
This requirement is often ignored or it is avoided by making the restrictive assumption that the initial data are zero.
To ensure that the initial data are well represented by the BTMR subspaces, we add auxiliary inputs determined
by the initial data. To obtain our error estimate, we approximate the contribution of the inhomogeneous initial
data by a suitable L2 input function.
Keywords
Balanced truncation, initial value problems, error bound, Hankel singular values.