Balanced Truncation Model Reduction with A Priori Error Bounds for LTI Systems with Nonzero Initial Value

by   Christian Schröder, et al.

In standard balanced truncation model order reduction, the initial condition is typically ignored in the reduction procedure and is assumed to be zero instead. However, such a reduced-order model may be a bad approximation to the full-order system, if the initial condition is not zero. In the literature there are several attempts for modified reduction methods at the price of having no error bound or only a posteriori error bounds which are often too expensive to evaluate. In this work we propose a new balancing procedure that is based on a shift transformation on the state. We first derive a joint projection reduced-order model in which the part of the system depending only on the input and the one depending only on the initial value are reduced at once and we prove an a priori error bound. With this result at hand, we derive a separate projection procedure in which the two parts are reduced separately. This gives the freedom to choose different reduction orders for the different subsystems. Moreover, we discuss how the reduced-order models can be constructed in practice. Since the error bounds are parameter-dependent we show how they can be optimized efficiently. We conclude this paper by comparing our results with the ones from the literature by a series of numerical experiments.


page 1

page 2

page 3

page 4


A time domain a posteriori error bound for balancing-related model order reduction

The aim in model order reduction is to approximate an input-output map d...

Effective error estimation for model reduction with inhomogeneous initial conditions

A priori error bounds have been derived for different balancing-related ...

Model Order Reduction for (Stochastic-) Delay Equations With Error Bounds

We analyze a structure-preserving model order reduction technique for de...

Model order reduction for bilinear systems with non-zero initial states – different approaches with error bounds

In this paper, we consider model order reduction for bilinear systems wi...

Full state approximation by Galerkin projection reduced order models for stochastic and bilinear systems

In this paper, the problem of full state approximation by model reductio...

Feedback control theory Model order reduction for stochastic equations

We analyze structure-preserving model order reduction methods for Ornste...

Low-dimensional approximations of high-dimensional asset price models

We consider high-dimensional asset price models that are reduced in thei...

Please sign up or login with your details

Forgot password? Click here to reset