Balanced Truncation Model Reduction for Lifted Nonlinear Systems

TL;DR

This paper introduces a balanced truncation model reduction method for nonlinear systems transformed into quadratic-bilinear form, demonstrating improved accuracy over traditional methods on a reactor model.

Contribution

It extends QB balanced truncation to lifted nonlinear systems with zero eigenvalues, enabling more accurate reduced models.

Findings

Reduced models outperform proper orthogonal decomposition in accuracy.

Multi-stage lifting effectively transforms nonlinear systems for model reduction.

Approach applicable to systems with time-varying and uncertain inputs.

Abstract

We present a balanced truncation model reduction approach for a class of nonlinear systems with time-varying and uncertain inputs. First, our approach brings the nonlinear system into quadratic-bilinear~(QB) form via a process called lifting, which introduces transformations via auxiliary variables to achieve the specified model form. Second, we extend a recently developed QB balanced truncation method to be applicable to such lifted QB systems that share the common feature of having a system matrix with zero eigenvalues. We illustrate this framework and the multi-stage lifting transformation on a tubular reactor model. In the numerical results we show that our proposed approach can obtain reduced-order models that are more accurate than proper orthogonal decomposition reduced-order models in situations where the latter are sensitive to the choice of training data.