Balanced Truncation Model Reduction for Lifted Nonlinear Systems

2019/07/28 by Boris Kramer, Karen Willcox, Kramer, Boris +1 · 2 citations
Physics and Astronomy · Mathematics · Engineering · #Model Reduction and Neural Networks #Numerical methods for differential equations #Vibration Control and Rheological Fluids

paper · pdf · doi:10.48550/arxiv.1907.12084

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.

Cited by

• Signature-Based Universal Bilinear Approximations for Nonlinear Systems and Model Order Reduction
• Structure-preserving Lift & Learn: Scientific machine learning for nonlinear conservative partial differential equations

Related

• Balanced truncation for model order reduction of linear dynamical\n systems with quadratic outputs
• Balanced Truncation Model Order Reduction For Quadratic-Bilinear Control Systems
• Balanced Truncation of Linear Systems with Quadratic Outputs in Limited Time and Frequency Intervals
• Balanced truncation model reduction for symmetric second order systems -- A passivity-based approach
• BT_INHOM -- MATLAB routines for balanced truncation model reduction for systems with nonzero initial value