Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective

  title={Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective},
  author={Ulrike Baur and Peter Benner and Lihong Feng},
  journal={Archives of Computational Methods in Engineering},
In the past decades, Model Order Reduction (MOR) has demonstrated its robustness and wide applicability for simulating large-scale mathematical models in engineering and the sciences. [] Key Result Besides reviewing existing methods and the computational techniques needed to implement them, open issues are discussed, and some new results are proposed.

A New Framework for Model Reduction of Complex Nonlinear Dynamical Systems

This dissertation develops a framework which measures the robustness and persistency of reduced order models, and uses SOD to identify the dynamically relevant modal structures of the control system and extends the proposed approach to model order reduction of nonlinear control systems.

Model Order Reduction for Differential-Algebraic Equations: A Survey

This paper discusses the model order reduction problem for descriptor systems, that is, systems with dynamics described by differential-algebraic equations, and reviews efforts in extending popular methods related to balanced truncation and rational interpolation to descriptor systems.

A Critical Exposition of Model Order Reduction Techniques: Application to a Slewing Flexible Beam

This review paper deals with MOR by critically comparing the most popular MOR techniques from the fields of structural dynamics, numerical mathematics and systems and control, and a table summarizing their most important features is proposed.

On the use of modal derivatives for nonlinear model order reduction

Modal derivative is an approach to compute a reduced basis for model order reduction of large‐scale nonlinear systems that typically stem from the discretization of partial differential equations. In

Computation-Efficient Simulation of Nonlinear Thermal Boundary Conditions for Large-Scale Models

A simplified nonlinear system description is proposed by decoupling non linear affected states, performing MOR of the remaining linear term and apply calculated projection to the nonlinear affected part, which prospectively enables high-performance approximation of non linear system behavior.

Mathematical and Computer Modelling of Dynamical Systems Methods , Tools and Applications in Engineering and Related Sciences

Numerical examples demonstrate that the modified ERA algorithm with tangentially interpolated data produces accurate reduced models while, at the same time, reducing the computational cost and memory requirements significantly compared to the standard ERA.

An Error Bound for Low Order Approximation of Dynamical Systems Subjected to Initial Conditions

In recent years, a great effort has been taken focused on the development of reduced order modeling techniques of dynamical systems. This necessity is pushed by the requirement for efficient

A new approach to model reduction of nonlinear control systems using smooth orthogonal decomposition

A new approach to model order reduction of nonlinear control systems is aimed at developing persistent reduced order models (ROMs) that are robust to the changes in system's energy level. A



A Survey of Model Reduction Methods for Parametric Systems ∗

This paper surveys state-of-the-art methods in parametric model reduction, describing the different approaches within each class of methods for handling parametric variation and providing a comparative discussion that lend insights to potential advantages and disadvantages in applying each of the methods.

Projection-based approaches for model reduction of weakly nonlinear, time-varying systems

  • J. Phillips
  • Mathematics
    IEEE Trans. Comput. Aided Des. Integr. Circuits Syst.
  • 2003
This paper reports on experiences with extending model reduction techniques to nonlinear systems of differential-algebraic equations, specifically, systems representative of RF circuit components, relying generally on perturbational techniques to handle deviations from the linear time-invariant case.

H2 Model Reduction for Large-Scale Linear Dynamical Systems

A new unifying framework for the optimal $\mathcal{H}_2$ approximation problem is developed using best approximation properties in the underlying Hilbert space and leads to a new set of local optimality conditions taking the form of a structured orthogonality condition.

Piecewise polynomial nonlinear model reduction

A novel, general approach towards model-order reduction (MOR) on nonlinear systems that combines good global and local approximation properties and generalizes recent piecewise linear approaches and ties them with polynomial-based MOR, thereby combining their advantages.

Gramian-Based Model Reduction for Data-Sparse Systems

This work shows how to compute a reduced-order system with a balancing-related model reduction method, based on the computation of the cross-Gramian X, which is the solution of a Sylvester equation.

A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices

  • M. RewienskiJacob K. White
  • Computer Science, Engineering
    IEEE/ACM International Conference on Computer Aided Design. ICCAD 2001. IEEE/ACM Digest of Technical Papers (Cat. No.01CH37281)
  • 2001
This paper presents an approach to the nonlinear model reduction based on representing the non linear system with a piecewise-linear system and then reducing each of the pieces with a Krylov projection, and shows that the macromodels obtained are significantly more accurate than models obtained with linear or the recently developed quadratic reduction techniques.

Dimension Reduction of Large-Scale Systems

The aim of this book is to survey some of the most successful model reduction methods in tutorial style articles and to present benchmark problems from several application areas for testing and comparing existing and new algorithms.

NORM: compact model order reduction of weakly nonlinear systems

  • P. LiL. Pileggi
  • Mathematics
    Proceedings 2003. Design Automation Conference (IEEE Cat. No.03CH37451)
  • 2003
The results indicate that a multiple-point version of NORM can substantially reduce the model size and approach the ultimate model compactness that is achievable for nonlinear system reduction.

Balanced Truncation Model Reduction of Large and Sparse Generalized Linear Systems

This paper proposes a modification of the LR-ADI iteration to solve largescale generalized Lyapunov equations together with a practical convergence criterion, and several other implementation refinements to extend the applicability of balanced truncation to sparse systems with up to O(105) states.