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Interpolatory Model Reduction of Large-Scale Dynamical Systems

  • Athanasios C. Antoulas
  • Christopher A. Beattie
  • Serkan Gugercin
Chapter

Abstract

Large scale dynamical systems are a common framework for the modeling and control of many complex phenomena of scientific interest and industrial value, with examples of diverse origin that include signal propagation and interference in electric circuits, storm surge prediction before an advancing hurricane, vibration suppression in large structures, temperature control in various media, neurotransmission in the nervous system, and behavior of micro-electro-mechanical systems. Direct numerical simulation of underlying mathematical models is one of few available means for accurate prediction and control of these complex phenomena. The need for ever greater accuracy compels inclusion of greater detail in the model and potential coupling to other complex systems leading inevitably to very large-scale and complex dynamical models. Simulations in such large-scale settings can make untenable demands on computational resources and efficient model utilization becomes necessary. Model reduction is one response to this challenge, wherein one seeks a simpler (typically lower order) model that nearly replicates the behavior of the original model. When high fidelity is achieved with a reduced-order model, it can then be used reliably as an efficient surrogate to the original, perhaps replacing it as a component in larger simulations or in allied contexts such as development of simpler, faster controllers suitable for real time applications.

Keywords

Transfer Function Interpolation Problem Interpolation Point Sparse Grid Linear Dynamical System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Athanasios C. Antoulas
    • 1
  • Christopher A. Beattie
    • 2
  • Serkan Gugercin
    • 2
  1. 1.Department of Electrical and Computer EngineeringRice UniversityHoustonUSA
  2. 2.Department of MathematicsVirginia TechBlacksburgUSA

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