Model order reduction for object-oriented models: a control systems perspective

References

• Casella , F. , Donida , F. and Lovera , M. 2008 . Beyond simulation: computer aided control system design using equation-based object oriented modelling for the next necade . 2nd International Workshop on Equation-Based Object-Oriented Languages and Tools . July 8 2008 , Paphos, Cyprus. pp. 35 – 45 . Linköping University Electronic Press .
   Google Scholar
• Feng , L. 2005 . Review of model order reduction methods for numerical simulation of nonlinear circuits . Appl. Math. Comput , 167 : 576 – 591 .
   Web of Science ®Google Scholar
• Feng , L. 2005 . Parameter independent model order reduction . Math. Comput. Simulat , 68 : 221 – 234 .
   Google Scholar
• Dong , N. and Roychowdhury , J. 2008 . General-purpose nonlinear model-order reduction using piecewise-polynomial representations . IEEE Trans. Computer-Aided Des. Int. Circuits Syst. , 27 : 249 – 264 .
   Google Scholar
• Schwarz , P. , Bastian , J. , Clauss , C. , Haase , J. , öhler , A. K , Otte , G. and Schneider , P. 2007 . A tool-box approach to computer-aided generation of reduced-order models . EUROSIM 2007 . September 2007 , Ljubljana, Slovenia. pp. 9 – 13 . EUROSIM .
   Google Scholar
• Sommer , R. , Halfmann , T. and Broz , J. 2008 . Automated behavioral modeling and analytical model-order reduction by application of symbolic circuit analysis for multi-physical systems . Simul. Model. Pract. Theory , 16 : 1024 – 1039 .
   Google Scholar
• Mattsson , S.E. , Elmqvist , H. and Otter , M. 1998 . Physical system modeling with Modelica . Control Eng. Pract , 6 : 501 – 510 .
   Google Scholar
• Fritzson , P. 2004 . Principles of Object-Oriented Modeling and Simulation with Modelica 2.1 , Piscataway, NJ : 1 Wiley-IEEE Press .
   Google Scholar
• The Modelica Association, Modelica Home Page. Available at http://www.modelica.org (http://www.modelica.org)
   Google Scholar
• Mattsson , S.E. and öderlind , G. S . 1993 . Index reduction in differential-algebraic equations using dummy derivatives . SIAM J. Sci. Comput , 14 : 677 – 692 .
   Web of Science ®Google Scholar
• Ljung , L. 2008 . Perspectives on system identification . 17th IFAC World Congress . July 2008 , Seul, South Korea. pp. 6 – 11 . Curran Associates, Inc .
   Google Scholar
• Casella , F. and Lovera , M. 2008 . LPV/LFT modelling and identification: overview, synergies and a case study . 2nd IEEE Multi-conference on Systems and Control . September 2008 , San Antonio, Texas, USA. pp. 3 – 5 . IEEE .
   Google Scholar
• Qin , S.J. and Badgwell , T.A. 2003 . A survey of industrial model predictive control technology . Control Eng. Pract. , 11 : 733 – 764 .
   Web of Science ®Google Scholar
• Zhou , K. , Doyle , J.C. and Glover , K. 1996 . Robust and Optimal Control , Englewood Cliffs, NJ : Prentice-Hall .
   Google Scholar
• Hsu , K. , Vincent , T. , Wolodkin , G. , Rangan , S. and Poolla , K. 2008 . An LFT approach to parameter estimation . Automatica , 44 : 3087 – 3092 .
   Google Scholar
• Casella , F. , Donida , F. and Lovera , M. Automatic generation of LFTs from object-oriented non-linear models with uncertain parameters . MATHMOD 2009, ARGESIM Report no. 35 . 2009 . Vienna, Austria, 11–13 February
   Google Scholar
• Casella , F. , Donida , F. and Lovera , M. 2008 . Automatic generation of LFTs from object-oriented Modelica models . 2nd IEEE Multi-Conference on Systems and Control . September 2008 , San Antonio, Texas, USA. pp. 3 – 5 . IEEE .
   Google Scholar
• Magni , J.F. 2006 . User manual of the Linear Fractional Representation Toolbox, version 2.0 , ONERA : TR 5/10403.01F DCSD .
   Google Scholar
• Leith , D.J. and Leithead , W.E. 2000 . Survey of gain-scheduling analysis and design . Int. J. Control , 73 : 1001 – 1025 .
   Web of Science ®Google Scholar
• Rugh , W. and Shamma , J. 2000 . Research on gain scheduling . Automatica , 36 : 1401 – 1425 .
   Web of Science ®Google Scholar
• Rewiénski , M. and White , J. 2006 . Model order reduction for nonlinear dynamical systems based on trajectory piecewise-linear approximations . Linear Algebra Appl. , 415 : 426 – 454 .
   Web of Science ®Google Scholar
• Rewiénski , M. and White , J. 2002 . A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices . IEEE Trans. Computer-Aided Des. Int. Circuits Syst. , 22 : 155 – 170 .
   Google Scholar
• Bond , B. and Daniel , L. 2007 . A piecewise-linear moment-matching approach to parameterized model-order reduction for highly nonlinear systems . IEEE Trans. Computer-Aided Design of Integrated Circuits Syst. , 26 : 2116 – 2129 .
   Google Scholar
• Muscato , G. 2000 . Parametric generalized singular perturbation approximation for model order reduction . IEEE Trans. Automatic Control , 45 : 339 – 343 .
   Google Scholar
• Shi , G. and Shi , C.J.R. 2005 . Model-order reduction by dominant subspace projection: error bound, subspace computation and circuit applications . IEEE Trans. Circuits Syst. , 52 : 975 – 993 .
   Google Scholar
• Wong , N. , Balakrishnan , V. , Koh , C. and Ng , T. 2006 . Two algorithms for fast and accurate passivity-preserving model order reduction . IEEE Trans. Computer-Aided Des. Int. Circuits Syst. , 25 : 2062 – 2075 .
   Web of Science ®Google Scholar
• Rathinam , M. and Petzold , L. 2003 . A new look at proper orthogonal decomposition . SIAM J. Num. Anal. , 41 : 1893 – 1925 .
   Web of Science ®Google Scholar
• Rugh , W. 1981 . Nonlinear System Theory-The Volterra Wiener Approach , Baltimore, MD : Johns Hopkins University Press .
   Google Scholar
• Roychowdhury , J. Reduced-order modelling of linear time-varying systems . IEEE/ACM international conference on Computer-aided design ICCAD '98 . New York, NY. pp. 92 – 95 . San Jose, CA : ACM .
   Google Scholar
• Phillips , J. 2000 . Projection frameworks for model reduction of weakly nonlinear systems . IEEE Design Automation Conference . June 2000 , Los Angeles, CA. pp. 5 – 9 . 184 – 189 . IEEE .
   Google Scholar
• Li , P. and Pileggi , L.T. 2003 . NORM: compact model order reduction of weakly nonlinear systems . Design Automation Conference . June 2003 , Anaheim, CA. pp. 2 – 6 . 472 – 477 . IEEE .
   Google Scholar
• Salimbahrami , B. and Lohmann , B. 2004 . A simulation-free nonlinear model order-reduction approach and comparison study . Math. Computer Model. Dyn. Syst. , 10 : 317 – 329 .
   Web of Science ®Google Scholar
• Eitelberg , E. 1981 . Model reduction by minimizing the weighted equation error . Int. J. Control , 34 : 1113 – 1123 .
   Web of Science ®Google Scholar
• Wichmann , R. , Popp , R. , Hartong , W. and Hedrich , L. 1999 . On the simplification of nonlinear DAE systems in analog circuit design . 2nd Workshop on Computer Algebra in Scientific Computing, CASC ‘99 . June 1999 , Munich, Germany. 31 May–4 . Springer Verlag .
   Google Scholar
• Mikelsons , L. , Ji , H. , Brandt , T. and Lenord , O. 2009 . Symbolic model reduction applied to realtime simulation of a construction Machine . 7th International Modelica Conference . September 2009 , Como, Italy. pp. 20 – 22 . Modelica Association .
   Google Scholar
• Halfmann , T. and Wichmann , T. 2006 . “ Symbolic methods in industrial analog circuit design ” . In Scientific Computing in Electrical Engineering , Edited by: Anile , A.M. , Ali , G. and Mascali , G. Springer Heidelberg .
   Google Scholar
• Ascher , U.M. and Petzold , L.R. 1998 . Computer Methods for Ordinary Diferential Equations and Differential-Algebraic Equations , Philadelphia, PA : SIAM .
   Google Scholar
• Loucas , L.S. and Stein , J.L. 1999 . Energy-based model reduction of linear systems . 4th International Conference on Bond Graph Modeling and Simulation ICBGM'99 . January 1999 , Francisco, CA. pp. 17 – 20 . SCS Publishing, San .
   Google Scholar
• Loucas , L.S. and Yildir , U.B. 2006 . Modelling and reduction techniques for studies of integrated hybrid vehicle systems . Math. Computer Model. Dyn. Syst. , 12 : 203 – 218 .
   Google Scholar