Tahavori, Maryamsadat

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    Aalborg UniversitetContributions to the model order reduction of large-scale dynamical systemsTahavori, MaryamsadatPublication date:2013Document VersionAccepted author manuscript, peer reviewed versionLink to publication from Aalborg UniversityCitation for published version (APA):Tahavori, M. (2013). Contributions to the model order reduction of large-scale dynamical systems.General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            ? Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            ? You may not further distribute the material or use it for any profit-making activity or commercial gain            ? You may freely distribute the URL identifying the publication in the public portal ?Take down policyIf you believe that this document breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will remove access tothe work immediately and investigate your claim.Downloaded from vbn.aau.dk on: December 27, 2020Contributions to the model order reduction of large‐scale dynamical systems 24 December, 2013  The accurate mathematical modeling of natural and man‐made processes  leads  to models of high complexity. The simulation, analysis, control, design and implementation of the systems of high  orders  are  difficult  and  costly  if  at  all  possible.  To  cope with  these  problems,  suitable methods  for model order reduction are required. Over the past  few decades, there has been increasing  interest  in  the  methods  which  reduce  the  order  of  dynamical  systems  while preserving the input‐output behavior and important features [1]‐[3].   The model  reduction  techniques  can  be  divided  into  two  broad  categories:  singular  value decomposition  (SVD) based methods and  the moment matching based  techniques. The SVD‐based methods have a guaranteed upper bound for the approximation error and they usually preserve  the  stability of  the original model  in  the  reduction process.  The moment matching based methods are usually more efficient computationally, but they have no guaranteed error bound. The stability of the reduced order model is not guaranteed when these methods apply [1]‐[3]. The balanced model reduction  introduced  in [4]  is one of the most common model reduction schemes. To  apply balanced  truncation,  the  system  is  first  represented  in  a basis where  the states which are difficult  to  reach are  simultaneously difficult  to observe. This  is achieved by simultaneously  diagonalizing  the  controllability  and  the  observability  gramians,  which  are solutions  to  the  controllability  and  the observability  Lyapunov  equations.  Then,  the  reduced model is obtained by truncating the states which have this property. Balanced model reduction method  is  modified  and  developed  from  different  viewpoints  [1]‐[12].  The  time‐interval balanced  truncation  is  among  the  methods  which  improves  the  accuracy  of  the  ordinary balanced  truncation  [5],  [6],  [10]. The  frequency‐interval balanced  truncation  is another well‐known method which  improves  the accuracy of  the ordinary balanced  truncation  [5],  [7]‐[9], [13].  In  both  classes  of  techniques  which  improve  the  accuracy  of  the  ordinary  balanced reduction  gramian  plays  a  key  role.  The  gramians  are  matrices  with  the  embedded controllability  and  observability  information.  The  controllability  and  observability  gramians were  first  introduced  in  [14]  and  [15]  and more  recently  in  [4].  It  is  well‐known  that  the controllability  gramian  shows  the  level  of  controllability.  Similarly,  the  observability  gramian contains  information  of  the  level  of  observability  for  a  system.  Apart  from  the well‐known application of gramians  in model reduction, they have been extended and have been used  in applications such as control configuration selection [16]‐[22].   References: 1. C. Antoulas, Approximation of Large-Scale Dynamical Systems, Advances in Design and Control. Philadelphia: SIAM, 2005. 2. G. Obinata, and B. D. O. Anderson, Model Reduction for Control System Design. London: Springer-Verlag, 2001. 3. S. Gugercin, and A. C. Antoulas, A Survey of Model Reduction by Balanced Truncation and Some New Results, International Journal of Control, vol. 77, pp. 748-766, 2004. 4. B. C. Moore, Principal component analysis in linear systems: controllability, observability, and model reduction , IEEE Transactions on Automatic Control , pp. 17-32, AC-26, 1981. 5. W. Gawronski, and J.-N. Juang , Model Reduction in Limited Time and Frequency Intervals , International Journal of System Sciences , vol. 21, no. 2, pp. 349-376, 1990. 6. M. Tahavori and H. R. Shaker, Model reduction via time-interval balanced stochastic truncation for linear time invariant systems. , International Journal of Systems Science, vol. 44, no. 3, pp. 493-501, 2013. 7. H. R. Shaker, and R. Wisniewski , Model reduction of switched systems based on switching generalized gramians, International Journal of Innovative Computing, Information and Control, vol. 8, no. 7(B),2012.  8. H. R. Shaker, and R. Wisniewski, Switched systems reduction framework based on convex combination of generalized gramians, Journal of Control Science and Engineering, 2009. 9. H. R. Shaker and R. Wisniewski, Generalized gramian framework for model/controller order reduction of switched systems, International Journal of Systems Science, vol.42, no.8, pp.1277-1291, 2011. 10. H. R. Shaker, and M. Tahavori, Time-Interval Model Reduction of Bilinear Systems, International Journal of Control, 2013. 11. M. Tahavori and H. R. Shaker, Relative error model reduction via time-weighted balanced stochastic singular perturbation , Journal of Systems Science , Journal of Vibration and Control, vol. 18, no.13, pp. 2006-2016, 2012. 12. M. Tahavori and H. R. Shaker, Time-weighted balanced stochastic model reduction, 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), pp. 7777-7781, 2011. 13. H. R. Shaker, and M. Tahavori,  Frequency-Interval Model Reduction of Bilinear Systems, IEEE Transactions on Automatic Control, will appear in July issue, 2014. 14. E. G. Lee and L. Marcus, Foundations of Optimal Control Theory, New York, Wiley, 1967. 15. R W. Brockett, Finite Dimensional Linear System, New York. Wiley, (1970). 16. H. R. Shaker, F. Shaker, Control Configuration Selection for Linear Stochastic Systems, Journal of Process Control, Vol. 24, Issue 1, pp. 146–151, 2014. 17. H. R. Shaker, M. Tahavori , Frequency-Interval Control Configuration Selection for Multivariable Bilinear Systems, Journal of Process Control, Vol. 23, No. 6, 2013, pp. 894-904, 2013. 18. H. R. Shaker and Jakob Stoustrup, An interaction measure for control configuration selection for multivariable bilinear systems, Nonlinear Dynamics, vol. 72, no. 1, 2013, pp. 165-174, 2013. 19. H. R. Shaker and M. Komareji , Control Configuration Selection for MIMO Nonlinear Systems, Industrial & Engineering Chemistry Research, 51(25), pp. 8583-8587, 2012. 20. H. R. Shaker and M. Tahavori, Optimal Sensor and Actuator Location for Unstable Systems, Journal of Vibration and Control, vol. 19, no. 12, pp. 1915-1920, 2012. 21. H. R. Shaker, and Jakob Stoustrup, Control Configuration Selection for Multivariable Descriptor Systems, Proceedings of American control conference, Canada, 2012 22. H. R. Shaker , M. Tahavori Control Reconfigurability of Bilinear Hydraulic Drive Systems, Proceedings of IEEE Conference on Fluid Power and Mechatronics, Beijing, China, 2011. 

Contributions to the model order reduction of large-scale dynamical systems

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Contributions to the model order reduction of large-scale dynamical systems

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