Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2010, Article ID 841830, 20 pages
http://dx.doi.org/10.1155/2010/841830
Research Article

Multimodeling Control via System Balancing

Faculty of Mechanical Engineering, University of Belgrade, 11120 Belgrade 35, Serbia

Received 19 February 2010; Accepted 14 April 2010

Academic Editor: Giuseppe Rega

Copyright © 2010 Nada Ratković Kovačević and Dobrila Škatarić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. C. Geromel and P. L. D. Peres, “Decentralised load-frequency control,” IEE Proceedings D, vol. 132, no. 5, pp. 225–230, 1985. View at Google Scholar · View at Zentralblatt MATH
  2. Z. Gajic and X. Shen, Parallel Algorithms for Optimal Control of Large Scale Linear Systems, Communications and Control Engineering Series, Springer, London, UK, 1993. View at MathSciNet
  3. P. V. Kokotović, H. K. Khalil, and J. O'Reilly, Singular Perturbation Methods in Control: Analysis and Design, Academic Press, Orlando, Fla, USA, 1986. View at MathSciNet
  4. Z. Gajić, M.-T. Lim, D. Škatarić, W.-C. Su, and V. Kecman, Optimal Control Weakly Coupled Systems and Applications, Automation and Control Engineering, CRC Press, Boca Raton, Fla, USA, 1st edition, 2009. View at MathSciNet
  5. H. Mukaidani and V. Dragan, “Control of deterministic and stochastic systems with several parameters—a survey,” Annals of the Academy of Romanian Scientists Series on Mathematics and Its Applications, vol. 1, pp. 112–158, 2009. View at Google Scholar
  6. H. Mukaidani, H. Xu, and K. Mizukami, “Recursive computation of Pareto optimal strategy for multiparameter singularly perturbed systems,” Dynamics of Continuous, Discrete & Impulsive Systems. Series B, vol. 9, no. 2, pp. 175–199, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. H. Mukaidani, H. Oya, and H. Xu, “Robust stabilization of multimodeling systems via guaranteed cost control theory,” Electrical Engineering in Japan, vol. 160, no. 4, pp. 49–59, 2007. View at Publisher · View at Google Scholar
  8. H. Mukaidani, “A new approach to robust guaranteed cost control for uncertain multimodeling systems,” Automatica, vol. 41, no. 6, pp. 1055–1062, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. H. Mukaidani, H. Xu, and K. Mizukami, “New results for near-optimal control of linear multiparameter singularly perturbed systems,” Automatica, vol. 39, no. 12, pp. 2157–2167, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. H. Mukaidani, T. Shimomura, and H. Xu, “Asymptotic expansions of solutions of cross-coupled algebraic Riccati equations of multimodeling systems related to Nash games,” Dynamics of Continuous, Discrete & Impulsive Systems. Series B, supplement, pp. 34–39, 2003. View at Google Scholar · View at MathSciNet
  11. H. Mukaidani, T. Shimomura, and H. Xu, “Near-optimal control of linear multiparameter singularly perturbed systems,” IEEE Transactions on Automatic Control, vol. 47, no. 12, pp. 2051–2057, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  12. C. Coumarbatch and Z. Gajic, “Exact decomposition of the algebraic Riccati equation of deterministic multimodeling optimal control problems,” IEEE Transactions on Automatic Control, vol. 45, no. 4, pp. 790–794, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. C. Coumarbatch and Z. Gajic, “Parallel optimal Kalman filtering for stochastic systems in multimodeling form,” Transactions of the ASME, vol. 122, no. 3, pp. 542–550, 2000. View at Publisher · View at Google Scholar
  14. Z. Gajic and H. Khalil, “Multimodel strategies under random disturbances and imperfect partial observations,” Automatica, vol. 22, no. 1, pp. 121–125, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. B. C. Moore, “Principal component analysis in linear systems: controllability, observability, and model reduction,” IEEE Transactions on Automatic Control, vol. 26, no. 1, pp. 17–32, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. Z. Gajic and M. Lelic, “Improvement of system order reduction via balancing using the method of singular perturbations,” Automatica, vol. 37, no. 11, pp. 1859–1865, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. H. K. Khalil and P. V. Kokotović, “Control strategies for decision makers using different models of the same system,” IEEE Transactions on Automatic Control, vol. 23, no. 2, pp. 289–298, 1978. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. D. Škatarić and Z. Gajic, “Linear control of nearly singularly perturbed hydropower plants,” Automatica, vol. 28, no. 1, pp. 159–163, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  19. D. Škatarić and N. Ratković, “Robust order reduction using system balancing with respect to the method of singular perturbation,” in Proceedings of the 10th World Multi-Conference on Systemics, Cybernetics and Informatics (WMSCI '06), pp. 353–358, Orlando, Fla, USA, 2006.
  20. K. Glover, “All optimal Hankel-norm approximations of linear multivariable systems and their L-error bounds,” International Journal of Control, vol. 39, no. 6, pp. 1115–1193, 1984. View at Publisher · View at Google Scholar · View at MathSciNet
  21. M. Vidyasagar, “The graph metric for unstable plants and robustness estimates for feedback stability,” IEEE Transactions on Automatic Control, vol. 29, no. 5, pp. 403–418, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. H. Kwakernaak and R. Sivan, Linear Optimal Control Systems, Wiley-Interscience, New York, NY, USA, 1972. View at MathSciNet