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Mixed Optimization Approach to Model Approximation of Descriptor Systems

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Abstract

A mixed optimal model approximation is presented to obtain reduced-order models for truly fast descriptor systems. By a projection from truly fast descriptor systems to discrete-time systems, a mixed optimal model approximation for truly fast descriptor systems is transformed to a mixed optimal model approximation of the corresponding discrete-time systems. The structure of the fast descriptor systems is preserved in the model approximation procedure. The expression of the error and its gradient are given explicitly in terms of the solutions of certain Lyapunov equations. A numerical example is provided to illustrate the effectiveness of the proposed method.

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References

  1. Obinata, G., and Anderson, B. D. O., Model Reduction for Control System Design, Springer Verlag, London, UK, 2001.

    MATH  Google Scholar 

  2. Xu, S., Lam, J., Huang, S., and Yang, C., H∞ Model Reduction for Linear Time-Delay Systems: Continuous-Time Case, International Journal of Control, Vol. 74, No. 11, pp. 1062–1074, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhang, L. Q., and Lam, J., Optimal Weighted L2 Model Reduction of Delay Systems, International Journal of Control, Vol. 72, No. 1, pp. 39–48, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhou, K., Essentials of Robust Control, Prentice Hall, Upper Saddle River, New Jersey, the United States of America, 1998.

    Google Scholar 

  5. Wilson, D. A., System Order Reduction Using the Hilbert-Schmidt Norm of the Hankel Operator, Modelling and Simulation of Systems, Vol. 3, pp. 287–289, 1988.

    Google Scholar 

  6. Yan, W. Y., and Lam, J., An Approximation Approach to H_2 Optional Model Reduction, IEEE Transactions on Automatic, Control, Vol. 44, No. 7, pp. 1341–1358, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  7. Duan, G., Howe, D. and Patton, R. J., Robust Fault Detection in Descriptor Linear Systems via Generalized Unknown Input Observers, International Journal of Systems Science, Vol. 33, No. 5, pp. 369–377, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  8. Guo, L., and Malabre, M., Robust H∞ Control for Descriptor Systems with Nonlinear Uncertainties, International Journal of Control, Vol. 76, No. 12, pp. 1254–1262, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  9. Liu, X., and Ho, D. W. C., Disturbance Decoupling of Linear Time-Varying Singular Systems, IEEE Transactions on Automatic Control, Vol. 47, No. 2, pp. 335–341, 2002.

    Article  MathSciNet  Google Scholar 

  10. Perev, K., and Shafai, B., Balanced Realization and Model Reduction of Singular Systems, International Journal of Systems Science, Vol. 25, No. 6, pp. 1039–1052, 1994.

    MathSciNet  MATH  Google Scholar 

  11. Gray, W. S., and Verriest, E. I., On the Sensitivity of Generalized State-Space Systems, Proceeding of the 28th Conference Decision and Control, Tampa, Florida, pp. 1337–1341, 1989.

  12. Lewis, F. L., Christodoulou, M. A., Mertzios, B. G. and HÖzcaldiran, K., Chained Aggregation of Singular Systems, IEEE Transactions on Automatic Control, Vol. 34, No. 9, pp. 1007–1012, 1989.

    Article  MATH  Google Scholar 

  13. Liu, W. Q., and Sreeram, V., Model Reduction of Singular Systems, International Journal of Systems Science, Vol. 32, No. 10, pp. 1205–1215, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhang, L. Q., Lam, J., and Zhang, Q. L., Optimal Model Reduction of Discrete-Time Descriptor Systems, International Journal of Systems Science, Vol. 32, No. 5, pp. 575–583, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  15. Zhang, Q. L., Sreeram, V., Wang, G., and Liu, W. Q., H∞, Suboptimal Model Reduction for Singular Systems, Proceedings of the American Control Conference, Anchorage, Alaska, pp. 1168–1173, 2002.

    Google Scholar 

  16. Bender, D. J., Lyapunov-Like Equation and Reachability/Observability Gramians for Descriptor Systems, IEEE Transactions on Automatic Control, Vol. 32, No. 4, pp. 343–348, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  17. Dai, L., Singular Control Systems, Springer Verlag, Berlin, Germany, 1989.

    Book  MATH  Google Scholar 

  18. Hanzon, B., The Area Enclosed by the (Oriented) Nyquist Diagram and the Hilbert-Schmidt-Hankel Norm of a Linear Systems, IEEE Transactions on Automatic Control, Vol. 37, No. 6, pp. 835–839, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  19. Wang, H., and Lam, J., Robust Fault Dectection for Uncertain Discrete-Time Systems, Journal of Guidance, Control, and Dynamics, Vol. 25, No. 2, pp. 291–301, 2002.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong, China

    Q. Wang & J. Lam (Professor)

  2. College of Science, Northeastern University, Shenyang, China

    Q. L. Zhang (Professor)

  3. College of Automation and Engineering, South China University of Technology, Guangzhou, China

    Q. Y. Wang

Authors
  1. Q. Wang
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  2. J. Lam
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  3. Q. L. Zhang
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  4. Q. Y. Wang
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Additional information

Communicated by M. J. Balas

This work was supported by Grant RGC HKU 7127/02P.

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Wang, Q., Lam, J., Zhang, Q.L. et al. Mixed Optimization Approach to Model Approximation of Descriptor Systems. J Optim Theory Appl 131, 265–280 (2006). https://doi.org/10.1007/s10957-006-9137-1

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  • DOI: https://doi.org/10.1007/s10957-006-9137-1

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