Robust Stabilization and Disturbance Rejection for Uncertain Systems by Decentralized Control

  • R. J. Veillette
  • J. V. Medanić
  • W. R. Perkins
Part of the Progress in Systems and Control Theory book series (PSCT, volume 6)

Abstract

This paper develops a decentralized control design which provides robust H disturbance rejection for a plant with structured uncertainty in a bounded admissible set. The design consists of an observer in each control channel, which includes estimates of the controls generated in the other channels and of the worst disturbance as determined by a state-feedback H solution. The observer gains are computed from a positive-definite solution of a Riccati-like algebraic equation. A convexity property of a matrix Riccati function is used to compute for the closed-loop system an H -norm bound smaller than the predetermined bound, and to find an enlarged admissible set of plant uncertainities.

Keywords

None None Disturbance Rejection Algebraic Riccati Equation Observer Gain Decentralize Control 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    E. J. Davison. The decentralized control of large scale systems, pages 61–91. Volume 1, JAI Press, 1984.Google Scholar
  2. [2]
    S. H. Wang and E. J. Davison. On the stabilization of decentralized control systems. IEEE Transactions on Automatic Control, AC-18(5): 473–478, October 1973.Google Scholar
  3. [3]
    B. D. O. Anderson and D. J. Clements. Algebraic characterization of fixed modes in decentralized control. Automatica, 17 (5): 703–712, 1981.CrossRefGoogle Scholar
  4. [4]
    J. P. Corfmat and A. S. Morse. Control of linear systems through specified input channels. SIAM J. Control and Optimization, 14 (1): 163–175, January 1976.CrossRefGoogle Scholar
  5. [5]
    W. Yan and R. R. Bitmead. Decentralized control of multi-channel systems with direct control feedthrough. Int. J. Control,49(6):20572075, August 1989.Google Scholar
  6. [6]
    E. J. Davison. The robust decentralized control of a general servomechanism problem. IEEE Transactions on Automatic Control, AC-21(1): 14–24, February 1976.Google Scholar
  7. [7]
    U. Ozgüner and W. R. Perkins Optimal control of multilevel large-scale systems. Int. J. Control, 28 (6): 967–980, December 1978.CrossRefGoogle Scholar
  8. [8]
    E. J. Davison. The robust decentralized control of a servomechanism problem with input-output connections. IEEE Transactions on Automatic Control, AC-23(2): 325–327, April 1979.Google Scholar
  9. [9]
    M. Ikeda and D. D. Siljak. Generalized decompositions of dynamic systems and vector Lyapunov functions. IEEE Transactions on Automatic Control, AC-26(5): 1118–1125, October 1981.Google Scholar
  10. [10]
    D. D. Siljak and M. B. Vukcevié. Decentralization, stabilization, and estimation of large-scale linear systems. IEEE Transactions on Automatic Control, AC-21: 363–366, June 1976.Google Scholar
  11. [11]
    E. J. Davison and W. Gesing. Sequential stability and optimization of large scale decentralized systems. Automatica, 15 (3): 307–324, May 1979.CrossRefGoogle Scholar
  12. [12]
    D. S. Bernstein. Sequential design of decentralized dynamic compensators using the optimal projection equations. Int. J. Control, 46 (5): 1569–1577, November 1987.CrossRefGoogle Scholar
  13. [13]
    J. C. Doyle, K. Glover, P. P. Khargonekar, and B. Francis. State-space solutions to standard H2 and H oo control problems. In Proceedings of the American Control Conference, pages 1691–1696, Atlanta, GA, 1988.Google Scholar
  14. [14]
    R. J. Veillette, J. V. Medanie, and W. R. Perkins. Robust stabilization and disturbance rejection for systems with structured uncertainty. To appear in the Proceedings of the 28th Conference on Decision and Control, (Tampa, FL), December 1989.Google Scholar
  15. [15]
    S. Weiland. Linear quadratic games, H oo and the Riccati equation. In Proceedings of the Workshop on the Riccati Equation in Control, Systems, and Signals, pages 156–159, Como, Italy, June 26–28, 1989.Google Scholar
  16. [16]
    P P Khargonekar, I. R. Petersen, and K. Zhou. Feedback stabilization of uncertain systems. In Proceedings of the 26th Allerton Conference on Communication, Control and Computation, pages 88–95, Monticello, IL, 1988.Google Scholar
  17. [17]
    R. J. Veillette and J. V. Medanié. An algebraic Riccati inequality and H,-norm bounds for stable systems. In Proceedings of the Workshop on the Riccati Equation in Control, Systems, and Signals, pages 63–68, Como, Italy, June 26–28, 1989.Google Scholar
  18. [18]
    K. Mârtensson. On the matrix Riccati equation. Information Sciences, 3 (1): 17–50, 1971.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • R. J. Veillette
    • 1
  • J. V. Medanić
    • 1
  • W. R. Perkins
    • 1
  1. 1.Coordinated Science LaboratoryUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Personalised recommendations