Advertisement

Large-Scale Systems: Optimality vs. Reliability

  • D. D. Siljak
  • S. K. Sundareshan

Abstract

Optimal control systems may become unstable if subject to structural perturbations whereby parts of the system are disconnected (and again connected) during operation. Multi-level schemes for controlling large-scale linear systems are proposed in this work, which provide a trade-off between reliability and optimality. By treating the interconnections among subsystems as perturbation terms, a two-level control strategy is developed. Local controls are used to optimize the decoupled subsystems with respect to quadratic costs, and global controls are applied to minimize the effects of interconnections. Although this control scheme results in a sub- optimal performance, it is inherently reliable.

Keywords

Global Control Structural Perturbation Gain Matrice Optimal Control System Positive Definite Solution 
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.
    Šiljak, D. D., “Stability of Large-Scale Systems”, Proc. Fifth IFAC Congr., Paris, 4(1972), C-32: 1–11.Google Scholar
  2. 2.
    Šiljak, D. D., “On Stability of Large-Scale Systems Under Structural Perturbations:, IEEE Trans., SMC-3(1973), 415–417.Google Scholar
  3. 3.
    Šiljak, D. D., and M. K. Sundareshan, “On IIierarchic Optimal Control of Large-Scale Systems”, Proc. Eighth Asilomar Conf., Pacific Grove, Calif., (1974), 495–502.Google Scholar
  4. 4.
    Popov, V. M., “Criterion of Quality for Non-Linear Controlled Systems”, Proc. First IFAC Congr., Moscow, 1 (1960), 173–176.Google Scholar
  5. 5.
    Rissanen, J. J., “Performance Deterioration of Optimum Systems” IEEE Trans., AC-11(1966), 530–532.Google Scholar
  6. 6.
    Bailey, F. N., and H. K. Ramapriyan, “Bounds on Suboptimality in the Control of Linear Dynamic Systems”, IEEE Trans., AC-IS (1973), 532–534.Google Scholar
  7. 7.
    Weissenberger, S., “Tolerance of Decentrally Optimal Controllers to Nonlinearity and Coupling”, Twelfth Allerton Conf., Monticello, 111., (1974), 87–95.Google Scholar
  8. 8.
    Johnson, C. D., “Accommodation of External Disturbances in Linear Regulator and Servomechanism Problems”, IEEE Trans., AC-16(1971), 635–644.Google Scholar
  9. 9.
    Rosenbrock, H. H., “Good, Bad, or Optimal”, IEEE Trans., AC-16 (1971), 552–554.Google Scholar
  10. 10.
    Šiljak, D. D., and M. B. Vukcevic, “On Hierarchic Stabilization of Large-Scale Linear Systems”, Proc. Eighth Asilomar Conf. Circuits, Systems, Computers, Pacific Grove, Calif., 1974, 503–507.Google Scholar
  11. 11.
    Šiljak, D. D., “Stabilization of Large-Scale Systems: A Spinning Flexible Spacecraft”, Proc. Sixth IFAC Congr., Boston, Mass., 1975, 35–1: 1–10.Google Scholar
  12. 12.
    Šiljak, D. D., and M. B. Vukčević, “Large-Scale Systems: Stability, Complexity, Reliability”, IEEE Proc., Special Issue on Recent Advances in System Theory, Edited by W. A. Porter, 1975 (to appear).Google Scholar
  13. 13.
    Šiljak, D. D., and M. B. Vukcevic, “Multilevel Control of Large Scale Systems: Decentralization, Stabilization, Estimation, and Reliability”, Recent Advances in Large-Scale Systems, Edited by R. Saeks, Point Lobos Press, 1975 (to appear).Google Scholar
  14. 14.
    Bryson, A. E., and Y. C. Ho, “Applied Optimal Control”, Blaisdell, Waltham, Massc, 1969.Google Scholar
  15. 15.
    Langenhop, C. E., “On Generalized Inverses of Matrices”, SIAM J. Appl. Math., 15(1967), 1239–1246.CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1976

Authors and Affiliations

  • D. D. Siljak
    • 1
  • S. K. Sundareshan
    • 1
  1. 1.Department of Electrical Engineering & Computer ScienceUniversity of Santa ClaraSanta ClaraUSA

Personalised recommendations