Skip to main content

Large-Scale Systems: Optimality vs. Reliability

  • Chapter
Directions in Large-Scale Systems

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Šiljak, D. D., “Stability of Large-Scale Systems”, Proc. Fifth IFAC Congr., Paris, 4(1972), C-32: 1–11.

    Google Scholar 

  2. Šiljak, D. D., “On Stability of Large-Scale Systems Under Structural Perturbations:, IEEE Trans., SMC-3(1973), 415–417.

    Google Scholar 

  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. Popov, V. M., “Criterion of Quality for Non-Linear Controlled Systems”, Proc. First IFAC Congr., Moscow, 1 (1960), 173–176.

    Google Scholar 

  5. Rissanen, J. J., “Performance Deterioration of Optimum Systems” IEEE Trans., AC-11(1966), 530–532.

    Google Scholar 

  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. Weissenberger, S., “Tolerance of Decentrally Optimal Controllers to Nonlinearity and Coupling”, Twelfth Allerton Conf., Monticello, 111., (1974), 87–95.

    Google Scholar 

  8. Johnson, C. D., “Accommodation of External Disturbances in Linear Regulator and Servomechanism Problems”, IEEE Trans., AC-16(1971), 635–644.

    Google Scholar 

  9. Rosenbrock, H. H., “Good, Bad, or Optimal”, IEEE Trans., AC-16 (1971), 552–554.

    Google Scholar 

  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. 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. 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. 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. Bryson, A. E., and Y. C. Ho, “Applied Optimal Control”, Blaisdell, Waltham, Massc, 1969.

    Google Scholar 

  15. Langenhop, C. E., “On Generalized Inverses of Matrices”, SIAM J. Appl. Math., 15(1967), 1239–1246.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1976 Plenum Press, New York

About this chapter

Cite this chapter

Siljak, D.D., Sundareshan, S.K. (1976). Large-Scale Systems: Optimality vs. Reliability. In: Ho, Y.C., Mitter, S.K. (eds) Directions in Large-Scale Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-2259-7_24

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-2259-7_24

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-2261-0

  • Online ISBN: 978-1-4684-2259-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics