On Decentralized Control of Large-Scale Systems

  • D. D. Šiljak
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Summary

A scheme is presented for decentralized control of large-scale linear systems which are composed of a number of interconnected subsystems. By ignoring the interconnections, local feedback controls are chosen to optimize each decoupled subsystem. Conditions are provided to establish compatibility of the individual local controllers and achieve stability of the overall system. Besides computational simplifications, the scheme is attractive because of its structural features and the fact that it produces a robust decentralized regulator for large dynamic systems, which can tolerate a wide range of nonlinearities and perturbations among the subsystems.

Keywords

Decen Subsys 

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References

  1. 1.
    Arrow, K. J.; Hurwicz, L.: Decentralization and Computation in Resource Allocation. Essays in Economics and Econometrics, R. W. Pfouts (ed.), University of North Carolina Press, Chapel Hill, North Carolina, 1963, 34–104.Google Scholar
  2. 2.
    Marschak, J.; Radner, R.: The Economic Theory of Teams, Yale University Press, Cowles Foundation Monograph 22, New Haven, Connecticut, 1971.Google Scholar
  3. 3.
    Kulikowski, R.: Optimum Control of Aggregated Multi-Level Systems, Proceedings of the Third IFAC Congress, London, 1966, 40A: 1–9.Google Scholar
  4. 4.
    McFadden, D.: On the Controllability of Decentralized Macro-economic System: The Assignment Problem, Mathematical Systems Theory and Economics, H. W. Kuhn and G. P. Szegö (eds.), Springer, 1969, 221–240.Google Scholar
  5. 5.
    Aoki, M.: Control of Large Scale Dynamic Systems by Aggregation, IEEE Transactions, AC-13, 1968, 246–253.Google Scholar
  6. 6.
    Aoki, M.: On Feedback Stabilizability of Decentralized Dynamic Systems, Automatica, 8, 1972, 163–173.MATHCrossRefGoogle Scholar
  7. 7.
    Bailey, F. N.: The Concept of Aggregation in System Stability Analysis, Proceedings of the Second Asilomar Conference on Circuits and Systems, Pacific Grove, California, 1968, 570–576.Google Scholar
  8. 8.
    Varaiya, P.: Trends in the Theory of Decision-Making in Large Systems, Annals of Economic and Social Measurement, 1/4, 1972, 493–500.Google Scholar
  9. 9.
    Lau, R.; Persiano, R. C. M.; Varaiya, P. P.: Decentralized Information and Control: A Network Example, IEEE Transactions, AC-17, 1972, 466–473.MathSciNetGoogle Scholar
  10. 10.
    Ho, Y. C.; Chu, K. C.: Team Decision Theory and Information Structures in Optimal Control Problems — Part I, IEEE Transactions, AC-17, 1972, 15–22.MathSciNetGoogle Scholar
  11. 11.
    Chu, K. C.: Team Decision Theory and Information Structures in Optimal Control Problems — Part II, IEEE Transactions, AC-17, 1972, 22–28.Google Scholar
  12. 12.
    Cormat, J. B.; Morse, A. S.: Stabilization with Decentralized Feedback Control, IEEE Transactions, AC-18, 1973, 673–682.Google Scholar
  13. 13.
    Chong, C. Y.; Athans, M.: On the Stochastic Control of Linear Systems with Different Information Sets, IEEE Transactions, AC-16, 1971, 423–430.MathSciNetGoogle Scholar
  14. 14.
    Davison, E. J.; Rau, N. S.: The Optimal Decentralized Control of a Power System Consisting of a Number of Interconnected Synchronous]Vlachines, International Journal of Control, 18, 1973, 1313–1328.CrossRefGoogle Scholar
  15. 15.
    Wang, S. H.; Davison, E. J.: On the Stabilization od Decentralized Control Systems, IEEE Transactions, AC-18, 1973, 473–478.MathSciNetGoogle Scholar
  16. 16.
    Davison, E. J.: The Decentralized Stabilization and Control of a Class of Unknown Non-Linear Time-Varying Systems, Automatica, 10, 1974, 309–316.MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Corfmat, J. P.; Morse, A. S.: Decentralized Control of Linear Multivariable Systems, Automatica, 12, 1976, 479–495.MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Sandell, N. R.; Varaiya, P.; Athans, M.: A Survey of Decentralized Control Methods for Large Scale Systems. Proceedings of the Engineering Foundation Conference on Systems Engineering for Power: Status and Prospects, Henniker, New Hampshire, 1975, 1–19.Google Scholar
  19. 19.
    Šiljak, D. D.; Vukčević, M. B.: Large-Scale Systems: Stability, Complexity, Reliability, Journal of the Franklin Institut, 301, 1976, 49–69.MATHCrossRefGoogle Scholar
  20. 20.
    Šiljak, D. D.; Vukčević, M. B.: Decentralization, Stabilization, and Estimation of Large-Scale Linear Systems, IEEE Transactions, AC-21, 1976, 363–366.Google Scholar
  21. 21.
    Šiljak, D. D.; Sundareshan, M. K.: A Multilevel Optimization of Large-Scale Dynamic Systems, IEEE Transactions, AC-21, 1976, 79–84.Google Scholar
  22. 22.
    Šiljak, D. D.: Multilevel Stabilization of Large-Scale Systems: A Spinning Flexible Spacecraft, Automatica, 12, 1976, 309–319.MATHCrossRefGoogle Scholar
  23. 23.
    Šiljak, D. D.; Vukčević, M. B.: Decentrally Stabilizable Linear and Bilinear Large-Scale Systems, International Journal of Control, (to appear).Google Scholar
  24. 24.
    Šiljak, D. D.; Vukčević, M. B.: On Decentralized Estimation, International Journal of Control, (to appear).Google Scholar
  25. 25.
    Šiljak, D. D.: Large-Scale Dynamic Systems: Stability and Structure, North-Holland, New York, 1978.MATHGoogle Scholar
  26. 26.
    Anderson, B. D. O.; Moore, J. B.: Linear Optimal Control, Prentice-Hall, Englewood Cliffs, New Jersey, 1971.Google Scholar
  27. 27.
    Popov, V. M.: Criterion of Quality for Non-Linear Controlled Systems, Proceedings of the First IFAC Congress, Moscow, 1, 1960, 173–176.Google Scholar
  28. 28.
    Rissanen, J. J.: Performance Deterioration of Optimum Systems, IEEE Transactions, AC-11, 1966, 530–532.Google Scholar
  29. 29.
    Šiljak, D. D.; Sundareshan, M. K.: Large-Scale Systems: Optim-ality Vs. Reliability, Directions in Large-Scale Systems, Many-Person Optimization and Decentralized Control, U. C. Ho and S. K. Mitter (eds.), Plenum Press, New York, 1976, 411–425.Google Scholar
  30. 30.
    Langenhop, C. E.: On Generalized Inverses of Matrices, SLAM Journal of Applied Mathematics, 15, 1967, 1239–1246.MathSciNetMATHCrossRefGoogle Scholar
  31. 31.
    Fiedler, M.; Pták, V.: On Matrices with Nonpositive Off-Diagonal Elements and Positive Principal Minors, Czechoslovakian Mathematical Journal, 12, 1962, 382–400.Google Scholar
  32. 32.
    Šiljak, D. D.: On Reachability of Dynamic Systems, International Journal of Systems Science, 8, 1977, 321–338.MATHCrossRefGoogle Scholar
  33. 33.
    Šiljak, D. D.: On Pure Structure of Dynamic Systems, Nonlinear Analysis, Theory, Methods, and Applications, 1, 1977, 397–413.MATHGoogle Scholar
  34. 34.
    Šiljak, D. D.: Vulnerability of Dynamic Systems, Proceedings of the IFAC Workshop on Control and Management of Integrated Industrial Complexes, Toulouse, France, 1977.Google Scholar

Copyright information

© Springer-Verlag, Berlin/Heidelberg 1978

Authors and Affiliations

  • D. D. Šiljak
    • 1
  1. 1.University of Santa ClaraSanta ClaraUSA

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