Skip to main content

The unfalsified control concept: A direct path from experiment to controller

  • Conference paper
  • First Online:
Book cover Feedback Control, Nonlinear Systems, and Complexity

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 202))

Abstract

The philosophical issues pertaining to the problem of going from experiment to controller design are discussed. The “unfalsified control” concept is introduced as a framework for determining control laws whose ability to meet given performance specifications is at least not invalidated (i.e., not falsified) by the available data. The approach is “model-free” in the sense that no plant model is required — only plant input-output data. When implemented in real time, the result is an adaptive robust controller which modifies itself whenever a new piece of data invalidates the present controller. A simple design example based on fixed-order LTI controllers and an L 2-inequality performance criterion is presented.

The task of science is to stake out the limits of the knowable and to center the consciousness within them.

Rudolf Virchow — Berlin, 1849

Research supported in part by AFOSR grant F49620-92-J-0014.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Zames. Functional analysis applied to nonlinear feedback systems. IEEE Trans. on Circuit Theory, CT-10:392–404, September 1963.

    Google Scholar 

  2. I.W. Sandberg. On the L 2-boundedness of solutions of nonlinear functional equations. Bell System Technical Journal, 43(4):1581–1599, July 1964.

    Google Scholar 

  3. I.W. Sandberg. A frequency-domain condition for the stability of feedback systems containing a single time-varying nonlinear element. Bell System Technical Journal, 43(4):1601–1608, July 1964.

    Google Scholar 

  4. G. Zames. On the input-output stability of time-varying nonlinear feedback systems — Part I: Conditions derived using concepts of loop gain, conicity, and positivity. IEEE Trans. on Automatic Control, AC-15(2):228–238, April 1966.

    Google Scholar 

  5. G. Zames. On the input-output stability of time-varying nonlinear feedback systems — Part II: Conditions involving circles in the frequency plane and sector nonlinearities. IEEE Trans. on Automatic Control, AC-15(3):465–467, July 1966.

    Google Scholar 

  6. M. G. Safonov. Robustness and Stability Aspects of Stochastic Multivariable Feedback System Design. PhD thesis, Dept. Elec. Eng., MIT, 1977. Supervised by Michael Athans.

    Google Scholar 

  7. M. G. Safonov and M. Athans. On stability theory. In Proc. 1978 IEEE Conf. on Decision and Control, pages 301–314, San Diego, CA, January 10–12, 1979. IEEE Press, New York.

    Google Scholar 

  8. M. G. Safonov. Stability and Robustness of Multivariable Feedback Systems. MIT Press, Cambridge, MA, 1980.

    Google Scholar 

  9. J. C. Willems. Paradigms and puzzles in the theory of dynamical systems. IEEE Trans. on Automatic Control, AC-36:259–294, 1991.

    Google Scholar 

  10. R. L. Kosut. Adaptive uncertainty modeling: On-line robust control design. In Proc. American Control Conf., pages 245–250, New York, June 1987. IEEE. Mineapolis, MN.

    Google Scholar 

  11. R. Smith and J. Doyle. Model invalidation—a connection between robust control and identification. In Proc. American Control. Conf., pages 1435–1440, Pittsburgh, PA, June 21–23, 1989. IEEE Press, New York.

    Google Scholar 

  12. J. M. Krause. Stability margins with real paramenter uncertainty: Test data implications. In Proc. American Control Conf., pages 1441–1445, Pittsburgh, PA, June 21–23, 1989. IEEE Press, New York.

    Google Scholar 

  13. R. L. Kosut, M. K. Lau, and S. P. Boyd. Set-membership identification of systems with parametric and nonparametric uncertainty. IEEE Trans. on Automatic Control, AC-37(7):929–941, July 1992.

    Google Scholar 

  14. K. Poolla, P. Khargonekar, J. Krause A. Tikku, and K. Nagpal. A time-domain approach to model validation. In Proc. American Control Conf., pages 313–317, New York, June 1992. IEEE. Chicago, IL.

    Google Scholar 

  15. J. J. Krause, G. Stein, and P. P. Khargonekar. Sufficient conditions for robust performance of adaptive controllers with general uncertainty structure. Automatica, 28(2):277–288, March 1992.

    Google Scholar 

  16. R. Smith. An informal review of model validation. In R. S. Smith and M. Dahleh, editors, The Modeling of Uncertainty in Control Systems: Proc. of the 1992 Santa Barbara Workshop, pages 51–59. Springer-Verlag, New York, 1994.

    Google Scholar 

  17. M. G. Safonov. Thoughts on identification for control. In R. S. Smith and M. Dahleh, editors, The Modeling of Uncertainty in Control Systems: Proc. of the 1992 Santa Barbara Workshop, pages 15–17. Springer-Verlag, New York, 1994.

    Google Scholar 

  18. T. C. Tsao and M. G. Safonov. A robust ellipsoidal-bound approach to direct adaptive control. In R. S. Smith and M. Dahleh, editors, The Modeling of Uncertainty in Control Systems: Proc. of the 1992 Santa Barbara Workshop, pages 181–196. Springer-Verlag, New York, 1994.

    Google Scholar 

  19. T. C. Tsao and M. G. Safonov. Set theoretic adaptor control systems. In Proc. American Control Conf., pages 3043–3047, San Francisco, CA, June 2–4, 1993. IEEE Press, New York.

    Google Scholar 

  20. T.-C. Tsao and M. G. Safonov. Convex set theoretic adaptor control systems. In Proc. IEEE Conf. on Decision and Control, pages 582–584, San Antonio, TX, December 15–17, 1993. IEEE Press, New York.

    Google Scholar 

  21. T. C. Tsao and M. Safonov. Data, consistency and feedback: A new approach to robust direct adaptive control. In Proc. American Control Conf., Baltimore, MD, June 29–July 1, 1994. IEEE Press, New York.

    Google Scholar 

  22. T. C. Tsao. Set Theoretic Adaptor Systems. PhD thesis, University of Southern California, May 1994. Supervised by M. G. Safonov.

    Google Scholar 

  23. B. Wie and D. S. Bernstein. Benchmark problems for robust control design. In Proc. American Control Conf., pages 2047–2048, Chicago, IL, June 24–26, 1992. IEEE Press, New York.

    Google Scholar 

  24. M. G. Safonov and R. Y. Chiang. CACSD using the state-space L theory-A design example. IEEE Trans. on Automatic Control, AC-33:477–479, 1988.

    Google Scholar 

  25. R. Y. Chiang and M. G. Safonov. Robust-Control Toolbox. Mathworks, South Natick, MA, 1988.

    Google Scholar 

  26. F. Schweppe. Recursive state estimation: Unknown but bounded errors and system inputs. IEEE Trans. on Automatic Control, 13:22–29, February 1968.

    Google Scholar 

  27. B. Kosko. Neural Networks and Fuzzy Systems. Prentice-Hall, Englewood-Cliffs, NJ, 1992.

    Google Scholar 

  28. B. Kosko and J. Dickerson. Function approximation with additive fuzzy systems. In H. Nguyen, M. Sugeno, R. Tong, and R. Yager, editors, Theoretical Aspects of Fuzzy Control, chapter 12. North Holland, New York, 1994. To appear.

    Google Scholar 

  29. R. Virchow. Der Mensch (On Man). Berlin, 1849. In Disease, Life and Man Selected Essays of Rudolf Virchow (trans. L. J. Rather), Stanford University Press, Stanford, CA, pp. 67–70, 1958.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Bruce Allen Francis Allen Robert Tannenbaum

Additional information

Dedicated to George Zames on his 60th birthday.

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag London Limited

About this paper

Cite this paper

Safonov, M.G., Tsao, TC. (1995). The unfalsified control concept: A direct path from experiment to controller. In: Francis, B.A., Tannenbaum, A.R. (eds) Feedback Control, Nonlinear Systems, and Complexity. Lecture Notes in Control and Information Sciences, vol 202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027678

Download citation

  • DOI: https://doi.org/10.1007/BFb0027678

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19943-4

  • Online ISBN: 978-3-540-39364-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics