Feedback stabilization over signal-to-noise ratio constrained channels

IEEE Transactions on Automatic Control

Volumn 52, Issue 8, 2007, Pages 1391-1403

  Braslavsky, Julio H ^a   Middleton, Richard H ^a   Freudenberg, James S ^b  

^a UNIVERSITY OF NEWCASTLE   (Australia)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Communication channels; Control systems; Feedback communication; Information rates; Linear quadratic Gaussian control; Networked control systems; Signal to noise ratio (SNR)

Indexed keywords

BANDWIDTH; COMMUNICATION CHANNELS (INFORMATION THEORY); CONSTRAINT THEORY; CONTROL SYSTEM STABILITY; SIGNAL TO NOISE RATIO; STATE FEEDBACK; TIME DELAY;

FEEDBACK STABILIZATION; LINEAR TIME INVARIANT FEEDBACK; SHANNON CAPACITY;

FEEDBACK CONTROL;

EID: 34548221472     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2007.902739     Document Type: Article

References (37)

1. P. Antsaklis and J. Baillieul, Eds., IEEE Trans. Autom. Control. Special Issue on Networked Control Syst., vol. 49, no. 9, Sep. 2004.
2. J. Baillieul, "Feedback coding for information based control: Operating near the data rate limit," in Proc. 41st IEEE Conf. Decision Contr. Las Vegas, NV, 2002.
3. G. N. Nair and R. E. Evans, "Stabilizability of stochastic linear systems with finite feedback data rates," SIAM J. Contr. Optimiz. vol. 43, no. 2, pp. 413-436, Jul. 2004.
4. S. Tatikonda and S. M. Mitter, "Control under communication constraints," IEEE Trans. Autom. Control, vol. 49, no. 7, pp. 1056-1068, Jul. 2004.
5. A. S. Matveev and A. V. Savkin, "An analogue for shannon information theory for networked control systems. Stabilization via a noisy discrete channel," in Proc. 43rd IEEE Conf. Decision Control, The Bahamas, 2004.
6. S. Yüksel and T. Basar, "Coding and control over discrete noisy forward and feedback channels," in Proc. 44th IEEE Conf. Decision and Control and the Europ. Control Conf. 2005, Seville, Spain, Dec. 2005, pp. 2517-2522.
7. G. N. Nair and R. J. Evans, "Exponential stabilisability of finite-dimensional linear systems with limited data rates," Automatica, vol. 39, no. 4, pp. 585-593, Apr. 2003.
8. C. E. Shannon, "A mathematical theory of communication," Bell Sys. Tech. J., vol. 27, pp. 379-423, 1948, 623-656.
9. C. E. Shannon, "Communication in the presence of noise," Proc. IRE vol. 37, pp. 10-21, 1949.
10. R. G. Gallager, Information Theory and Reliable Communication. New York: Wiley, 1968.
11. T. M. Cover and J. A.Thomas, Elements of Information Theory. New York: Wiley, 1991.
12. J. S. Freudenberg and D. P. Looze, "Right half plane poles and zeros and design tradeoffs in feedback systems," IEEE Trans. Autom. Control, vol. 30, no. 6, pp. 555-565, Jun. 1985.
13. D. P. Looze and J. S. Freudeberg, "Limitations of feedback properties imposed by open-loop right half plane poles," IEEE Trans. Autom. Control, vol. 36, no. 6, pp. 736-739, Jun. 1991.
14. R. H. Middleton, "Trade-offs in linear control systems design," Automatica, vol. 27, no. 2, pp. 281-292, Mar. 1991.
15. M. M. Seron, J. H. Braslavsky, and G. C. Goodwin, Fundamental Limitations in Filtering and Control. New York: Springer, 1997.
16. J. H. Braslavsky, R. H. Middleton, and J. Freudenberg, "Effects of time delay on feedback stabilisation over signal-to-noise ratio constrained channels," in Proc. l6th IFAC World Congress, Prague, Czech Republic, Jul. 2005.
17. G. N. Nair and R. E. Evans, "Stabilization with data-rate limited feedback: Tightest attainable bounds," Syst. Contr. Lett., vol. 41, pp. 49-56, 2000.
18. J. H. Braslavsky, R. H. Middleton, and J. S. Freudenberg, "Feedback stabilisation over signal-to-noise ratio constrained channels," in Proc. 2004 Amer. Control Conf., Boston, MA, 2004, vol. 6, pp. 4903-4908.
19. R. H. Middleton, J. H. Braslavsky, and J. S. Freudenberg, "Stabilization of non-minimum phase plants over signal-to-noise ratio constrained channels," in Proc. 5th Asian Control Conf., Melbourne, Australia, Jul. 2004, pp. 1924-1932.
20. K. J. Åström, Introduction to Stochastic Control Theory. New York: Cademic, 1970.
21. G. N. Nair, R. J. Evans, I. M. Y. Mareels, and W. Moran, "Topological feedback entropyand nonlinear stabilization," TAC, vol. 49, no. 9, pp. 1585-1597,Sep. 2004.
22. A. Sahaj and S. Mitter, "The necessity and sufficiency of anytime capacity for stabilization of a linear system over a noisy communication link - Part I: Scalar systems," IEEE Trans. Inf. Theory, vol. 52, no. 8, p. 3369-3395, Aug. 2006.
23. R. H. Middleton and G. C. Goodwin, Digital Control and Estimation: A Unified Approach.: Prentice Hall, 1990.
24. K. J. Åström and B. Wittenmark, Computer-Controlled Systems, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall Int., 1997.
25. N. Elia, "When Bode meets Shannon: Control-oriented feedback communication schemes," IEEE Trans. Autom. Control, vol. 49, no. 9, pp. 1477-1488, Sep. 2004.
26. P. T. Kabamba, "Control of linear systems using generalized sampled-data hold functions," IEEE Trans. Autom. Control, pp. 772-783, Sep. 1987.
27. G. F. Franklin, J. D. Powell, and M. Workman, Digital Control of Dynamic Systems, 3rd ed. Reading, MA: Addison-Wesley, 1998.
28. N. Levinson and R. M. Redheffer, Complex Variables. New York: Holden Day, 1970.
29. J. S. Freudenberg, R. H. Middleton, and J. H. Braslavsky, "Inherent design limitations for linear sampled-data feedback systems," Int. J. Contr., vol. 61, no. 6, pp. 1387-1421, 1995.
30. J. S. Freudenberg, R. H. Middleton, and J. H. Braslavsky, "Robustness of zero shifting via generalized sampled-data hold functions," IEEE Trans. Autom. Control, vol. 42, no. 12, pp. 1681-1692, Dec. 1997.
31. R. H. Middleton and J. S. Freudenberg, "Non-pathological sampling for generalized sampled-data hold functions," Automatica, vol. 31, no. 2, pp. 315-319, 1995.
32. J. H. Braslavsky, M. M. Seron, D. Q. Mayne, and P. V. Kokotović, "Limiting performance of optimal linear filters," Automatica, vol. 35, no. 2, pp. 189-199, Feb. 1999.
33. H. Kwakernaak and R. Sivan, Linear Optimal Control Systems. New York: Wiley Intersci., 1972.
34. J. Chen, L. Qiu, and O. Toker, "Limitations on maximal tracking accuracy," IEEE Trans. Autom. Control, vol. 45, no. 2, pp. 326-331, February 2000.
35. B.A. Francis, A Course in H∞ Control Theory. New York: Springer-Verlag, 1987.
36. J. B. Conway, Functions of One Complex Variable, 2nd ed. New York: Springer-Verlag, 1978.
37. M. Vidyasagar, Control System Synthesis: A Factorization Approach. Cambridge, MA: MIT Press, 1985.