INFORMATION-THEORETIC VIEW OF CONTROL

Prateep Roy, Arben Çela, Yskandar Hamam

2009

Abstract

In this paper we are presenting the information-theoretic explanation of Bod´e Sensitivity Integral, a fundamental limitation of control theory, controllability grammian and the issues of control under communication constraints. As resource-economic use of information is of prime concern in communication-constrained control problems, we need to emphasize more on informational aspect which has got direct relation with uncertainties in terms of Shannon Entropy and Mutual Information. Bode Integral which is directly related to the disturbances can be correlated with the difference of entropies between the disturbance-input and measurable output of the system. These disturbances due to communication channel-induced noises and limited bandwidth are causing the information packet-loss and delays resulting in degradation of control performances.

References

  1. Sandberg H. and Bernhardsson B.(2005), A Bode Sensitivity Integral for Linear Time-Periodic Systems, IEEE Trans. Autom. Control, Vol. 50, No. 12, December.
  2. Antsaklis P. and Baillieul J. (2007), Special Issue on the Technology of Networked Control Systems, Proc. of the IEEE, Vol. 95, No. 1.
  3. Nair G. and Evans R.(2004), Stabilizability of stochastic linear systems with finite feedback data rates, SIAM J. Control Optim., Vol. 43, No. 2, p. 413-436.
  4. Tatikonda S. and Mitter S.(2004), Control under communication constraints, IEEE Trans. Autom. Control, Vol. 49, No. 7, p. 1056-1068.
  5. Martins N., Dahleh M., and Doyle J.(2007), Fundamental limitations of disturbance attenuation in the presence of side information, IEEE Trans. Autom. Control, Vol. 52, No. 1, p. 56-66.
  6. Bode H.(1945), Network Analysis and Feedback Amplifier Design, D. Van Nostrand, 1945.
  7. Iglesias P.(2001), Trade-offs in linear time-varying systems : An analogue of Bode's sensitivity integral, Automatica, Vol. 37, No. 10, p. 1541-1550.
  8. Middleton D.(1960), An Introduction to Statistical Communication Theory, McGraw-Hill Pub., p. 315.
  9. Cover and Thomas(2006), Elements of Information Theory, 2nd Ed., John Wiley and Sons.
  10. Shannon C.(1948), The Mathematical Theory of Communication, Bell Systems Tech. J. Vol. 27, p. 379-423, p. 623-656, July, October.
  11. Zang G. and Iglesias P.(2003), Nonlinear extension of Bode's integral based on an information theoretic interpretation, Systems and Control Letters, Vol. 50, p. 1129.
  12. Mehta P., Vaidya U. and Banaszuk A.(2006), Markov Chains, Entropy, and Fundamental Limitations in Nonlinear Stabilization, Proc. of the 45th IEEE Conference on Decision & Control, San Diego, USA, December 13-15.
  13. Freudenberg J. and Looze D.(1988), Frequency Domain Properties of Scalar and Multivariable Feedback Systems, Lecture Notes in Control and Information Sciences, Vol. 104, Springer-Verlag, New York.
  14. Zang G.(2004), Bode's integral extensions in linear timevarying and nonlinear systems, Ph.D. Dissertation, Dept. Elect. Comput. Eng., Johns Hopkins Univ., USA.
  15. Iglesias P.(2002), Logarithmic integrals and system dynamics : An analogue of Bode's sensitivity integral for continuous-time time-varying systems, Linear Alg. Appl., Vol. 343-344, p. 451-471.
  16. Sung H. and Hara S.(1989), Properties of complementary sensitivity function in SISO digital control systems, Int. J. Control, Vol.50, No. 4, p. 1283-1295.
  17. Sung H. and Hara S.(1988), Properties of sensitivity and complementary sensitivity functions in single-input single-output digital control systems, Int. J. Control, Vol. 48, No. 6, p. 2429-2439.
  18. Okano K, Hara S. and Ishii H.(2008), Characterization of a complementary sensitivity property in feedback control: An information theoretic approach, Proc. of the 17th IFAC-World Congress, Seoul, Korea, July 6-11, p. 5185-5190.
  19. Jialing L.(2006), Fundamental Limits in Gaussian Channels with Feedback: Confluence of Communication, Estimation and Control, Ph.D. Thesis, Iowa State University.
  20. Liu J. and Elia N. (2006), Convergence of Fundamental Limitations in Information, Estimation, and Control, Proceedings of the 45th IEEE Conference on Decision & Control, San Diego, USA, December.
  21. Kalman R., Ho Y. and Narendra K.(1963), Controllability of linear dynamical systems, Contributions to Differential Equations, Vol. 1, No. 2, p. 189-213.
  22. Mitra D.(1969), W-matrix and the Geometry of Model Equivalence and Reduction, Proc. of the IEE, Vol. 116, No.6, June, p. 1101-1106.
  23. Ben Gaid M. M., and C¸ ela A.(2006), Trading Quantization Precision for Sampling Rates in Networked Systems with Limited Communication, Proceedings of the 45th IEEE Conference on Decision & Control, San Diego, CA, USA, December 13-15.
Download


Paper Citation


in Harvard Style

Roy P., Çela A. and Hamam Y. (2009). INFORMATION-THEORETIC VIEW OF CONTROL . In Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO, ISBN 978-989-674-001-6, pages 5-12. DOI: 10.5220/0002166600050012


in Bibtex Style

@conference{icinco09,
author={Prateep Roy and Arben Çela and Yskandar Hamam},
title={INFORMATION-THEORETIC VIEW OF CONTROL},
booktitle={Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,},
year={2009},
pages={5-12},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002166600050012},
isbn={978-989-674-001-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,
TI - INFORMATION-THEORETIC VIEW OF CONTROL
SN - 978-989-674-001-6
AU - Roy P.
AU - Çela A.
AU - Hamam Y.
PY - 2009
SP - 5
EP - 12
DO - 10.5220/0002166600050012