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Information and Control in Networks pp 3–37Cite as

Elements of Information Theory for Networked Control Systems

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 450))

Abstract

Next generation cyber-physical systems challenge the standard assumption of classical control theory that communication can be performed instantaneously, reliably, and with infinite precision. This motivated, at the turning of the millennium, the birth of a new chapter of control theory relating the ability to control dynamical systems to the characteristics of the communication channels used in the feedback loop. Potential applications of the theory include remote robot control, automated highway navigation using wireless sensor systems, automatic control for unmanned aerial vehicles, and design of critical energy, transportation, and health care systems. In this chapter we review a series of contributions at the intersection of information and control theories, briefly describe applications, sketch mathematical arguments, and illustrate in a tutorial style the main information-theoretic and control-theoretic tools used to derive these results. We also draw a connection between control over networks and some recent advancements in feedback communication, and mention some open problems related to error correcting codes for interactive communications.

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References

  1. Adler, R.L., Konheim, A.G., McAndrew, M.H.: Topological entropy. Trans. Am. Math. Soc. 114, 309–319 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  2. Andrievsky, B., Matveev, A., Fradkov, A.: Control and estimation under information constraints: toward a unified theory of control, computation and communications. Autom. Remote Control 71, 572–633 (2010). Original Russian text in Autom. Telemekh. 4, 34–99 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ardestanizadeh, E., Franceschetti, M.: Control-theoretic approach to communication with feedback. IEEE Trans. Autom. Control (2012)

    Google Scholar 

  4. Ardestanizadeh, E., Minero, P., Franceschetti, M.: LQG control approach to Gaussian broadcast channels with feedback. IEEE Trans. Inf. Theory 58(8), 5267–5278 (2012)

    Article  MathSciNet  Google Scholar 

  5. Baillieul, J.: Feedback designs for controlling device arrays with communication channel bandwidth constraints. In: ARO Workshop on Smart Structures, Penn. State U., USA (1999)

    Google Scholar 

  6. Baillieul, J.: Feedback designs in information-based control. In: Pasik-Duncan, B. (ed.) Proceedings of the Workshop on Stochastic Theory and Control. Springer, Lawrence (2001)

    Google Scholar 

  7. Baillieul, J., Antsaklis, P.J. (eds.): Special issue on Networked Control Systems. IEEE Trans. Autom. Control 49(9) (2004)

    Google Scholar 

  8. Baillieul, J., Antsaklis, P.J.: Control and communication challenges in networked real-time systems. Proc. IEEE 95(1), 9–28 (2007)

    Article  Google Scholar 

  9. Borkar, V., Mitter, S.: LQG Control with Communication Constraints. LIDS-P. Massachusetts Institute of Technology, Laboratory for Information and Decision Systems (1995)

    Google Scholar 

  10. Borkar, V., Mitter, S.: LQG Control with Communication Constraints. Communications, Computation, Control and Signal Processing: A Tribute to Thomas Kailath. Kluwer Academic, Dordrecht (1997)

    Google Scholar 

  11. Braslavsky, J., Middleton, R., Freudenberg, J.: Feedback stabilization over signal-to-noise ratio constrained channels. IEEE Trans. Autom. Control 52(8), 1391–1403 (2007)

    Article  MathSciNet  Google Scholar 

  12. Brockett, R., Liberzon, D.: Quantized feedback stabilization of linear systems. IEEE Trans. Autom. Control 45(7), 1279–1289 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  13. Como, G., Fagnani, F., Zampieri, S.: Anytime reliable transmission of real-valued information through digital noisy channels. SIAM J. Control Optim. 48(6), 3903–3924 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Costa, M., Cover, T.: On the similarity of the entropy power inequality and the Brunn-Minkowski inequality. IEEE Trans. Inf. Theory 30(6), 837–839 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  15. Costa, O., Fragoso, D., Marques, R.: Discrete-Time Markov Jump Linear Systems. Probability and Its Applications. Springer, Berlin (2004)

    Google Scholar 

  16. Cover, T., Thomas, J.: Elements of Information Theory. Wiley, New York (2006)

    MATH  Google Scholar 

  17. Coviello, L., Minero, P., Franceschetti, M.: Stabilization over Markov feedback channels: the general case. IEEE Trans. Autom. Control 58(2), 349–362 (2013)

    Article  MathSciNet  Google Scholar 

  18. Delchamps, D.: Stabilizing a linear system with quantized state feedback. IEEE Trans. Autom. Control 35(8), 916–924 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  19. El Gamal, A., Kim, Y.H.: Network Information Theory. Cambridge University Press, Cambridge (2011)

    Book  MATH  Google Scholar 

  20. Elia, N.: When Bode meets Shannon: control-oriented feedback communication schemes. IEEE Trans. Autom. Control 49(9), 1477–1488 (2004)

    Article  MathSciNet  Google Scholar 

  21. Elia, N.: Remote stabilization over fading channels. Syst. Control Lett. 54(3), 237–249 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  22. Elia, N., Mitter, S.K.: Stabilization of linear systems with limited information. IEEE Trans. Autom. Control 46(9), 1384–1400 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  23. Forney, G.D.: Convolutional codes II. Maximum-likelihood decoding. Inf. Control 25(3), 222–266 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  24. Franceschetti, M., Javidi, T., Kumar, P.R., Mitter, S.K., Teneketzis, D. (eds.): Special issue on Control and Communications. IEEE J. Sel. Areas Commun. 26(4) (2008)

    Google Scholar 

  25. Freudenberg, J., Middleton, R.H., Solo, V.: Stabilization and disturbance attenuation over a Gaussian communication channel. IEEE Trans. Autom. Control 55(3), 795–799 (2010)

    Article  MathSciNet  Google Scholar 

  26. Gupta, V., Spanos, D., Hassibi, B., Murray, R.M.: Optimal LQG control across packet-dropping links. Syst. Control Lett. 56(6), 439–446 (2007)

    Article  MATH  Google Scholar 

  27. Gupta, V., Dana, A., Hespanha, J., Murray, R., Hassibi, B.: Data transmission over networks for estimation and control. IEEE Trans. Autom. Control 54(8), 1807–1819 (2009)

    Article  MathSciNet  Google Scholar 

  28. Gupta, V., Martins, N., Baras, J.: Optimal output feedback control using two remote sensors over erasure channels. IEEE Trans. Autom. Control 54(7), 1463–1476 (2009)

    Article  MathSciNet  Google Scholar 

  29. Gurt, A., Nair, G.N.: Internal stability of dynamic quantised control for stochastic linear plants. Automatica 45(6), 1387–1396 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  30. Hespanha, J., Naghshtabrizi, P., Xu, Y.: A survey of recent results in networked control systems. Proc. IEEE 95(1), 138–162 (2007)

    Article  Google Scholar 

  31. Huang, M., Nair, G., Evans, R.: Finite horizon LQ optimal control and computation with data rate constraints. In: 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC’05, pp. 179–184 (2005)

    Google Scholar 

  32. Imer, O.C., Yüksel, S., Başar, T.: Optimal control of LTI systems over unreliable communication links. Automatica 42(9), 1429–1439 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  33. Kim, Y.H.: Feedback capacity of the first-order moving average Gaussian channel. IEEE Trans. Inf. Theory 52(7), 3063–3079 (2006)

    Article  Google Scholar 

  34. Kim, Y.H.: Feedback capacity of stationary Gaussian channels. IEEE Trans. Inf. Theory 56(1), 57–85 (2010)

    Article  Google Scholar 

  35. Kim, K.D., Kumar, P.R.: Cyber-physical systems: a perspective at the centennial. Proc. IEEE 100(13), 1287–1308 (2012)

    Google Scholar 

  36. Korner, J., Orlitsky, A.: Zero-error information theory. IEEE Trans. Inf. Theory 44(6), 2207–2229 (1998)

    Article  MathSciNet  Google Scholar 

  37. Liberzon, D.: On stabilization of linear systems with limited information. IEEE Trans. Autom. Control 48(2), 304–307 (2003)

    Article  MathSciNet  Google Scholar 

  38. Lin, S., Costello, D.J. Jr.: Error Control Coding: Fundamentals and Applications. Prentice Hall, New York (1983). TUB-HH 2413-469 3

    Google Scholar 

  39. Martins, N., Dahleh, M., Elia, N.: Feedback stabilization of uncertain systems in the presence of a direct link. IEEE Trans. Autom. Control 51(3), 438–447 (2006)

    Article  MathSciNet  Google Scholar 

  40. Matveev, A.S., Savkin, A.V.: The problem of LQG optimal control via a limited capacity communication channel. Syst. Control Lett. 53(1), 51–64 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  41. Matveev, A., Savkin, A.: Comments on “control over noisy channels” and relevant negative results. IEEE Trans. Autom. Control 50(12), 2105–2110 (2005)

    Article  MathSciNet  Google Scholar 

  42. Matveev, A.S., Savkin, A.V.: An analogue of Shannon information theory for detection and stabilization via noisy discrete communication channels. SIAM J. Control Optim. 46(4), 1323–1367 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  43. Matveev, A.S., Savkin, A.V.: Shannon zero error capacity in the problems of state estimation and stabilization via noisy communication channels. Int. J. Control 80(2), 241–255 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  44. Matveev, A., Savkin, A.: Estimation and Control over Communication Networks. Birkhäuser, Basel (2009). Control Engineering

    MATH  Google Scholar 

  45. Middleton, R., Rojas, A., Freudenberg, J., Braslavsky, J.: Feedback stabilization over a first order moving average Gaussian noise channel. IEEE Trans. Autom. Control 54(1), 163–167 (2009)

    Article  MathSciNet  Google Scholar 

  46. Minero, P., Franceschetti, M., Dey, S., Nair, G.: Data rate theorem for stabilization over time-varying feedback channels. IEEE Trans. Autom. Control 54(2), 243–255 (2009)

    Article  MathSciNet  Google Scholar 

  47. Mo, Y., Sinopoli, B.: Kalman filtering with intermittent observations: tail distribution and critical value. IEEE Trans. Autom. Control 57(3), 677–689 (2012)

    Article  MathSciNet  Google Scholar 

  48. Nahi, N.: Optimal recursive estimation with uncertain observation. Automatica 15(4), 457–462 (1969)

    MathSciNet  MATH  Google Scholar 

  49. Nair, G.N., Evans, R.J.: Stabilizability of stochastic linear systems with finite feedback data rates. SIAM J. Control Optim. 43(2), 413–436 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  50. Nair, G., Fagnani, F., Zampieri, S., Evans, R.: Feedback control under data rate constraints: an overview. Proc. IEEE 95(1), 108–137 (2007)

    Article  Google Scholar 

  51. Ostrovsky, R., Rabani, Y., Schulman, L.: Error-correcting codes for automatic control. IEEE Trans. Inf. Theory 55(7), 2931–2941 (2009)

    Article  MathSciNet  Google Scholar 

  52. Sahai, A.: Anytime information theory. Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA (2001)

    Google Scholar 

  53. Sahai, A., Mitter, S.K.: 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 52(8), 3369–3395 (2006)

    Article  MathSciNet  Google Scholar 

  54. Sahai, A., Mitter, S.K.: The necessity and sufficiency of anytime capacity for stabilization of a linear system over a noisy communication link—Part II: vector systems (2006). Available on-line at arXiv:cs/0610146v2 [cs.IT]

  55. Schalkwijk, J.P.M., Kailath, T.: A coding scheme for additive noise channels with feedback—I: no bandwidth constraint. IEEE Trans. Inf. Theory 12, 172–182 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  56. Schenato, L., Sinopoli, B., Franceschetti, M., Poolla, K., Sastry, S.: Foundations of control and estimation over lossy networks. Proc. IEEE 95(1), 163–187 (2007)

    Article  Google Scholar 

  57. Schulman, L.: Coding for interactive communication. IEEE Trans. Inf. Theory 42(6), 1745–1756 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  58. Shannon, C.E.: The zero-error capacity of a noisy channel. IRE Trans. Inf. Theory 2, 8–19 (1956)

    Article  MathSciNet  Google Scholar 

  59. Shi, L., Epstein, M., Murray, R.: Kalman filtering over a packet-dropping network: a probabilistic perspective. IEEE Trans. Autom. Control 55(3), 594–604 (2010)

    Article  MathSciNet  Google Scholar 

  60. Simşek, T., Jain, R., Varaiya, P.: Scalar estimation and control with noisy binary observations. IEEE Trans. Autom. Control 49(9), 1598–1603 (2004)

    Article  Google Scholar 

  61. Sinopoli, B., Schenato, L., Franceschetti, M., Poolla, K., Jordan, M., Sastry, S.: Kalman filtering with intermittent observations. IEEE Trans. Autom. Control 49(9), 1453–1464 (2004)

    Article  MathSciNet  Google Scholar 

  62. Soummya, K., Sinopoli, B., Moura, J.M.F.: Kalman filtering with intermittent observations: weak convergence to a stationary distribution. IEEE Trans. Autom. Control 57(2), 405–420 (2012)

    Article  Google Scholar 

  63. Sukhavasi, R., Hassibi, B.: Error correcting codes for distributed control (2011). Available on-line at arXiv:1112.4236v2 [cs.IT]

  64. Tatikonda, S., Mitter, S.K.: Control over noisy channels. IEEE Trans. Autom. Control 49(7), 1196–1201 (2004)

    Article  MathSciNet  Google Scholar 

  65. Tatikonda, S., Mitter, S.K.: Control under communication constraints. IEEE Trans. Autom. Control 49(7), 1056–1068 (2004)

    Article  MathSciNet  Google Scholar 

  66. Tatikonda, S., Sahai, A., Mitter, S.K.: Stochastic linear control over a communication channel. IEEE Trans. Autom. Control 49(9), 1549–1561 (2004)

    Article  MathSciNet  Google Scholar 

  67. Witsenhausen, H.S.: A counterexample in stochastic optimum control. SIAM J. Control 6(1), 131–147 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  68. Wong, W.S., Brockett, R.: Systems with finite communication bandwidth constraints. I. State estimation problems. IEEE Trans. Autom. Control 42(9), 1294–1299 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  69. Wong, W.S., Brockett, R.: Systems with finite communication bandwidth constraints. II. Stabilization with limited information feedback. IEEE Trans. Autom. Control 44(5), 1049–1053 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  70. You, K., Xie, L.: Minimum data rate for mean square stabilization of discrete LTI systems over lossy channels. IEEE Trans. Autom. Control 55(10), 2373–2378 (2010)

    Article  MathSciNet  Google Scholar 

  71. You, K., Xie, L.: Minimum data rate for mean square stabilizability of linear systems with Markovian packet losses. IEEE Trans. Autom. Control 56(4), 772–785 (2011)

    Article  MathSciNet  Google Scholar 

  72. Yüksel, S.: Stochastic stabilization of noisy linear systems with fixed-rate limited feedback. IEEE Trans. Autom. Control 55(12), 2847–2853 (2010)

    Article  Google Scholar 

  73. Yüksel, S., Başar, T.: Control over noisy forward and reverse channels. IEEE Trans. Autom. Control 56(5), 1014–1029 (2011)

    Article  Google Scholar 

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Acknowledgement

This research was supported by LCCC—Linnaeus Grant VR 2007-8646, Swedish Research Council.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of California, San Diego, CA, 92093, USA

    Massimo Franceschetti

  2. Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Paolo Minero

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  1. Massimo Franceschetti
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  2. Paolo Minero
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Correspondence to Massimo Franceschetti .

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Editors and Affiliations

  1. Department of Automatic Control, Lund University, Lund, Sweden

    Giacomo Como

  2. Department of Automatic Control, Lund University, Lund, Sweden

    Bo Bernhardsson

  3. Department of Automatic Control, Lund University, Lund, Sweden

    Anders Rantzer

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Franceschetti, M., Minero, P. (2014). Elements of Information Theory for Networked Control Systems. In: Como, G., Bernhardsson, B., Rantzer, A. (eds) Information and Control in Networks. Lecture Notes in Control and Information Sciences, vol 450. Springer, Cham. https://doi.org/10.1007/978-3-319-02150-8_1

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  • DOI: https://doi.org/10.1007/978-3-319-02150-8_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02149-2

  • Online ISBN: 978-3-319-02150-8

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