Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
167 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
42 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Consistency of Value of Information: Effects of Packet Loss and Time Delay in Networked Control Systems Tasks (2403.11932v1)

Published 18 Mar 2024 in cs.IT, math.IT, and math.OC

Abstract: In this chapter, we study the consistency of the value of information$\unicode{x2014}$a semantic metric that claims to determine the right piece of information in networked control systems tasks$\unicode{x2014}$in a lossy and delayed communication regime. Our analysis begins with a focus on state estimation, and subsequently extends to feedback control. To that end, we make a causal tradeoff between the packet rate and the mean square error. Associated with this tradeoff, we demonstrate the existence of an optimal policy profile, comprising a symmetric threshold scheduling policy based on the value of information for the encoder and a non-Gaussian linear estimation policy for the decoder. Our structural results assert that the scheduling policy is expressible in terms of $3d-1$ variables related to the source and the channel, where $d$ is the time delay, and that the estimation policy incorporates no residual related to signaling. We then construct an optimal control policy by exploiting the separation principle.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (38)
  1. E. Uysal, O. Kaya, A. Ephremides, J. Gross, M. Codreanu, P. Popovski, M. Assaad, G. Liva, A. Munari, B. Soret, T. Soleymani, and K. H. Johansson, “Semantic communications in networked systems: A data significance perspective,” IEEE Network, vol. 36, no. 4, pp. 233–240, 2022.
  2. T. Soleymani, J. S. Baras, and S. Hirche, “Value of information in feedback control: Quantification,” IEEE Trans. on Automatic Control, vol. 67, no. 7, pp. 3730–3737, 2022.
  3. T. Soleymani, J. S. Baras, S. Hirche, and K. H. Johansson, “Value of information in feedback control: Global optimality,” IEEE Trans. on Automatic Control, vol. 68, no. 6, pp. 3641–3647, 2023.
  4. T. Soleymani, Value of Information Analysis in Feedback Control. PhD thesis, Technical University of Munich, 2019.
  5. T. Soleymani, J. S. Baras, and K. H. Johansson, “Relation between value and age of information in feedback control,” Age of Information: Foundations and Applications, p. 283, 2023.
  6. J. P. Hespanha, P. Naghshtabrizi, and Y. Xu, “A survey of recent results in networked control systems,” Proceedings of the IEEE, vol. 95, no. 1, pp. 138–162, 2007.
  7. G. N. Nair, F. Fagnani, S. Zampieri, and R. J. Evans, “Feedback control under data rate constraints: An overview,” Proceedings of the IEEE, vol. 95, no. 1, pp. 108–137, 2007.
  8. T. Soleymani, J. S. Baras, S. Hirche, and K. H. Johansson, “Feedback control over noisy channels: Characterization of a general equilibrium,” IEEE Transactions on Automatic Control, vol. 67, no. 7, pp. 3396–3409, 2021.
  9. O. C. Imer and T. Başar, “Optimal estimation with limited measurements,” Intl. Journal of Systems, Control and Communications, vol. 2, no. 1-3, pp. 5–29, 2010.
  10. G. M. Lipsa and N. C. Martins, “Remote state estimation with communication costs for first-order LTI systems,” IEEE Trans. on Automatic Control, vol. 56, no. 9, pp. 2013–2025, 2011.
  11. G. M. Lipsa and N. C. Martins, “Optimal state estimation in the presence of communication costs and packet drops,” in Proc. Allerton Conference on Communication, Control, and Computing, pp. 160–169, 2009.
  12. A. Molin and S. Hirche, “Event-triggered state estimation: An iterative algorithm and optimality properties,” IEEE Trans. on Automatic Control, vol. 62, no. 11, pp. 5939–5946, 2017.
  13. J. Chakravorty and A. Mahajan, “Fundamental limits of remote estimation of autoregressive Markov processes under communication constraints,” IEEE Trans. on Automatic Control, vol. 62, no. 3, pp. 1109–1124, 2016.
  14. J. Chakravorty and A. Mahajan, “Remote-state estimation with packet drop,” Proc. Workshop Distrib. Estimation Control Netw. Syst., vol. 49, no. 22, pp. 7–12, 2016.
  15. J. Chakravorty and A. Mahajan, “Structure of optimal strategies for remote estimation over Gilbert-Elliott channel with feedback,” in Proc. Symposium on Information Theory, pp. 1272–1276, 2017.
  16. M. Rabi, G. V. Moustakides, and J. S. Baras, “Adaptive sampling for linear state estimation,” SIAM Journal on Control and Optimization, vol. 50, no. 2, pp. 672–702, 2012.
  17. N. Guo and V. Kostina, “Optimal causal rate-constrained sampling for a class of continuous Markov processes,” IEEE Trans. on Information Theory, vol. 67, no. 12, pp. 7876–7890, 2021.
  18. N. Guo and V. Kostina, “Optimal causal rate-constrained sampling of the Wiener process,” IEEE Trans. on Automatic Control, in press, 2021.
  19. Y. Sun, Y. Polyanskiy, and E. Uysal, “Sampling of the Wiener process for remote estimation over a channel with random delay,” IEEE Trans. on Information Theory, vol. 66, no. 2, pp. 1118–1135, 2019.
  20. B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. I. Jordan, and S. S. Sastry, “Kalman filtering with intermittent observations,” IEEE Trans. on Automatic Control, vol. 49, no. 9, pp. 1453–1464, 2004.
  21. J. Wu, G. Shi, B. D. Anderson, and K. H. Johansson, “Kalman filtering over Gilbert–Elliott channels: Stability conditions and critical curve,” IEEE Trans. on Automatic Control, vol. 63, no. 4, pp. 1003–1017, 2017.
  22. D. E. Quevedo, A. Ahlén, and K. H. Johansson, “State estimation over sensor networks with correlated wireless fading channels,” IEEE Trans. on Automatic Control, vol. 58, no. 3, pp. 581–593, 2013.
  23. L. Schenato, “Optimal estimation in networked control systems subject to random delay and packet drop,” IEEE Trans. on Automatic Control, vol. 53, no. 5, pp. 1311–1317, 2008.
  24. V. Gupta, A. F. Dana, J. P. Hespanha, R. M. Murray, and B. Hassibi, “Data transmission over networks for estimation and control,” IEEE Trans. on Automatic Control, vol. 54, no. 8, pp. 1807–1819, 2009.
  25. T. Soleymani, J. S. Baras, and K. H. Johansson, “State estimation over delayed and lossy channels: An encoder-decoder synthesis,” IEEE Trans. on Automatic Control, 2023.
  26. H. J. Kushner, “On the optimum timing of observations for linear control systems with unknown initial state,” IEEE Trans. on Automatic Control, vol. 9, no. 2, pp. 144–150, 1964.
  27. L. Meier, J. Peschon, and R. M. Dressler, “Optimal control of measurement subsystems,” IEEE Trans. on Automatic Control, vol. 12, no. 5, pp. 528–536, 1967.
  28. T. Soleymani, S. Hirche, and J. S. Baras, “Optimal self-driven sampling for estimation based on value of information,” in Proc. Int. Workshop on Discrete Event Systems, pp. 183–188, 2016.
  29. T. Soleymani, S. Hirche, and J. S. Baras, “Optimal stationary self-triggered sampling for estimation,” in Proc. IEEE Conf. on Decision and Control, pp. 3084–3089, 2016.
  30. A. S. Leong, S. Dey, and D. E. Quevedo, “Sensor scheduling in variance based event triggered estimation with packet drops,” IEEE Trans. on Automatic Control, vol. 62, no. 4, pp. 1880–1895, 2017.
  31. A. S. Leong, S. Dey, and D. E. Quevedo, “Transmission scheduling for remote state estimation and control with an energy harvesting sensor,” Automatica, vol. 91, pp. 54–60, 2018.
  32. H. Witsenhausen, “On the structure of real-time source coders,” Bell System Technical Journal, vol. 58, no. 6, pp. 1437–1451, 1979.
  33. J. Walrand and P. Varaiya, “Optimal causal coding-decoding problems,” IEEE Trans. on Information Theory, vol. 29, no. 6, pp. 814–820, 1983.
  34. S. Yüksel, “On optimal causal coding of partially observed Markov sources in single and multiterminal settings,” IEEE Trans. on Information Theory, vol. 59, no. 1, pp. 424–437, 2012.
  35. V. S. Borkar, S. K. Mitter, and S. Tatikonda, “Optimal sequential vector quantization of Markov sources,” SIAM journal on control and optimization, vol. 40, no. 1, pp. 135–148, 2001.
  36. A. Khina, V. Kostina, A. Khisti, and B. Hassibi, “Tracking and control of gauss–markov processes over packet-drop channels with acknowledgments,” IEEE Trans. on Control of Network Systems, vol. 6, no. 2, pp. 549–560, 2018.
  37. T. Tanaka, K.-K. K. Kim, P. A. Parrilo, and S. K. Mitter, “Semidefinite programming approach to Gaussian sequential rate-distortion trade-offs,” IEEE Trans. on Automatic Control, vol. 62, no. 4, pp. 1896–1910, 2016.
  38. K. J. Åström, Introduction to Stochastic Control Theory. Dover Publications, 2006.
Citations (3)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets