Event-Triggered Feedback in Control, Estimation, and Optimization

Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 406)


Networked control systems often send information across the communication network in a periodic manner. The selected period, however, must assure adequate system performance over a wide range of operating conditions and this conservative’ choice may result in significant over-provisioning of the communication network. This observation has motivated the use of sporadic transmission across the network’s feedback channels. Event-triggering represents one way of generating such sporadic transmissions. In event-triggered feedback, a sensor transmits when some internal measure of the novelty in the sensor information exceeds a specified threshold. In particular, this means that when the gap between the current and the more recently transmitted sensor measurements exceeds a state-dependent threshold, then the information is transmitted across the channel. The state-dependent thresholds are chosen in a way that preserves commonly used stability concepts such as input-to-state stability or \({\mathcal L}_2\) stability. This approach for threshold selection therefore provides a systematic way of triggering transmissions that provides some guarantees on overall control system performance. While early work in event-triggering focused on control applications, this technique can also be used in distributed estimation and distributed optimization. This chapter reviews recent progress in the use of state-dependent event-triggering in embedded control, networked control systems, distributed estimation, and distributed optimization.


Network Control System Central Processing Unit Utilization Stability Concept Broadcast Protocol Control System Performance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Anta, A., Tabuada, P.: Self-triggered stabilization of homogeneous control systems. In: Proceedings of the American Control Conference, Seattle, Washington, USA, June 11-13, 2008, pp. 4129–4134 (2008)Google Scholar
  2. 2.
    Arzen, K.-E.: A simple event-based PID controller. In: Procedings of the 14th World Congress of the International Federation of Automatic Control (IFAC), Beijing, P.R. China (1999)Google Scholar
  3. 3.
    Arzen, K.-E., Cervin, A., Eker, J., Sha, L.: An introduction to control and scheduling co-design. In: IEEE Conference on Decision and Control, Sydney, NSW, Australia, vol. 5, pp. 4865–4870 (December 2000)Google Scholar
  4. 4.
    Astrom, K.J., Bernhardsson, B.M.: Comparison of Riemann and Lebesgue sampling for first order stochastic systems. In: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, USA, December 10-13, vol. 2, pp. 2011–2016 (2002)Google Scholar
  5. 5.
    Bao, L., Skoglund, M., Johansson, K.H.: Encoder-decoder design for event-triggered feedback control over bandlimited channels. In: American Control Conference, Minneapolis, Minnesota, USA (2006)Google Scholar
  6. 6.
    Bertsekas, D.P.: Nonlinear programming. Athena Scientific, Belmont (1999)Google Scholar
  7. 7.
    Bhattacharya, R., Balas, G.J.: Anytime control algorithm: model reduction approach. Journal of Guidance, Control and Dynamics 27(5), 767–776 (2004)CrossRefGoogle Scholar
  8. 8.
    Buttazzo, G., Lipari, G., Abeni, L.: Elastic task model for adaptive rate control. In: IEEE Real-Time Systems Symposium (RTSS), pp. 286–295 (1998)Google Scholar
  9. 9.
    Caccamo, M., Buttazzo, G., Sha, L.: Elastic feedback control. In: IEEE Euromicro Conference on Real-Time Systems, ECRTS (2000)Google Scholar
  10. 10.
    Camacho, A., Marti, P., Velasco, M., Bini, E.: Demo abstract: Implementation of self-triggered controllers. In: Demo Session of 15th IEEE Real-time and Embedded Technology and Applications Symposium (RTAS 2009), San Francisco, California, USA (2009)Google Scholar
  11. 11.
    Carnevale, D., Teel, A.R., Nesic, D.: A Lyapunov proof of improved maximum allowable transfer interval for networked control systems. IEEE Transactions on Automatic Control 52, 892–897 (2007)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Cervin, A., Eker, J.: Control-scheduling codesign of real-time systems: the control server approach. Journal of Embedded Computing 1(2), 209–224 (2004)Google Scholar
  13. 13.
    Cervin, A., Henningsson, T.: Scheduling of event-triggered controllers on a shared network. In: Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico (December 2008)Google Scholar
  14. 14.
    Chen, W.P., Hou, J.C., Sha, L., Caccamo, M.: A distributed, energy-aware, utility-based approach for data transport in wireless sensor networks. In: Proceedings of the IEEE Milcom (2005)Google Scholar
  15. 15.
    Chen, W.P., Sha, L.: An energy-aware data-centric generic utility based approach in wireless sensor networks. In: IPSN, pp. 215–224 (2004)Google Scholar
  16. 16.
    Chiang, M., Bell, J.: Balancing supply and demand of bandwidth in wireless cellular networks: utility maximization over powers and rates. In: Proc. IEEE INFOCOM, vol. 4, pp. 2800–2811 (2004)Google Scholar
  17. 17.
    Chiang, M., Low, S.H., Calderbank, A.R., Doyle, J.C.: Layering as optimization decomposition: A mathematical theory of network architectures. Proceedings of the IEEE 95(1), 255–312 (2007)CrossRefGoogle Scholar
  18. 18.
    Cogill, R.: Event-based control using quadratic approximate value functions. In: IEEE Conference on Decision and Control, Shanghai, China (2009)Google Scholar
  19. 19.
    Cogill, R., Lall, S., Hespanha, J.P.: A constant factor approximation algorithm for event-based sampling. In: Proceedings of the American Control Conference, New York City, USA (July 2007)Google Scholar
  20. 20.
    Fleming, W.H., Rishel, R.W.: Deterministic and stochastic control. Springer, Heidelberg (1975)zbMATHGoogle Scholar
  21. 21.
    Fontanelli, D., Greco, L., Bicchi, A.: Anytime control algorithms for embedded real-time systems. In: Hybrid Systems: computation and control (2008)Google Scholar
  22. 22.
    Gai, P., Abeni, L., Giorgi, M., Buttazzo, G.: A new kernel approach for modular real-time systems development. In: Proceedings of the 13th IEEE Euromicro Conference on Real-Time Systems (2001)Google Scholar
  23. 23.
    Heemels, W.P.M.H., Gorter, R.J.A., van Zijl, A., van den Bosch, P., Weiland, S.: Asynchronous measurement and control: a case study on motor synchronization. Control Engineering Practice 7, 1467–1482 (1999)CrossRefGoogle Scholar
  24. 24.
    Heemels, W.P.M.H., Sandee, J.H., van den Bosch, P.P.J.: Analysis of event-driven controllers for linear systems. International Journal of Control 81(4), 571–590 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  25. 25.
    Heemels, W.P.M.H., Teel, A.R., van de Wouw, N., Nesic, D.: Networked control systems with communication constraints: tradeoffs between sampling intervals, delays and performance. Submitted to the 2009 European Control Conference, ECC (2009)Google Scholar
  26. 26.
    Henningsson, T., Cervin, A.: Comparison of LTI and event-based control for a moving cart with quantized position measurements. In: European Control Conference, Budapest, Hungary (August 2009)Google Scholar
  27. 27.
    Henningsson, T., Johannesson, E., Cervin, A.: Sporadic event-based control of first-order linear stochastic systems. Automatica 44(11), 2890–2895 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    Ho, Y.C., Servi, L., Suri, R.: A class of center-free resource allocation algorithms. In: Large Scale Systems Theory and Applications: Proceedings of the IFAC Symposium, Toulouse, France, June 24-26, 1980, p. 475. Franklin Book Co. (1981)Google Scholar
  29. 29.
    Hristu-Varsakelis, D., Kumar, P.R.: Interrupt-based feedback control over shared communication medium. Technical Report TR 2003-34, University of Maryland, ISR (2003)Google Scholar
  30. 30.
    Imer, O.C., Basar, T.: Optimal estimation with limited measurements. In: Proceedings of the IEEE Conference on Decision and Control, Seville, Spain (2005)Google Scholar
  31. 31.
    Imer, O.C., Basar, T.: To measure or to control: optimal control of LTI systems with scheduled measurements and controls. In: American Control Conference (2006)Google Scholar
  32. 32.
    Isidori, A.: Nonlinear Control Systems II. Springer, Heidelberg (1999)CrossRefzbMATHGoogle Scholar
  33. 33.
    Johansson, B., Rabi, M., Johansson, M.: A simple peer-to-peer algorithm for distributed optimization in sensor networks. In: Proceedings of the 46th IEEE Conference on Decision and Control, pp. 4705–4710 (2007)Google Scholar
  34. 34.
    Johansson, B., Soldati, P., Johansson, M.: Mathematical Decomposition Techniques for Distributed Cross-Layer Optimization of Data Networks. IEEE Journal on Selected Areas in Communications 24(8), 1535–1547 (2006)CrossRefGoogle Scholar
  35. 35.
    Karatzas, I., Wang, H.: Utility maximization with discretionary stopping. SIAM Journal on Control and Optimization 39(1), 306–329 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  36. 36.
    Kelly, F.P., Maulloo, A.K., Tan, D.K.H.: Rate control for communication networks: shadow prices, proportional fairness and stability. Journal of the Operational Research Society 49(3), 237–252 (1998)zbMATHGoogle Scholar
  37. 37.
    Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice-Hall, Englewood Cliffs (2002)zbMATHGoogle Scholar
  38. 38.
    Kim, B.H., Baldick, R.: A comparison of distributed optimal power flow algorithms. IEEE Transactions on Power Systems 15(2), 599–604 (2000)CrossRefGoogle Scholar
  39. 39.
    Kofman, I., Braslavsky, J.H.: Level crossing sampling in feedback stabilization under data-rate constraints. In: IEEE Conference on Decision and Control, San Diego, CA, USA (2006)Google Scholar
  40. 40.
    Lehmann, D., Lunze, J.: Event-based control: a state-feedback approach. In: Proceedings of the European Control Conference, Budapest, Hungary, pp. 1716–1721 (2009)Google Scholar
  41. 41.
    Lemmon, M., Chantem, T., Hu, X.S., Zyskowski, M.: On self-triggered full-information h-infinity controllers. In: Hybrid Systems: computation and control, Pisa, Italy (July 2007)Google Scholar
  42. 42.
    Li, L., Lemmon, M.D.: Optimal event triggered transmission of information in distributed state estimation problems. In: American Control Conference, Baltimore, MD, USA (2010)Google Scholar
  43. 43.
    Liberzon, D.: On stabilization of linear systems with limited information. IEEE Transactions on Automatic Control 48, 304–307 (2003)CrossRefMathSciNetGoogle Scholar
  44. 44.
    Low, S.H., Lapsley, D.E.: Optimization flow control, I: basic algorithm and convergence. IEEE/ACM Transactions on Networking (TON) 7(6), 861–874 (1999)CrossRefGoogle Scholar
  45. 45.
    Lu, C., Stankovic, J.A., Son, S.H., Tao, G.: Feedback control real-time scheduling: Framework, modeling and algorithms. Real-time Systems 23(1-2), 85–126 (2002)CrossRefzbMATHGoogle Scholar
  46. 46.
    Madan, R., Lall, S.: Distributed algorithms for maximum lifetime routing in wireless sensor networks. In: IEEE GLOBECOM 2004, vol. 2 (2004)Google Scholar
  47. 47.
    Matveev, A., Savkin, A.: The problem of state estimation via asynchronous communication channels with irregular transmission times. IEEE Transactions on Automatic Control 48(4), 670–676 (2003)CrossRefMathSciNetGoogle Scholar
  48. 48.
    Mazo, M., Tabuada, P.: On event-triggered and self-triggered control over sensor/actuator networks. In: Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico (December 2008)Google Scholar
  49. 49.
    Nedic, A., Ozdaglar, A.: Distributed subgradient methods for multi-agent optimization. IEEE Transactions on Automatic Control 54(1), 48–61 (2009)CrossRefMathSciNetGoogle Scholar
  50. 50.
    Nesic, D., Teel, A.R.: Input-output stability properties of networked control systems. IEEE Transactions on Automatic Control 49(10), 1650–1667 (2004)CrossRefMathSciNetGoogle Scholar
  51. 51.
    Nesic, D., Teel, A.R.: Input-to-state stability of networked control systems. Automatica 40(12), 2121–2128 (2004)zbMATHMathSciNetGoogle Scholar
  52. 52.
    Olfati-Saber, R., Fax, J.A., Murray, R.M.: Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE 95(1), 215–233 (2007)CrossRefGoogle Scholar
  53. 53.
    Palomar, D.P., Chiang, M.: Alternative Distributed Algorithms for Network Utility Maximization: Framework and Applications. IEEE Transactions on Automatic Control 52(12), 2254–2269 (2007)CrossRefMathSciNetGoogle Scholar
  54. 54.
    Polak, E.: Stability and graphical analysis of first order of pulse-width modulated sampled data regulator systems. IRE Trans. Automatic Control  AC-6(3), 276–282 (1963)CrossRefGoogle Scholar
  55. 55.
    Qiu, Y., Marbach, P.: Bandwidth allocation in ad hoc networks: A price-based approach. In: Proceedings of IEEE INFOCOM 2003, vol. 2, pp. 797–807 (2003)Google Scholar
  56. 56.
    Rabbat, M., Nowak, R.: Distributed optimization in sensor networks. In: Proceedings of the third international symposium on Information processing in sensor networks, pp. 20–27 (2004)Google Scholar
  57. 57.
    Rabi, M., Johansson, K.H., Johansson, M.: Optimal stopping for event-triggered sensing and actuation. In: Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico (December 2008)Google Scholar
  58. 58.
    Rabi, M., Moustakides, G.V., Baras, J.S.: Efficient sampling for keeping track of an Ornstein-Uhlenbeck process. In: Proceedings of the Mediterranean conference on control and automation (2006)Google Scholar
  59. 59.
    Rabi, M., Moustakides, G.V., Baras, J.S.: Multiple sampling for estimation on a finite horizon. In: 45th IEEE Conference on Decision and Control, pp. 1351–1357 (2006)Google Scholar
  60. 60.
    Rabi, M., Moustakides, G.V., Baras, J.S.: Adaptive sampling for linear state estimation. Submitted to the SIAM journal on Control and Optimization (December 2008)Google Scholar
  61. 61.
    Rabi, M.: Packet based Inference and Control. PhD thesis, University of Maryland (2006)Google Scholar
  62. 62.
    Rabi, M., Baras, J.S.: Level-triggered control of a scalar linear system. In: Proceedings of the 16th Mediterranean Conference on Control and Automation, Athens, Greece (July 2007)Google Scholar
  63. 63.
    Sandee, J.H.: Event-driven Control in Theory and Practice: tradeoffs in software and control performance. PhD thesis, Technische Universiteit Eindhoven (2006)Google Scholar
  64. 64.
    Sandee, J.H., Heemels, W.P.M.H., van den Bosch, P.P.J.: Case studies in event-driven control. In: Hybrid Systems: computation and control, Pisa, Italy (April 2007)Google Scholar
  65. 65.
    Sandee, J.H., Visser, P.M., Heemels, W.P.M.H.: Analysis and experimental validation of processor load for event-driven controllers. In: IEEE Conference on Control and Applications (CCA), Munich, Germany, pp. 1879–1884 (2006)Google Scholar
  66. 66.
    Seto, D., Lehoczky, J.P., Sha, L., Shin, K.G.: On task schedulability in real-time control systems. In: IEEE Real-time Technology and Applications Symposium (RTAS), pp. 13–21 (1996)Google Scholar
  67. 67.
    Sijs, J., Lasar, M.: On event based state estimation. In: Majumdar, R., Tabuada, P. (eds.) HSCC 2009. LNCS, vol. 5469, pp. 336–350. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  68. 68.
    Sinopoli, B., Schenato, L., Franceschetti, M., Poolla, K., Jordan, M., Sastry, S.: Kalman filtering with intermittent observations. IEEE Transactions on Automatic Control 49(9), 1453–1464 (2004)CrossRefMathSciNetGoogle Scholar
  69. 69.
    Speranzon, A., Fischione, C., Johansson, K.H.: Distributed and Collaborative Estimation over Wireless Sensor Networks. In: Proceedings of the IEEE Conference on Decision and Control, pp. 1025–1030 (2006)Google Scholar
  70. 70.
    Tabuada, P.: Event-triggered real-time scheduling of stabilizing control tasks. IEEE Transactions on Automatic Control 52(9), 1680–1685 (2007)CrossRefMathSciNetGoogle Scholar
  71. 71.
    Tabuada, P., Wang, X.: Preliminary results on state-triggered scheduling of stabilizing control tasks. In: IEEE Conference on Decision and Control (2006)Google Scholar
  72. 72.
    Tsitsiklis, J., Bertsekas, D., Athans, M.: Distributed asynchronous deterministic and stochastic gradient optimization algorithms. IEEE Transactions on Automatic Control 31(9), 803–812 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  73. 73.
    Tsypkin, Y.Z.: Relay Control Systems. Cambridge University Press, Cambridge (1984)zbMATHGoogle Scholar
  74. 74.
    van der Schaft, A.J.: L2-gain and passivity techniques in nonlinear control. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  75. 75.
    Velasco, M., Marti, P., Fuertes, J.M.: The self triggered task model for real-time control systems. In: Work-in-Progress Session of the 24th IEEE Real-time Systems Symposium (RTSS 2003), Cancun, Mexico (December 2003)Google Scholar
  76. 76.
    Voulgaris, P.: Control of asynchronous sampled data systems. IEEE Transactions on Automatic Control 39(7), 1451–1455 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  77. 77.
    Wan, P., Lemmon, M.: Distributed Flow Control using Embedded Sensor-Actuator Networks for the Reduction of Combined Sewer Overflow (CSO) Events. In: Proceedings of the 46th IEEE Conference on Decision and Control, pp. 1529–1534 (2007)Google Scholar
  78. 78.
    Wan, P., Lemmon, M.D.: Distributed network utility maximization using event-triggered augmented lagrangian methods. In: Proceedings of the American Control Conference, St. Louis, MO, USA (June 2009)Google Scholar
  79. 79.
    Wan, P., Lemmon, M.D.: Event-triggered distributed optimization in sensor networks. In: Information Processing in Sensor Networks (IPSN), San Francisco, California, USA (April 2009)Google Scholar
  80. 80.
    Wang, X., Lemmon, M.D.: Decentralized event-triggered broadcasts over networked control systems. In: Hybrid Systems: computation and control, St. Louis, Missouri (April 2008)Google Scholar
  81. 81.
    Wang, X., Lemmon, M.D.: Event-triggered broadcasting across distributed networked control systems. In: Proceedings of the American Control Conference, Seattle, Washington, USA (June 2008)Google Scholar
  82. 82.
    Wang, X., Lemmon, M.D.: Event-triggering in distributed networked control systems. Submitted to the IEEE Transactions on Automatic Control (February 2009)Google Scholar
  83. 83.
    Wang, X., Lemmon, M.D.: Self-triggered feedback control systems with finite-gain l2 stability. IEEE Transactions on Automatic Control 54(3), 452–467 (2009)CrossRefMathSciNetGoogle Scholar
  84. 84.
    Wang, X., Lemmon, M.D.: Self-triggered feedback systems with state-independent disturbances. In: Proceedings of the American Control Conference, St. Louis Missouri, USA (June 2009)Google Scholar
  85. 85.
    Wen, J.T., Arcak, M.: A unifying passivity framework for network flow control. IEEE Transactions on Automatic Control 49(2), 162–174 (2004)CrossRefMathSciNetGoogle Scholar
  86. 86.
    Xiao, L., Johansson, M., Boyd, S.P.: Simultaneous routing and resource allocation via dual decomposition. IEEE Transactions on Communications 52(7), 1136–1144 (2004)CrossRefGoogle Scholar
  87. 87.
    Xu, Y., Hespanha, J.P.: Optimal communication logics in networked control systems. In: Proceedings of the IEEE Conference on Decision and Control, Nassau, Bahamas, vol. 4, pp. 3527–3532 (2004)Google Scholar
  88. 88.
    Xu, Y., Hespanha, J.P.: Communication logic design and analysis for networked control systems. In: Menini, L., Zaccarian, L., Abdallah, C.T. (eds.) Current Trends in Nonlinear Systems and Control, Systems and Control: Foundations and Applications, pp. 495–514. Birkhäuser, Boston (2006)CrossRefGoogle Scholar
  89. 89.
    Xue, Y., Li, B., Nahrstedt, K.: Optimal resource allocation in wireless ad hoc networks: a price-based approach. IEEE Transactions on Mobile Computing 5(4), 347–364 (2006)CrossRefGoogle Scholar
  90. 90.
    Zhang, W., Branicky, M.S., Phillips, S.M.: Stability of networked control systems. IEEE Control Systems Magazine 21(1), 84–99 (2001)CrossRefGoogle Scholar
  91. 91.
    Zhu, B., Sinopoli, B., Poolla, K., Sastry, S.: Estimation over wireless sensor networks. In: American Control Conference, pp. 2732–2737 (2007)Google Scholar

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© Springer London 2010

Authors and Affiliations

  1. 1.University of Notre DameNotre DameUSA

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