Abstract
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.
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Keywords
- Network Control System
- Central Processing Unit Utilization
- Stability Concept
- Broadcast Protocol
- Control System Performance
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References
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)
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)
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)
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)
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)
Bertsekas, D.P.: Nonlinear programming. Athena Scientific, Belmont (1999)
Bhattacharya, R., Balas, G.J.: Anytime control algorithm: model reduction approach. Journal of Guidance, Control and Dynamics 27(5), 767–776 (2004)
Buttazzo, G., Lipari, G., Abeni, L.: Elastic task model for adaptive rate control. In: IEEE Real-Time Systems Symposium (RTSS), pp. 286–295 (1998)
Caccamo, M., Buttazzo, G., Sha, L.: Elastic feedback control. In: IEEE Euromicro Conference on Real-Time Systems, ECRTS (2000)
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)
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)
Cervin, A., Eker, J.: Control-scheduling codesign of real-time systems: the control server approach. Journal of Embedded Computing 1(2), 209–224 (2004)
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)
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)
Chen, W.P., Sha, L.: An energy-aware data-centric generic utility based approach in wireless sensor networks. In: IPSN, pp. 215–224 (2004)
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)
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)
Cogill, R.: Event-based control using quadratic approximate value functions. In: IEEE Conference on Decision and Control, Shanghai, China (2009)
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)
Fleming, W.H., Rishel, R.W.: Deterministic and stochastic control. Springer, Heidelberg (1975)
Fontanelli, D., Greco, L., Bicchi, A.: Anytime control algorithms for embedded real-time systems. In: Hybrid Systems: computation and control (2008)
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)
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)
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)
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)
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)
Henningsson, T., Johannesson, E., Cervin, A.: Sporadic event-based control of first-order linear stochastic systems. Automatica 44(11), 2890–2895 (2008)
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)
Hristu-Varsakelis, D., Kumar, P.R.: Interrupt-based feedback control over shared communication medium. Technical Report TR 2003-34, University of Maryland, ISR (2003)
Imer, O.C., Basar, T.: Optimal estimation with limited measurements. In: Proceedings of the IEEE Conference on Decision and Control, Seville, Spain (2005)
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)
Isidori, A.: Nonlinear Control Systems II. Springer, Heidelberg (1999)
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)
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)
Karatzas, I., Wang, H.: Utility maximization with discretionary stopping. SIAM Journal on Control and Optimization 39(1), 306–329 (2000)
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)
Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice-Hall, Englewood Cliffs (2002)
Kim, B.H., Baldick, R.: A comparison of distributed optimal power flow algorithms. IEEE Transactions on Power Systems 15(2), 599–604 (2000)
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)
Lehmann, D., Lunze, J.: Event-based control: a state-feedback approach. In: Proceedings of the European Control Conference, Budapest, Hungary, pp. 1716–1721 (2009)
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)
Li, L., Lemmon, M.D.: Optimal event triggered transmission of information in distributed state estimation problems. In: American Control Conference, Baltimore, MD, USA (2010)
Liberzon, D.: On stabilization of linear systems with limited information. IEEE Transactions on Automatic Control 48, 304–307 (2003)
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)
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)
Madan, R., Lall, S.: Distributed algorithms for maximum lifetime routing in wireless sensor networks. In: IEEE GLOBECOM 2004, vol. 2 (2004)
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)
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)
Nedic, A., Ozdaglar, A.: Distributed subgradient methods for multi-agent optimization. IEEE Transactions on Automatic Control 54(1), 48–61 (2009)
Nesic, D., Teel, A.R.: Input-output stability properties of networked control systems. IEEE Transactions on Automatic Control 49(10), 1650–1667 (2004)
Nesic, D., Teel, A.R.: Input-to-state stability of networked control systems. Automatica 40(12), 2121–2128 (2004)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Rabi, M.: Packet based Inference and Control. PhD thesis, University of Maryland (2006)
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)
Sandee, J.H.: Event-driven Control in Theory and Practice: tradeoffs in software and control performance. PhD thesis, Technische Universiteit Eindhoven (2006)
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)
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)
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)
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)
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)
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)
Tabuada, P.: Event-triggered real-time scheduling of stabilizing control tasks. IEEE Transactions on Automatic Control 52(9), 1680–1685 (2007)
Tabuada, P., Wang, X.: Preliminary results on state-triggered scheduling of stabilizing control tasks. In: IEEE Conference on Decision and Control (2006)
Tsitsiklis, J., Bertsekas, D., Athans, M.: Distributed asynchronous deterministic and stochastic gradient optimization algorithms. IEEE Transactions on Automatic Control 31(9), 803–812 (1986)
Tsypkin, Y.Z.: Relay Control Systems. Cambridge University Press, Cambridge (1984)
van der Schaft, A.J.: L2-gain and passivity techniques in nonlinear control. Springer, Heidelberg (2000)
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)
Voulgaris, P.: Control of asynchronous sampled data systems. IEEE Transactions on Automatic Control 39(7), 1451–1455 (1994)
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)
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)
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)
Wang, X., Lemmon, M.D.: Decentralized event-triggered broadcasts over networked control systems. In: Hybrid Systems: computation and control, St. Louis, Missouri (April 2008)
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)
Wang, X., Lemmon, M.D.: Event-triggering in distributed networked control systems. Submitted to the IEEE Transactions on Automatic Control (February 2009)
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)
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)
Wen, J.T., Arcak, M.: A unifying passivity framework for network flow control. IEEE Transactions on Automatic Control 49(2), 162–174 (2004)
Xiao, L., Johansson, M., Boyd, S.P.: Simultaneous routing and resource allocation via dual decomposition. IEEE Transactions on Communications 52(7), 1136–1144 (2004)
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)
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)
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)
Zhang, W., Branicky, M.S., Phillips, S.M.: Stability of networked control systems. IEEE Control Systems Magazine 21(1), 84–99 (2001)
Zhu, B., Sinopoli, B., Poolla, K., Sastry, S.: Estimation over wireless sensor networks. In: American Control Conference, pp. 2732–2737 (2007)
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Lemmon, M. (2010). Event-Triggered Feedback in Control, Estimation, and Optimization. In: Bemporad, A., Heemels, M., Johansson, M. (eds) Networked Control Systems. Lecture Notes in Control and Information Sciences, vol 406. Springer, London. https://doi.org/10.1007/978-0-85729-033-5_9
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