On time-triggered and event-based control of integrator systems over a shared communication system

Mathematics of Control, Signals and Systems - Tập 25 - Trang 517-557 - 2013
Rainer Blind1, Frank Allgöwer1
1Institute for Systems Theory and Automatic Control, University of Stuttgart, Stuttgart, Germany

Tóm tắt

When analyzing networked control systems, where the control loop is closed over a communication system, it is crucial to take the communication system into account. Hence, time-triggered and event-based control of an integrator system with noise over a shared communication system is analyzed. Thereby, analytical models of different communication systems are used and the analysis is focused on the effect of the communication system on the performance, as well as the interaction between control and communication. For time-triggered control, where the event times are known in advance, a deterministic communication protocol can be used. Hence, time-triggered control with the two most well-known deterministic communication protocols, time division multiple access (TDMA) and frequency division multiple access (FDMA), is analyzed. For event-based control, where the events appear at random times, a contention-based communication protocol should be used. Hence, event-based control is analyzed with different contention-based communication protocols: pure ALOHA, slotted ALOHA, a queueing system, and Erlang’s loss model. It turns out that time-triggered control with either TDMA or FDMA outperforms event-based control with pure or slotted ALOHA. However, event-based control with a properly designed queueing system gives an even better performance. Thus, we conclude that it is crucial to take the details of the communication system into account.

Tài liệu tham khảo

Åström KJ, Bernhardsson BM (2002) Comparison of Riemann and Lebesgue sampling for first order stochastic systems. In: Proceedings of the conference on decision and control (CDC), Las Vegas, Nevada, USA, pp 2011–2016 Abramson N (1970) THE ALOHA SYSTEM—another alternative for computer communications. In: Proceedings of the fall joint computer conference, pp 281–286 Abramson N (2009) The ALOHANet—surfing for wireless data. IEEE Commun Mag 47(12):21–25 Aldous D (1987) Ultimate instability of exponential back-off protocol for acknowledgment-based transmission control of random access communication channels. IEEE Trans Inf Theory 33(2):219–223 Anta A, Tabuada P (2010) To sample or not to sample: self-triggered control for nonlinear systems. IEEE Trans Autom Control 55(9):2030–2042 Blind R, Allgöwer F (2011) Analysis of networked event-based control with a shared communication medium: part I—pure ALOHA. In: Proceedings of the 18th IFAC World Congress, Milano, Italy, pp 10092–10097 Blind R, Allgöwer F (2011) Analysis of networked event-based control with a shared communication medium: part II—slotted ALOHA. In: Proceedings of the 18th IFAC World Congress, Milano, Italy, pp 8830–8835 Blind R, Allgöwer F (2011) On the optimal sending rate for networked control systems with a shared communication medium. In: Proceedings of the conference on decision and control (CDC), Orlando, FL, USA, pp 4704–4709 Brun O, Garcia JM (2000) Analytical solution of finite capacity M/D/1 queues. J Appl Probab 37(4):1092–1098 Cervin A, Henningsson T (2008) Scheduling of event-triggered controllers on a shared network. In: Proceedings of the conference on decision and control (CDC), Cancun, Mexico, pp 3601–3606 Davis MHA, Howl JM (1997) A Markovian analysis of the finite-buffer M/D/1 queue. Proc R Soc Lond Ser A Math Phys Eng Sci 453(1964):1947–1962 Erlang AW (1917) Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges. Post Off Electr Eng J 10:189–197 Feller W (1950) An introduction to probability theory and its applications, 1st edn. Wiley, New York Heemels WPMH, Sandee JH (2008) Analysis of event-driven controllers for linear systems. Int J Control 81(4):571–590 Henningsson T, Cervin A (2010) A simple model for the interference between event-based control loops using a shared medium. In: Proceedings of the conference on decision and control (CDC), Atlanta, GA, USA, pp 3240–3245 Henningsson T, Johannesson E, Cervin A (2008) Sporadic event-based control of first-order linear stochastic systems. Automatica 44(11):2890–2895 Heyman DP, Sobel MJ (1982) Stochastic models in operations research, vol I. McGraw-Hill Book Company, New York Hristu-Varsakelis D, Kumar P (2002) Interrupt-based feedback control over a shared communication medium. In: Proceedings of the conference on decision and control (CDC), Las Vegas, Nevada, USA, pp 3223–3228 Jacobson V (1988) Congestion avoidance and control. ACM SIGCOMM Comput Commun Rev 18(4):314–329 Kelly F (1985) Stochastic models of computer communication systems. J R Stat Soc Ser B (Methodological) 47(3):379–395 Kleinrock L (1975) Queueing systems: volume I—theory. Wiley Insterscience, New York Kleinrock L, Lam SS (1973) Packet-switching in a slotted satellite channel. National Computer Conference, AFIPS Conference Proceedings, New York, NY, USA, pp 703–710 Kleinrock L, Tobagi F (1975) Packet switching in radio channels: part I—carrier sense multiple-access modes and their throughput-delay characteristics. IEEE Trans Commun 23(12):1400–1416 Kofman E, Braslavsky JH (2006) Level crossing sampling in feedback stabilization under data-rate constraints. In: Proceedings of the conference on decision and control (CDC), San Diego, CA, USA, pp 4423–4428 Lam S, Kleinrock L (1975) Packet switching in a multiaccess broadcast channel: dynamic control procedures. IEEE Trans Commun 23(9):891–904 Lam SS, Kleinrock L (1975) Dynamic control schemes for a packet switched multi-access broadcast channel. National Computer Conference, AFIP Conference Proceedings, Anaheim, CA, USA, pp 143–153 Liu X, Goldsmith A (2004) Wireless medium access control in networked control systems. In: Proceedings of the American Control Conference (ACC), Boston, MA, USA, pp 3605–3610 Lunze J, Lehmann D (2010) A state-feedback approach to event-based control. Automatica 46(1):211–215 Mazo M, Tabuada P (2011) Decentralized event-triggered control over wireless sensor/actuator networks. IEEE Trans Autom Control 56(10):2456–2461 Mesquita AR, Hespanha JP, Nair GN (2012) Redundant data transmission in control/estimation over lossy networks. Automatica 48(8):1612–1620 Molin A, Hirche S (2011) Optimal design of decentralized event-triggered controllers for large-scale systems with contention-based communication. In: Proceedings of the conference on decision and control (CDC), Orlando, FL, USA, pp 4710–4716 Navarro DJ, Fuss IG (2009) Fast and accurate calculations for first-passage times in Wiener diffusion models. J Math Psychol 53(4):222–230 Rabi M, Johansson KH (2009) Scheduling packets for event-triggered control. In: Proceedings of European Control Conference (ECC), Budapest, Hungary, pp 3779–3784 Rabi M, Moustakides GV, Baras JS (2012) Adaptive sampling for linear state estimation. SIAM J Control Optim 50(2):672–702 Rabi M, Stabellini L (2008) Analysis of networked estimation under contention-based medium access. In: Proceedings of the IFAC World Congress, Seoul, Korea, pp 10283–10288 Ramesh C, Sandberg H, Johansson KH (2011) Steady state performance analysis of multiple state-based schedulers with CSMA. in: Proceedings of the conference on decision and control (CDC), Orlando, FL, USA, pp 4729–4734 Roberts L (1975) ALOHA packet system with and without slots and capture. ACM SIGCOMM Comput Commun Rev 5(2):28–42 Rom R, Sidi M (1990) Multiple access protocols. Springer, New York Sant D (1980) Throughput of unslotted ALOHA channels with arbitray packet interarrival time distributions. IEEE Trans Commun 28(8):1422–1425 Sommer J, Blind R (2007) Optimized resource dimensioning in an embedded CAN-CAN gateway. In: International symposium on industrial embedded systems, pp 55–62 Tabuada P (2007) Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans Autom Control 52(9):1680–1685 Tanenbaum AS (2003) Computer networks. Pearson Education, New Jersey Walsh GC, Ye H, Bushnell L (1999) Stability analysis of networked control systems. In: Proceedings of the American Control Conference (ACC), San Diego, CA, USA, pp 2876–2880 Wang X, Lemmon MD (2008) Event-triggered broadcasting across distributed networked control systems. In: Proceedings of the American Control Conference (ACC), Seattle, WA, USA, pp 3139–3144 Wang X, Lemmon MD (2011) Event-triggering in distributed networked control systems. IEEE Trans Autom Control 56(3):586–601 Feller William (1954) Diffusion processes in one dimension. Trans Am Math Soc 77(1):1–31 Zhang W (2003) Stabilization of networked control systems over a sharing link using ALOHA. In: Proceeding of the Conference on Decision and Control (CDC) (December), Maui, Hawaii USA, pp 204–209