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Dynamic Periodic Event-Triggered Control for Linear Systems

Published: 13 April 2017 Publication History

Abstract

In event-triggered control systems, events are typically generated when a static function of the output (or state) of the system exceeds a given threshold. Recently, event-generators have been proposed that generate events based on an additional dynamic variable, with dynamics that depend on the output of the system. It is shown that these dynamic event-generators are able to guarantee the same performance as their static counterparts, while typically generating significantly fewer events. However, all dynamic event-generators available in literature require continuous measuring of the output of the plant, which is difficult to realize on digital platforms. In this paper, we propose new dynamic event-generators for linear systems, which require only periodic sampling of the output, and are therefore easy to implement on digital platforms. Based on hybrid modelling techniques combined with constructive designs of Lyapunov/storage functions for the resulting hybrid models, it is shown that these (dynamic periodic) event-generators lead to closed-loop systems which are globally exponentially stable (GES) with a guaranteed decay rate and MC L2-stable with a guaranteed L2-gain. The benefits of these new event-generators are also demonstrated via a numerical example.

Supplementary Material

ZIP File (hscc042.zip)
This directory contains code to recreate the examples from [D.P. Borgers, V.S. Dolk, and W.P.M.H. Heemels, 'Dynamic Periodic Event-Triggered Control for Linear Systems,' Hybrid Systems: Computation and Control 2017]. Questions and bug reports can be sent to [email protected] Niek Borgers, Victor Dolk, and Maurice Heemels 02-02-2017

References

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D. P. Borgers, V. S. Dolk, and W. P. M. H. Heemels. Dynamic event-triggered control with time-regularization for linear systems. In 55th IEEE Conf. Decision and Control, pages 1352--1357, 2016.
[3]
D. P. Borgers, R. Postoyan, A. Anta, P. Tabuada, D. Nesić, and W. P. M. H. Heemels. Periodic event-triggered control of nonlinear systems using overapproximation techniques. Submitted.
[4]
C. G. Cassandras. The event-driven paradigm for control, communication and optimization. J. Control and Decision, 1(1):3--17, 2014.
[5]
X. Chen and F. Hao. Periodic event-triggered state-feedback and output-feedback control for linear systems. Int. J. Control, Automation and Systems, 13(4):779--787, 2015.
[6]
R. Cogill. Event-based control using quadratic approximate value functions. In 48th IEEE Conf. Decision and Control and Chinese Control Conf., pages 5883--5888, 2009.
[7]
V. S. Dolk, D. P. Borgers, and W. P. M. H. Heemels. Output-based and decentralized dynamic event-triggered control with guaranteed $\mathcalL_p$-gain performance and Zeno-freeness. IEEE Trans. Automat. Contr., 62(1):34--49, 2017.
[8]
A. Eqtami, D. V. Dimarogonas, and K. J. Kyriakopoulos. Event-triggered control for discrete-time systems. In Proc. Amer. Control Conf., pages 4719--4724, 2010.
[9]
P. Gahinet and P. Apkarian. A linear matrix inequality approach to H_∞ control. Int. J. Robust Nonlinear Control, 4(4):421--448, 1994.
[10]
A. Girard. Dynamic triggering mechanisms for event-triggered control. IEEE Trans. Automat. Contr., 60(7):1992--1997, 2015.
[11]
R. Goebel, R. G. Sanfelice, and A. R. Teel. Hybrid Dynamical Systems: Modeling, Stability, and Robustness. Princeton University Press, 2012.
[12]
W. P. M. H. Heemels, M. C. F. Donkers, and A. R. Teel. Periodic event-triggered control for linear systems. IEEE Trans. Automat. Contr., 58(4):847--861, 2013.
[13]
W. P. M. H. Heemels, G. E. Dullerud, and A. R. Teel. L_2-gain analysis for a class of hybrid systems with applications to reset and event-triggered control: A lifting approach. IEEE Trans. Automat. Contr., 61(10):2766--2781, 2016.
[14]
W. P. M. H. Heemels, J. H. Sandee, and P. P. J. van den Bosch. Analysis of event-driven controllers for linear systems. Int. J. Control, 81(4):571--590, 2008.
[15]
T. Henningsson, E. Johannesson, and A. Cervin. Sporadic event-based control of first-order linear stochastic systems. Automatica, 44(11):2890--2895, 2008.
[16]
L. Li and M. Lemmon. Weakly coupled event triggered output feedback system in wireless networked control systems. In Allerton Conf. Commun., Control and Computing, 2011.
[17]
J. Löfberg. YALMIP: a toolbox for modeling and optimization in MATLAB. In IEEE Int. Symp. Computer Aided Control Systems Design, pages 284--289, 2004.
[18]
M. Miskowicz. Send-on-delta concept: An event-based data reporting strategy. Sensors, 6(1):49--63, 2006.
[19]
A. Molin and S. Hirche. On the optimality of certainty equivalence for event-triggered control systems. IEEE Trans. Automat. Contr., 58(2):470--474, 2013.
[20]
R. Postoyan, A. Anta, W. P. M. H. Heemels, P. Tabuada, and D. Nešić. Periodic event-triggered control for nonlinear systems. In 52nd IEEE Conf. Decision and Control, pages 7397--7402, 2013.
[21]
R. Postoyan, P. Tabuada, D. Nesić, and A. Anta. A framework for the event-triggered stabilization of nonlinear systems. IEEE Trans. Automat. Contr., 60(4):982--996, 2015.
[22]
A. Schaft, van der. $L_2$-Gain and Passivity Techniques in Nonlinear Control, volume 218 of Lecture Notes in Control and Information Sciences. Springer Verlag, Berlin, Germany, 1996.
[23]
P. Tabuada. Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans. Automat. Contr., 52(9):1680--1685, 2007.
[24]
W. Wang, R. Postoyan, D. Nesić, and W. P. M. H. Heemels. Stabilization of nonlinear systems using state-feedback periodic event-triggered controllers. In IEEE 55th Conf. Decision and Control, pages 6808--6813, 2016.
[25]
J. C. Willems. Dissipative dynamical systems part I: General theory. Arch. Rational Mech. Anal., 45(5):321--351, 1972.
[26]
J. K. Yook, D. M. Tilbury, and N. R. Soparkar. Trading computation for bandwidth: reducing communication in distributed control systems using state estimators. IEEE Trans. Contr. Syst. Technol., 10(4):503--518, 2002.
[27]
T. Başar and P. Bernhard. H∞-Optimal Control and Relaxed Minimax Design Problems: A Dynamic Game Approach. Birkhauser, Boston, MA, USA, 2nd edition, 1995.
[28]
D. P. Borgers, V. S. Dolk, and W. P. M. H. Heemels. Dynamic event-triggered control with time-regularization for linear systems. In 55th IEEE Conf. Decision and Control, pages 1352--1357, 2016.
[29]
D. P. Borgers, R. Postoyan, A. Anta, P. Tabuada, D. Nesić, and W. P. M. H. Heemels. Periodic event-triggered control of nonlinear systems using overapproximation techniques. Submitted.
[30]
C. G. Cassandras. The event-driven paradigm for control, communication and optimization. J. Control and Decision, 1(1):3--17, 2014.
[31]
X. Chen and F. Hao. Periodic event-triggered state-feedback and output-feedback control for linear systems. Int. J. Control, Automation and Systems, 13(4):779--787, 2015.
[32]
R. Cogill. Event-based control using quadratic approximate value functions. In 48th IEEE Conf. Decision and Control and Chinese Control Conf., pages 5883--5888, 2009.
[33]
V. S. Dolk, D. P. Borgers, and W. P. M. H. Heemels. Output-based and decentralized dynamic event-triggered control with guaranteed L_p-gain performance and Zeno-freeness. IEEE Trans. Automat. Contr., 62(1):34--49, 2017.
[34]
A. Eqtami, D. V. Dimarogonas, and K. J. Kyriakopoulos. Event-triggered control for discrete-time systems. In Proc. Amer. Control Conf., pages 4719--4724, 2010.
[35]
P. Gahinet and P. Apkarian. A linear matrix inequality approach to H_∞ control. Int. J. Robust Nonlinear Control, 4(4):421--448, 1994.
[36]
A. Girard. Dynamic triggering mechanisms for event-triggered control. IEEE Trans. Automat. Contr., 60(7):1992--1997, 2015.
[37]
R. Goebel, R. G. Sanfelice, and A. R. Teel. Hybrid Dynamical Systems: Modeling, Stability, and Robustness. Princeton University Press, 2012.
[38]
W. P. M. H. Heemels, M. C. F. Donkers, and A. R. Teel. Periodic event-triggered control for linear systems. IEEE Trans. Automat. Contr., 58(4):847--861, 2013.
[39]
W. P. M. H. Heemels, G. E. Dullerud, and A. R. Teel. L_2-gain analysis for a class of hybrid systems with applications to reset and event-triggered control: A lifting approach. IEEE Trans. Automat. Contr., 61(10):2766--2781, 2016.
[40]
W. P. M. H. Heemels, J. H. Sandee, and P. P. J. van den Bosch. Analysis of event-driven controllers for linear systems. Int. J. Control, 81(4):571--590, 2008.
[41]
T. Henningsson, E. Johannesson, and A. Cervin. Sporadic event-based control of first-order linear stochastic systems. Automatica, 44(11):2890--2895, 2008.
[42]
L. Li and M. Lemmon. Weakly coupled event triggered output feedback system in wireless networked control systems. In Allerton Conf. Commun., Control and Computing, 2011.
[43]
J. Löfberg. YALMIP: a toolbox for modeling and optimization in MATLAB. In IEEE Int. Symp. Computer Aided Control Systems Design, pages 284--289, 2004.
[44]
M. Miskowicz. Send-on-delta concept: An event-based data reporting strategy. Sensors, 6(1):49--63, 2006.
[45]
A. Molin and S. Hirche. On the optimality of certainty equivalence for event-triggered control systems. IEEE Trans. Automat. Contr., 58(2):470--474, 2013.
[46]
R. Postoyan, A. Anta, W. P. M. H. Heemels, P. Tabuada, and D. Nesić. Periodic event-triggered control for nonlinear systems. In 52nd IEEE Conf. Decision and Control, pages 7397--7402, 2013.
[47]
R. Postoyan, P. Tabuada, D. Nesić, and A. Anta. A framework for the event-triggered stabilization of nonlinear systems. IEEE Trans. Automat. Contr., 60(4):982--996, 2015.
[48]
A. Schaft, van der. L_2-Gain and Passivity Techniques in Nonlinear Control, volume 218 of Lecture Notes in Control and Information Sciences. Springer Verlag, Berlin, Germany, 1996.
[49]
P. Tabuada. Event-triggered real-time scheduling of stabilizing control tasks. IEEE Trans. Automat. Contr., 52(9):1680--1685, 2007.
[50]
W. Wang, R. Postoyan, D. Nesić, and W. P. M. H. Heemels. Stabilization of nonlinear systems using state-feedback periodic event-triggered controllers. In IEEE 55th Conf. Decision and Control, pages 6808--6813, 2016.
[51]
J. C. Willems. Dissipative dynamical systems part I: General theory. Arch. Rational Mech. Anal., 45(5):321--351, 1972.
[52]
J. K. Yook, D. M. Tilbury, and N. R. Soparkar. Trading computation for bandwidth: reducing communication in distributed control systems using state estimators. IEEE Trans. Contr. Syst. Technol., 10(4):503--518, 2002.

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cover image ACM Conferences
HSCC '17: Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control
April 2017
288 pages
ISBN:9781450345903
DOI:10.1145/3049797
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 13 April 2017

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Author Tags

  1. Riccati differential equations
  2. event-triggered control
  3. global exponential stability
  4. hybrid systems
  5. impulsive systems
  6. l2 stability

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HSCC '17 Paper Acceptance Rate 29 of 76 submissions, 38%;
Overall Acceptance Rate 153 of 373 submissions, 41%

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  • (2024)Accelerated Gradient Flow for Directed Graphs With Event-Based BroadcastingIEEE Transactions on Control of Network Systems10.1109/TCNS.2023.329011211:1(510-522)Online publication date: Mar-2024
  • (2024)Dynamic Periodic Event-Triggered Control for Networked Control Systems Under Packet DropoutsIEEE Transactions on Automation Science and Engineering10.1109/TASE.2023.323537521:1(906-920)Online publication date: Jan-2024
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