logo

SCIENCE CHINA Information Sciences, Volume 63 , Issue 5 : 150209(2020) https://doi.org/10.1007/s11432-019-2688-1

Event-based triggering mechanisms for nonlinear control systems

More info
  • ReceivedApr 25, 2019
  • AcceptedSep 23, 2019
  • PublishedMar 27, 2020

Abstract

This study examines triggered implementations of stabilizing controllers for general nonlinear systems. By using perturbation theory and Taylor's theorem, we propose new event-triggering and self-triggering mechanisms for general nonlinear control systems that are not necessarily input-to-state stable with respect to measurement errors. Both mechanisms are presented based on mild conditions and can ensure the uniform ultimate boundedness of the solutions of the resulting closed-loop control systems. The ultimate bounds can be made arbitrarily small by adjusting the design parameters. The effectiveness of the theoretical results is illustrated by simulations.


Acknowledgment

This work was supported by National Science Foundation for Young Scientists of China (Grant No. 61803069) and Fundamental Research Funds for the Central Universities of China (Grant Nos. DUT17GJ203, DUT17RC(3)088).


References

[1] Yu H, Antsaklis P J. Event-triggered output feedback control for networked control systems using passivity: Achieving stability in the presence of communication delays and signal quantization. Automatica, 2013, 49: 30-38 CrossRef Google Scholar

[2] Wang X F, Lemmon M D. Event-Triggering in Distributed Networked Control Systems. IEEE Trans Automat Contr, 2011, 56: 586-601 CrossRef Google Scholar

[3] Wang X F, Lemmon M D. On event design in event-triggered feedback systems. Automatica, 2011, 47: 2319-2322 CrossRef Google Scholar

[4] Heemels W P M H, Sandee J H, Van Den Bosch P P J. Analysis of event-driven controllers for linear systems. Int J Control, 2008, 81: 571-590 CrossRef Google Scholar

[5] Tabuada P. Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks. IEEE Trans Automat Contr, 2007, 52: 1680-1685 CrossRef Google Scholar

[6] Selivanov A, Fridman E. IEEE Trans Automat Contr, 2016, 61: 3221-3226 CrossRef Google Scholar

[7] Zhang X M, Han Q L, Zhang B L. An Overview and Deep Investigation on Sampled-Data-Based Event-Triggered Control and Filtering for Networked Systems. IEEE Trans Ind Inf, 2017, 13: 4-16 CrossRef Google Scholar

[8] Gu Z, Yue D, Tian E G. On designing of an adaptive event-triggered communication scheme for nonlinear networked interconnected control systems. Inf Sci, 2018, 422: 257-270 CrossRef Google Scholar

[9] Cuenca A, Antunes D J, Castillo A. Periodic Event-Triggered Sampling and Dual-Rate Control for a Wireless Networked Control System With Applications to UAVs. IEEE Trans Ind Electron, 2019, 66: 3157-3166 CrossRef Google Scholar

[10] Brunner F D, Heemels W P M H, Allg?wer F. Event-triggered and self-triggered control for linear systems based on reachable sets. Automatica, 2019, 101: 15-26 CrossRef Google Scholar

[11] Borgers D P, Postoyan R, Anta A. Periodic event-triggered control of nonlinear systems using overapproximation techniques. Automatica, 2018, 94: 81-87 CrossRef Google Scholar

[12] Asadi Khashooei B, Antunes D J, Heemels W P M H. A Consistent Threshold-Based Policy for Event-Triggered Control. IEEE Control Syst Lett, 2018, 2: 447-452 CrossRef Google Scholar

[13] Abdelrahim M, Postoyan R, Daafouz J. Automatica, 2018, 87: 337-344 CrossRef Google Scholar

[14] Li F Z, Liu Y G. Global practical tracking with prescribed transient performance for inherently nonlinear systems with extremely severe uncertainties. Sci China Inf Sci, 2019, 62: 22204 CrossRef Google Scholar

[15] Zheng C, Li L, Wang L Y. How much information is needed in quantized nonlinear control?. Sci China Inf Sci, 2018, 61: 092205 CrossRef Google Scholar

[16] Heemels W P M H, Johansson K H, Tabuada P. An introduction to event-triggered and self-triggered control. In: Proceedings of 51rd IEEE Conference on Decision and Control, Maui, 2012. 3270--3285. Google Scholar

[17] Girard A. Dynamic Triggering Mechanisms for Event-Triggered Control. IEEE Trans Automat Contr, 2015, 60: 1992-1997 CrossRef Google Scholar

[18] Postoyan R, Tabuada P, Nesic D. A Framework for the Event-Triggered Stabilization of Nonlinear Systems. IEEE Trans Automat Contr, 2015, 60: 982-996 CrossRef Google Scholar

[19] Sontag E, Teel A. Changing supply functions in input/state stable systems. IEEE Trans Automat Contr, 1995, 40: 1476-1478 CrossRef Google Scholar

[20] Freeman R. Global internal stabilizability does not imply global external stabilizability for small sensor disturbances. IEEE Trans Automat Contr, 1995, 40: 2119-2122 CrossRef Google Scholar

[21] Fah N C S. Input-to-state stability with respect to measurement disturbances for one-dimensional systems. ESAIM-COCV, 1999, 4: 99-121 CrossRef Google Scholar

[22] Khalil H. Nonlinear Systems. 3rd ed. Upper saddle River: Prentice Hall, 2002. Google Scholar

[23] Wang X F, Lemmon M D. Self-Triggered Feedback Control Systems With Finite-Gain ${\cal~L}_{2}$ Stability. IEEE Trans Automat Contr, 2009, 54: 452-467 CrossRef Google Scholar

[24] Mazo Jr. M, Anta A, Tabuada P. An ISS self-triggered implementation of linear controllers. Automatica, 2010, 46: 1310-1314 CrossRef Google Scholar

[25] Anta A, Tabuada P. To Sample or not to Sample: Self-Triggered Control for Nonlinear Systems. IEEE Trans Automat Contr, 2010, 55: 2030-2042 CrossRef Google Scholar

[26] Anta A, Tabuada P. Exploiting Isochrony in Self-Triggered Control. IEEE Trans Automat Contr, 2012, 57: 950-962 CrossRef Google Scholar

[27] Lin Y D, Sontag E D, Wang Y. A Smooth Converse Lyapunov Theorem for Robust Stability. SIAM J Control Optim, 1996, 34: 124-160 CrossRef Google Scholar

[28] Mazo M, Tabuada P. Decentralized Event-Triggered Control Over Wireless Sensor/Actuator Networks. IEEE Trans Automat Contr, 2011, 56: 2456-2461 CrossRef Google Scholar

Copyright 2020  CHINA SCIENCE PUBLISHING & MEDIA LTD.  中国科技出版传媒股份有限公司  版权所有

京ICP备14028887号-23       京公网安备11010102003388号