Event-triggered dynamic output-feedback control for a class of Lipschitz nonlinear systems

Zhiqian LIU; Xuyang LOU; Jiajia JIA

doi:10.1631/FITEE.2100552

Your Location：

Home >

Browse articles >

Event-triggered dynamic output-feedback control for a class of Lipschitz nonlinear systems

Regular Papers | Updated：2023-01-11

- Event-triggered dynamic output-feedback control for a class of Lipschitz nonlinear systems
- 一类Lipschitz非线性系统的事件触发动态输出反馈控制
- Frontiers of Information Technology & Electronic Engineering Vol. 23, Issue 11, Pages: 1684-1699(2022)
- Affiliations：
  
  Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China
- Author bio：
  
  ‡Corresponding author
- Funds：
- DOI：10.1631/FITEE.2100552
  CLC： TP13
- Received：29 November 2021，
  
  Accepted：21 December 2021，
  
  Published Online：23 April 2022，
  
  Published：0 November 2022
- Accepted：
Scan QR Code
Zhiqian LIU, Xuyang LOU, Jiajia JIA. Event-triggered dynamic output-feedback control for a class of Lipschitz nonlinear systems[J]. Frontiers of Information Technology & Electronic Engineering, 2022, 23(11): 1684-1699.
DOI：

Zhiqian LIU, Xuyang LOU, Jiajia JIA. Event-triggered dynamic output-feedback control for a class of Lipschitz nonlinear systems[J]. Frontiers of Information Technology & Electronic Engineering, 2022, 23(11): 1684-1699. DOI： 10.1631/FITEE.2100552.

摘要

本文研究一类Lipschitz非线性系统的动态输出反馈控制问题。首先，针对该系统设计了一个连续时间控制器，并且给出了系统稳定的充分条件。其次，针对该Lipschitz非线性系统提出一种新的事件触发机制，在该触发机制中引入了新的事件触发条件，并构建了事件触发控制下的闭环混杂系统。在混杂系统框架下建立了闭环系统稳定的充分条件。此外，给出了最小事件间隔的上界，以避免Zeno现象。最后，通过在神经网络系统和基因调控网络系统中的数值仿真验证了理论结果及所提方法的优越性。

Abstract

This paper investigates the problem of dynamic output-feedback control for a class of Lipschitz nonlinear systems. First

a continuous-time controller is constructed and sufficient conditions for stability of the nonlinear systems are presented. Then

a novel event-triggered mechanism is proposed for the Lipschitz nonlinear systems in which new event-triggered conditions are introduced. Consequently

a closed-loop hybrid system is obtained using the event-triggered control strategy. Sufficient conditions for stability of the closed-loop system are established in the framework of hybrid systems. In addition

an upper bound of a minimum inter-event interval is provided to avoid the Zeno phenomenon. Finally

numerical examples of a neural network system and a genetic regulatory network system are provided to verify the theoretical results and to show the superiority of the proposed method.

关键词

Keywords

references

Abdelrahim M , Postoyan R , Daafouz J , et al. , 2016 . Stabilization of nonlinear systems using event-triggered output feedback controllers . IEEE Trans Automat Contr , 61 ( 9 ): 2682 - 2687 . doi: 10.1109/tac.2015.2502145 http://doi.org/10.1109/tac.2015.2502145

Andrieu V , Praly L , 2009 . A unifying point of view on output feedback designs for global asymptotic stabilization . Automatica , 45 ( 8 ): 1789 - 1798 . doi: 10.1016/j.automatica.2009.04.015 http://doi.org/10.1016/j.automatica.2009.04.015

Angulo MT , Moog CH , Liu YY , 2019 . A theoretical framework for controlling complex microbial communities . Nat Commun , 10 ( 1 ): 1045 . doi: 10.1038/s41467-019-08890-y http://doi.org/10.1038/s41467-019-08890-y

Casey R , de Jong H , Gouzé JL , 2006 . Piecewise-linear models of genetic regulatory networks: equilibria and their stability . J Math Biol , 52 ( 1 ): 27 - 56 . doi: 10.1007/s00285-005-0338-2 http://doi.org/10.1007/s00285-005-0338-2

Chen J , Chen BM , Sun J , 2019 . Complex system and intelligent control: theories and applications . Front Inform Technol Electron Eng , 20 ( 1 ): 1 - 3 . doi: 10.1631/FITEE.1910000 http://doi.org/10.1631/FITEE.1910000

Chen PN , Cheng DZ , Jiang ZP , 2006 . A constructive approach to local stabilization of nonlinear systems by dynamic output feedback . IEEE Trans Automat Contr , 51 ( 7 ): 1166 - 1171 . doi: 10.1109/tac.2006.878753 http://doi.org/10.1109/tac.2006.878753

Collins EG , Selekwa MAF , Walker RB , et al. , 2006 . A stacked model structure for off-line parameter variation estimation in multi-equilibria nonlinear systems . Eur J Contr , 12 ( 4 ): 353 - 364 . doi: 10.3166/ejc.12.353-364 http://doi.org/10.3166/ejc.12.353-364

Dong JX , Yang GH , 2008 . Dynamic output feedback control synthesis for continuous-time T-S fuzzy systems via a switched fuzzy control scheme . IEEE Trans Syst Man Cybern B Cybern , 38 ( 4 ): 1166 - 1175 . doi: 10.1109/tsmcb.2008.923530 http://doi.org/10.1109/tsmcb.2008.923530

Donkers MCF , Heemels WPMH , 2012 . Output-based event-triggered control with guaranteed <math id="M569"><mrow><msub><mi mathvariant="script">L</mi><mi>∞</mi></msub></mrow></math> -gain and improved and decentralized event-triggering . IEEE Trans Automat Contr , 57 ( 6 ): 1362 - 1376 . doi: 10.1109/tac.2011.2174696 http://doi.org/10.1109/tac.2011.2174696

Ekramian M , 2020 . Static output feedback problem for Lipschitz nonlinear systems . J Franklin Inst , 357 ( 3 ): 1457 - 1472 . doi: 10.1016/j.jfranklin.2019.10.031 http://doi.org/10.1016/j.jfranklin.2019.10.031

Goebel R , Sanfelice RG , Teel AR , 2012 . Hybrid Dynamical Systems: Modeling, Stability, and Robustness . Princeton University Press , Princeton, USA .

Gu Z , Huan Z , Yue D , et al. , 2018 . Event-triggered dynamic output feedback control for networked control systems with probabilistic nonlinearities . Inform Sci , 457-458 : 99 - 112 . doi: 10.1016/j.ins.2018.05.007 http://doi.org/10.1016/j.ins.2018.05.007

Hamid SR , Nazir MS , Rehan M , et al. , 2019 . New results on regional observer-based stabilization for locally Lipschitz nonlinear systems . Chaos Solit Fract , 123 : 173 - 184 . doi: 10.1016/j.chaos.2019.04.004 http://doi.org/10.1016/j.chaos.2019.04.004

Kammogne AST , Kountchou MN , Kengne R , et al. , 2020 . Polynomial robust observer implementation based passive synchronization of nonlinear fractional-order systems with structural disturbances . Front Inform Technol Electron Eng , 21 ( 9 ): 1369 - 1386 . doi: 10.1631/FITEE.1900430 http://doi.org/10.1631/FITEE.1900430

Khalil HK , 2014 . Nonlinear Control, Global Edition . Pearson Education , USA .

Li FF , Sun JT , 2010 . Asymptotic stability of a genetic network under impulsive control . Phys Lett A , 374 ( 31-32 ): 3177 - 3184 . doi: 10.1016/j.physleta.2010.05.054 http://doi.org/10.1016/j.physleta.2010.05.054

Liu S , Song Y , Wei GL , et al. , 2017 . Event-triggered dynamic output feedback RMPC for polytopic systems with redundant channels: input-to-state stability . J Franklin Inst , 354 ( 7 ): 2871 - 2892 . doi: 10.1016/j.jfranklin.2017.02.008 http://doi.org/10.1016/j.jfranklin.2017.02.008

Liu W , Wang ZM , Dai HH , et al. , 2016 . Dynamic output feedback control for fast sampling discrete-time singularly perturbed systems . IET Contr Theory Appl , 10 ( 15 ): 1782 - 1788 . doi: 10.1049/iet-cta.2016.0121 http://doi.org/10.1049/iet-cta.2016.0121

Meslem N , Prieur C , 2015 . Event-based controller synthesis by bounding methods . Eur J Contr , 26 : 12 - 21 . doi: 10.1016/j.ejcon.2015.09.004 http://doi.org/10.1016/j.ejcon.2015.09.004

Molaei B , 2008 . Optimization of dynamic output feedback controller for piecewise affine systems: an LMI approach . J Circ Syst Comput , 17 ( 2 ): 263 - 277 . doi: 10.1142/s021812660800423x http://doi.org/10.1142/s021812660800423x

Nesic D , Teel AR , Carnevale D , 2009 . Explicit computation of the sampling period in emulation of controllers for nonlinear sampled-data systems . IEEE Trans Automat Contr , 54 ( 3 ): 619 - 624 . doi: 10.1109/tac.2008.2009597 http://doi.org/10.1109/tac.2008.2009597

Park JH , 2005 . On design of dynamic output feedback controller for GCS of large-scale systems with delays in interconnections: LMI optimization approach . Appl Math Comput , 161 ( 2 ): 423 - 432 . doi: 10.1016/j.amc.2003.12.037 http://doi.org/10.1016/j.amc.2003.12.037

Peng C , Yang TC , 2013 . Event-triggered communication and <math id="M570"><mrow><msub><mi mathvariant="script">H</mi><mi>∞</mi></msub></mrow></math> control co-design for networked control systems . Automatica , 49 ( 5 ): 1326 - 1332 . doi: 10.1016/j.automatica.2013.01.038 http://doi.org/10.1016/j.automatica.2013.01.038

Pertew AM , Marquez HJ , Zhao Q , 2006 . <math id="M571"><mrow><msub><mi mathvariant="script">H</mi><mi>∞</mi></msub></mrow></math> observer design for Lipschitz nonlinear systems . IEEE Trans Automat Contr , 51 ( 7 ): 1211 - 1216 . doi: 10.1109/tac.2006.878784 http://doi.org/10.1109/tac.2006.878784

Pham TP , Sename O , Dugard L , 2019 . Unified <math id="M572"><mrow><msub><mi mathvariant="script">H</mi><mi>∞</mi></msub></mrow></math> observer for a class of nonlinear Lipschitz systems: application to a real ER automotive suspension . IEEE Contr Syst Lett , 3 ( 4 ): 817 - 822 . doi: 10.1109/lcsys.2019.2919813 http://doi.org/10.1109/lcsys.2019.2919813

Qian CJ , Lin W , 2001 . A continuous feedback approach to global strong stabilization of nonlinear systems . IEEE Trans Automat Contr , 46 ( 7 ): 1061 - 1079 . doi: 10.1109/9.935058 http://doi.org/10.1109/9.935058

Qiu JL , 2007 . Exponential stability of impulsive neural networks with time-varying delays and reaction–diffusion terms . Neurocomputing , 70 ( 4-6 ): 1102 - 1108 . doi: 10.1016/j.neucom.2006.08.003 http://doi.org/10.1016/j.neucom.2006.08.003

Rehan M , Jameel A , Ahn CK , 2018 . Distributed consensus control of one-sided Lipschitz nonlinear multiagent systems . IEEE Trans Syst Man Cybern Syst , 48 ( 8 ): 1297 - 1308 . doi: 10.1109/tsmc.2017.2667701 http://doi.org/10.1109/tsmc.2017.2667701

Sanchez EN , Perez JP , 2003 . Input-to-state stabilization of dynamic neural networks . IEEE Trans Syst Man Cybern A Syst Hum , 33 ( 4 ): 532 - 535 . doi: 10.1109/tsmca.2003.811509 http://doi.org/10.1109/tsmca.2003.811509

Shu F , Zhai JY , 2020 . Event-triggered practical finite-time output feedback stabilisation for switched non-linear time-delay systems . IET Contr Theory Appl , 14 ( 6 ): 824 - 833 . doi: 10.1049/iet-cta.2019.1093 http://doi.org/10.1049/iet-cta.2019.1093

Tabuada P , 2007 . Event-triggered real-time scheduling of stabilizing control tasks . IEEE Trans Automat Contr , 52 ( 9 ): 1680 - 1685 . doi: 10.1109/tac.2007.904277 http://doi.org/10.1109/tac.2007.904277

Theodosis D , Dimarogonas DV , 2019 . Event-triggered control of nonlinear systems with updating threshold . IEEE Contr Syst Lett , 3 ( 3 ): 655 - 660 . doi: 10.1109/lcsys.2019.2915719 http://doi.org/10.1109/lcsys.2019.2915719

Wang ZD , Qiao H , Burnham KJ , 2002 . On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters . IEEE Trans Automat Contr , 47 ( 4 ): 640 - 646 . doi: 10.1109/9.995042 http://doi.org/10.1109/9.995042

Yu H , Antsaklis PJ , 2013 . Event-triggered output feedback control for networked control systems using passivity: achieving <math id="M573"><mrow><msub><mi mathvariant="script">L</mi><mn>2</mn></msub></mrow></math> stability in the presence of communication delays and signal quantization . Automatica , 49 ( 1 ): 30 - 38 . doi: 10.1016/j.automatica.2012.09.005 http://doi.org/10.1016/j.automatica.2012.09.005

Zhang JH , Feng G , 2014 . Event-driven observer-based output feedback control for linear systems . Automatica , 50 ( 7 ): 1852 - 1859 . doi: 10.1016/j.automatica.2014.04.026 http://doi.org/10.1016/j.automatica.2014.04.026

Zhang XM , Han QL , 2016 . A decentralized event-triggered dissipative control scheme for systems with multiple sensors to sample the system outputs . IEEE Trans Cybern , 46 ( 12 ): 2745 - 2757 . doi: 10.1109/TCYB.2015.2487420 http://doi.org/10.1109/TCYB.2015.2487420

Zhang XM , Han QL , 2017 . Event-triggered <math id="M574"><mrow><msub><mi mathvariant="script">H</mi><mi>∞</mi></msub></mrow></math> control for a class of nonlinear networked control systems using novel integral inequalities . Int J Robust Nonl Contr , 27 ( 4 ): 679 - 700 . doi: 10.1002/rnc.3598 http://doi.org/10.1002/rnc.3598

Zhang Z , Li HP , Shi Y , et al. , 2020 . Cooperative optimal control for Lipschitz nonlinear systems over generally directed topologies . Automatica , 122 : 109279 . doi: 10.1016/j.automatica.2020.109279 http://doi.org/10.1016/j.automatica.2020.109279

Zhou J , Wen CY , Li TS , 2012 . Adaptive output feedback control of uncertain nonlinear systems with hysteresis nonlinearity . IEEE Trans Automat Contr , 57 ( 10 ): 2627 - 2633 . doi: 10.1109/tac.2012.2190208 http://doi.org/10.1109/tac.2012.2190208

Zuo ZY , Lin ZL , Ding ZT , 2016 . Truncated prediction output feedback control of a class of Lipschitz nonlinear systems with input delay . IEEE Trans Circ Syst II Expr Briefs , 63 ( 8 ): 788 - 792 . doi: 10.1109/tcsii.2016.2531053 http://doi.org/10.1109/tcsii.2016.2531053

Views

230

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

Event-triggered adaptive tracking control of a class of nonlinear systems with asymmetric time-varying output constraints

Design and experimental validation of event-triggered multi-vehicle cooperation in conflicting scenarios

Event-triggered adaptive finite-time control for nonlinear systems under asymmetric time-varying state constraints

Event-based H_∞ control for piecewise-affine systems subject to actuator saturation

Related Author

Lidong ZHANG

Yitao YANG

Zhihua ZHONG

Yifan JIA

Jin HUANG

Xingyu LI

Yingjun QIAO

Zhanyi HU

Related Institution

School of Science, Tianjin University of Technology

School of Vehicle and Mobility, Tsinghua University

Chinese Academy of Engineering

MOE Key Laboratory of Road and Traffic Engineering, Tongji University

School of Aeronautics and Astronautics, Shanghai Jiao Tong University

Chat

Address：Zhejiang University Press, 148 Tianmushan Road, Hangzhou, China Postal code：310028
Tel：+86-571-88273162 Email：fitee@zju.edu.cn
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰