In this paper, the problem of dynamic event-triggered impulsive control for a class of nonlinear systems is studied. Based on the input-to-state stability results of nonlinear systems, a dynamic event-triggered control strategy is designed to stabilize the nonlinear system, and the lower bound of triggering is set. By using Lyapunov method, a sufficient condition for the stabilization of nonlinear systems is obtained. The conservation of the original theorem is maintained while the number of transmissions is greatly reduced. Numerical simulations show the effectiveness of the theoretical results.
References
[1]
Tabuada, P. (2007) Event-Triggered Real-Time Scheduling of Stabilizing Control Tasks. IEEETransactionsonAutomaticControl, 52, 1680-1685. https://doi.org/10.1109/tac.2007.904277
[2]
Wang, X. and Lemmon, M. (2011) On Event Design in Event-Triggered Feedback Systems. Automatica, 47, 2319-2322. https://doi.org/10.1016/j.automatica.2011.05.027
[3]
Wang, X. and Lemmon, M.D. (2011) Event-Triggering in Distributed Networked Control Systems. IEEETransactionsonAutomaticControl, 56, 586-601. https://doi.org/10.1109/tac.2010.2057951
[4]
Yue, D., Tian, E. and Han, Q. (2013) A Delay System Method for Designing Event-Triggered Controllers of Networked Control Systems. IEEETransactionsonAutomaticControl, 58, 475-481. https://doi.org/10.1109/tac.2012.2206694
[5]
Garcia, E., Cao, Y. and Casbeer, D.W. (2017) Periodic Event-Triggered Synchronization of Linear Multi-Agent Systems with Communication Delays. IEEETransactionsonAutomaticControl, 62, 366-371. https://doi.org/10.1109/tac.2016.2555484
[6]
Dimarogonas, D.V., Frazzoli, E. and Johansson, K.H. (2012) Distributed Event-Triggered Control for Multi-Agent Systems. IEEETransactionsonAutomaticControl, 57, 1291-1297. https://doi.org/10.1109/tac.2011.2174666
[7]
Yi, X., Yang, T., Wu, J. and Johansson, K.H. (2019) Distributed Event-Triggered Control for Global Consensus of Multi-Agent Systems with Input Saturation. Automatica, 100, 1-9. https://doi.org/10.1016/j.automatica.2018.10.032
[8]
Guan, Z.H. and Chen, G. (2000) On Impulsive Control of a Periodically Forced Chaotic Pendulum System. IEEE Transactions on Automatic Control, 45, 1724-1727.
[9]
Yang, T. (2001) Impulsive Control Theory. Springer-Verlag.
[10]
Haddad, W.M., Chellaboina, V.S. and Nersesov, S.G. (2006) Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control. Princeton University Press.
[11]
Sun, J. and Zhang, Y. (2003) Impulsive Control of a Nuclear Spin Generator. JournalofComputationalandAppliedMathematics, 157, 235-242. https://doi.org/10.1016/s0377-0427(03)00454-0
[12]
Verriest, E.I. (2003) Regularization Method for Optimally Switched and Impulsive Systems with Biomedical Applications. 42nd IEEE International Conference on Decision and Control, Maui, 9-12 December 2003, 2156-2161. https://doi.org/10.1109/cdc.2003.1272937
[13]
Masutani, Y. (2006) Flyaround Maneuvers on a Satellite Orbit by Impulsive Thrust Control. Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation, Seoul, 21-26 May 2001, 421-426.
[14]
Choi, J.H. and Grizzle, J.W. (2005) Feedback Control of an Underactuated Planar Bipedal Robot with Impulsive Foot Action. Robotica, 23, 567-580. https://doi.org/10.1017/s0263574704001250
[15]
Liu, X., Cao, J., Yu, W. and Song, Q. (2016) Nonsmooth Finite-Time Synchronization of Switched Coupled Neural Networks. IEEETransactionsonCybernetics, 46, 2360-2371. https://doi.org/10.1109/tcyb.2015.2477366
[16]
Chen, S., Song, G., Zheng, B. and Li, T. (2019) Finite-Time Synchronization of Coupled Reaction-Diffusion Neural Systems via Intermittent Control. Automatica, 109, Article ID: 108564. https://doi.org/10.1016/j.automatica.2019.108564
[17]
Hong, Y., Xu, Y. and Huang, J. (2002) Finite-Time Control for Robot Manipulators. Systems&ControlLetters, 46, 243-253. https://doi.org/10.1016/s0167-6911(02)00130-5
[18]
Zou, A. (2014) Finite-Time Output Feedback Attitude Tracking Control for Rigid Spacecraft. IEEETransactionsonControlSystemsTechnology, 22, 338-345. https://doi.org/10.1109/tcst.2013.2246836
[19]
Yang, H., Jiang, B., Cocquempot, V. and Chen, M. (2013) Spacecraft Formation Stabilization and Fault Tolerance: A State-Varying Switched System Approach. Systems&ControlLetters, 62, 715-722. https://doi.org/10.1016/j.sysconle.2013.05.007
[20]
Girard, A. (2015) Dynamic Triggering Mechanisms for Event-Triggered Control. IEEETransactionsonAutomaticControl, 60, 1992-1997. https://doi.org/10.1109/tac.2014.2366855
[21]
Åarzén, K. (1999) A Simple Event-Based PID Controller. IFACProceedingsVolumes, 32, 8687-8692. https://doi.org/10.1016/s1474-6670(17)57482-0
[22]
Li, X., Peng, D. and Cao, J. (2020) Lyapunov Stability for Impulsive Systems via Event-Triggered Impulsive Control. IEEETransactionsonAutomaticControl, 65, 4908-4913. https://doi.org/10.1109/tac.2020.2964558
[23]
Sontag, E.D. and Wang, Y. (1995) On Characterizations of the Input-to-State Stability Property. Systems&ControlLetters, 24, 351-359. https://doi.org/10.1016/0167-6911(94)00050-6