Synchronization issue of uncertain time-delay systems based on flexible impulsive control

Biwen Li; Qiaoping Huang; Biwen Li; Qiaoping Huang

doi:10.3934/math.20241291

AIMS Mathematics

2024, Volume 9, Issue 10: 26538-26556. doi: 10.3934/math.20241291

Previous Article Next Article

Research article

Synchronization issue of uncertain time-delay systems based on flexible impulsive control

Biwen Li ,
Qiaoping Huang ^,

Huangshi Key Laboratory of Metaverse and Virtual Simulation, School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, Hubei, China

Received: 25 July 2024 Revised: 27 August 2024 Accepted: 09 September 2024 Published: 13 September 2024
MSC : 93C30

This paper discusses a synchronization issue of uncertain time-delay systems via flexible delayed impulsive control. A new Razumikhin-type inequality is presented, considering adjustable parameters the $ \varpi(t) $, which relies on flexible impulsive gain. For the uncertain time-delay systems where delay magnitude is not constrained to impulsive intervals, sufficient conditions for global exponential synchronization (GES) are established. Furthermore, based on Lyapunov theory, a new differential inequality and linear matrix inequality design, and a flexible impulsive control method is introduced through using the variable impulsive gain and time-varying delays. It is interesting to find that uncertain time-delay systems can maintain GES by adjusting the impulsive gain and impulsive delay. Finally, two simulations are given to illustrate the effectiveness of the derived results.
- impulsive control,
- time delay,
- synchronization,
- impulsive gain,
- parametric uncertainty
Citation: Biwen Li, Qiaoping Huang. Synchronization issue of uncertain time-delay systems based on flexible impulsive control[J]. AIMS Mathematics, 2024, 9(10): 26538-26556. doi: 10.3934/math.20241291

Related Papers:

Abstract

This paper discusses a synchronization issue of uncertain time-delay systems via flexible delayed impulsive control. A new Razumikhin-type inequality is presented, considering adjustable parameters the $ \varpi(t) $, which relies on flexible impulsive gain. For the uncertain time-delay systems where delay magnitude is not constrained to impulsive intervals, sufficient conditions for global exponential synchronization (GES) are established. Furthermore, based on Lyapunov theory, a new differential inequality and linear matrix inequality design, and a flexible impulsive control method is introduced through using the variable impulsive gain and time-varying delays. It is interesting to find that uncertain time-delay systems can maintain GES by adjusting the impulsive gain and impulsive delay. Finally, two simulations are given to illustrate the effectiveness of the derived results.

References

[1]	Z. Wu, J. Sun, R. Xu, Consensus-based connected vehicles platoon control via impulsive control method, Physica A, 580 (2021), 126190. https://doi.org/10.1016/j.physa.2021.126190 doi: 10.1016/j.physa.2021.126190
[2]	X. Liu, K. Zhang, Synchronization of linear dynamical networks on time scales: pinning control via delayed impulses, Automatica, 72 (2016), 147–152. https://doi.org/10.1016/j.automatica.2016.06.001 doi: 10.1016/j.automatica.2016.06.001
[3]	B. Liu, Z. Sun, Y. Luo, Y. Zhong, Uniform synchronization for chaotic dynamical systems via event-triggered impulsive control, Physica A, 531 (2019), 121725. https://doi.org/10.1016/j.physa.2019.121725 doi: 10.1016/j.physa.2019.121725
[4]	B. Jiang, J. Lu, X. Li, J. Qiu, Event-triggered impulsive stabilization of systems with external disturbances, IEEE Trans. Automat. Contr., 67 (2022), 2116–2122. https://doi.org/10.1109/TAC.2021.3108123 doi: 10.1109/TAC.2021.3108123
[5]	A. Khadra, X. Z. Liu, X. Shen, Impulsively synchronizing chaotic systems with delay and applications to secure communication, Automatica, 41 (2005), 1491–1502. https://doi.org/10.1016/j.automatica.2005.04.012 doi: 10.1016/j.automatica.2005.04.012
[6]	F. Cacace, V. Cusimano, P. Palumbo, Optimal impulsive control with application to antiangiogenic tumor therapy, IEEE Trans. Contr. Syst. Technol., 28 (2020), 106–117. https://doi.org/10.1109/TCST.2018.2861410 doi: 10.1109/TCST.2018.2861410
[7]	P. S. Rivadeneira, C. H. Moog, Observability criteria for impulsive control systems with applications to biomedical engineering processes, Automatica, 55 (2015), 125–131. https://doi.org/10.1016/j.automatica.2015.02.042 doi: 10.1016/j.automatica.2015.02.042
[8]	C. Treesatayapun, Impulsive optimal control for drug treatment of influenza A virus in the host with impulsive-axis equivalent model, Inform. Sciences, 576 (2021), 122–139. https://doi.org/10.1016/j.ins.2021.06.051 doi: 10.1016/j.ins.2021.06.051
[9]	H. Yang, X. Wang, S. Zhong, L. Shu, Synchronization of nonlinear complex dynamical systems via delayed impulsive distributed control, Appl. Math. Comput., 320 (2018), 75–85. https://doi.org/10.1016/j.amc.2017.09.019 doi: 10.1016/j.amc.2017.09.019
[10]	W. Chen, X. Lu, W. Zheng, Impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks, IEEE Trans. Neural Netw. Learn. Syst., 26 (2015), 734–748. https://doi.org/10.1109/TNNLS.2014.2322499 doi: 10.1109/TNNLS.2014.2322499
[11]	M. Li, X. Li, X. Han, J. Qiu, Leader-following synchronization of coupled time-delay neural networks via delayed impulsive control, Neurocomputing, 357 (2019), 101–107. https://doi.org/10.1016/j.neucom.2019.04.063 doi: 10.1016/j.neucom.2019.04.063
[12]	E. I. Verriest, F. Delmotte, M. Egerstedt, Control of epidemics by vaccination, Proceedings of the 2005, American Control Conference, Portland, OR, USA, 2005,985–990. https://doi.org/10.1109/ACC.2005.1470088
[13]	E. I. Verriest, Optimal control for switched point delay systems with refractory period, IFAC Proceedings Volumes, 38 (2005), 413–418. https://doi.org/10.3182/20050703-6-CZ-1902.00930 doi: 10.3182/20050703-6-CZ-1902.00930
[14]	F. Delmotte, E. I. Verriest, M. Egerstedt, Optimal impulsive control of delay systems, ESAIM: COCV, 14 (2008), 767–779. https://doi.org/10.1051/cocv:2008009 doi: 10.1051/cocv:2008009
[15]	X. Yang, X. Li, J. Lu, Z. Cheng, Synchronization of time-delayed complex networks with switching topology via hybrid actuator fault and impulsive effects control, IEEE Trans. Cybernetics, 50 (2020), 4043–4052. https://doi.org/10.1109/TCYB.2019.2938217 doi: 10.1109/TCYB.2019.2938217
[16]	J. Almeida, C. Silvestre, A. Pascoal, Synchronization of multiagent systems using event-triggered and self-triggered broadcasts, IEEE Trans. Automat. Contr., 62 (2017), 4741–4746. https://doi.org/10.1109/TAC.2017.2671029 doi: 10.1109/TAC.2017.2671029
[17]	J. Lu, Y. Wang, X. Shi, J. Cao, Finite-time bipartite consensus for multiagent systems under detail-balanced antagonistic interactions, IEEE Trans. Syst. Man Cybern. Syst., 51 (2021), 3867–3875. https://doi.org/10.1109/TSMC.2019.2938419 doi: 10.1109/TSMC.2019.2938419
[18]	X. Li, J. Cao, D. W. C. Ho, Impulsive control of nonlinear systems with time-varying delay and applications, IEEE Trans. Cybernetics, 50 (2020), 2661–2673. https://doi.org/10.1109/TCYB.2019.2896340 doi: 10.1109/TCYB.2019.2896340
[19]	W. Chen, W. Zheng, X. Lu, Impulsive stabilization of a class of singular systems with time-delays, Automatica, 83 (2017), 28–36. https://doi.org/10.1016/j.automatica.2017.05.008 doi: 10.1016/j.automatica.2017.05.008
[20]	Z. Tang, J. H. Park, J. Feng, Impulsive effects on quasi-synchronization of neural networks with parameter mismatches and time-varying delay, IEEE Trans. Neural Netw. Learn. Syst., 29 (2018), 908–919. https://doi.org/10.1109/TNNLS.2017.2651024 doi: 10.1109/TNNLS.2017.2651024
[21]	Z. Yang, D. Xu, Stability analysis and design of impulsive control systems with time delay, IEEE Trans. Automat. Contr., 52 (2007), 1448–1454. https://doi.org/10.1109/TAC.2007.902748 doi: 10.1109/TAC.2007.902748
[22]	W. Ren, J. Xiong, Stability analysis of impulsive switched time-delay systems with state-dependent impulses, IEEE Trans. Automat. Contr., 64 (2019), 3928–3935. https://doi.org/10.1109/TAC.2018.2890768 doi: 10.1109/TAC.2018.2890768
[23]	X. Liu, Stability of impulsive control systems with time delay, Math. Comput. Model., 39 (2004), 511–519. https://doi.org/10.1016/S0895-7177(04)90522-5 doi: 10.1016/S0895-7177(04)90522-5
[24]	W. Chen, Z. Ruan, W. Zheng, Stability and $L_2$-gain analysis for linear time-delay systems with delayed impulses: an augmentation-based switching impulse approach, IEEE Trans. Automat. Contr., 64 (2019), 4209–4216. https://doi.org/10.1109/TAC.2019.2893149 doi: 10.1109/TAC.2019.2893149
[25]	X. Wu, Y. Tang, W. Zheng, Input-to-state stability of impulsive stochastic delayed systems under linear assumptions, Automatica, 66 (2016), 195–204. https://doi.org/10.1016/j.automatica.2016.01.002 doi: 10.1016/j.automatica.2016.01.002
[26]	X. Li, S. Song, Stabilization of delay systems: delay-dependent impulsive control, IEEE Trans. Automat. Contr., 62 (2017), 406–411. https://doi.org/10.1109/TAC.2016.2530041 doi: 10.1109/TAC.2016.2530041
[27]	A. Haq, Existence and controllability of second‐order nonlinear retarded integro‐differential systems with multiple delays in control, Asian J. Control, 25 (2023), 623–628. https://doi.org/10.1002/asjc.2780 doi: 10.1002/asjc.2780
[28]	B. Wang, C. Wang, Periodic and event‐based impulse control for linear stochastic systems with multiplicative noise, Asian J. Control, 25 (2023), 2415–2423. https://doi.org/10.1002/asjc.3040 doi: 10.1002/asjc.3040
[29]	S. Luo, F. Deng, W. Chen, Stability analysis and synthesis for linear impulsive stochastic systems, Int. J. Robust Nonlinear Control, 28 (2018), 4424–4437. https://doi.org/10.1002/rnc.4244 doi: 10.1002/rnc.4244
[30]	J. Lu, D. W. C. Ho, J. Cao, A unified synchronization criterion for impulsive dynamical networks, Automatica, 46 (2010), 1215–1221. https://doi.org/10.1016/j.automatica.2010.04.005 doi: 10.1016/j.automatica.2010.04.005
[31]	S. Cai, P. Zhou, Z. Liu, Synchronization analysis of directed complex networks with time-delayed dynamical nodes and impulsive effects, Nonlinear Dyn., 76 (2014), 1677–1691. https://doi.org/10.1007/s11071-014-1238-z doi: 10.1007/s11071-014-1238-z
[32]	X. Li, P. Li, Stability of time-delay systems with impulsive control involving stabilizing delays, Automatica, 124 (2021), 109336. https://doi.org/10.1016/j.automatica.2020.109336 doi: 10.1016/j.automatica.2020.109336
[33]	T. Liang, Y. Li, W. Xue, Y. Li, T. Jiang, Performance and analysis of recursive constrained least Lncosh algorithm under impulsive noises, IEEE Trans. Circuits Syst. II, 68 (2021), 2217–2221. https://doi.org/10.1109/TCSII.2020.3037877 doi: 10.1109/TCSII.2020.3037877
[34]	O. M. Kwon, J. H. Park, S. M. Lee, On robust stability for uncertain neural networks with interval time-varying delays, IET Control Theory Appl., 2 (2008), 625–634. https://doi.org/10.1049/iet-cta:20070325 doi: 10.1049/iet-cta:20070325
[35]	A. Wu, H. Liu, Z. Zeng, Observer design and $H_\infty$ performance for discrete-time uncertain fuzzy-logic systems, IEEE Trans. Cybernetics, 51 (2021), 2398–2408. https://doi.org/10.1109/tcyb.2019.2948562 doi: 10.1109/tcyb.2019.2948562
[36]	C. Ge, X. Liu, C. Hua, J. H. Park, Exponential synchronization of the switched uncertain neural networks with mixed delays based on sampled-data control, J. Franklin Inst., 359 (2022), 2259–2282. https://doi.org/10.1016/j.jfranklin.2022.01.025 doi: 10.1016/j.jfranklin.2022.01.025
[37]	W. Huang, Q. Song, Z. Zhao, Y. Liu, F. Alsaadi, Robust stability for a class of fractional-order complex-valued projective neural networks with neutral-type delays and uncertain parameters, Neurocomputing, 450 (2021), 339–410. https://doi.org/10.1016/j.neucom.2021.04.046 doi: 10.1016/j.neucom.2021.04.046
[38]	H. Zhao, D. Liu, S. Lv, Robust maximum correntropy criterion subband adaptive filter algorithm for impulsive noise and noisy input, IEEE Trans. Circuits Syst. II, 69 (2021), 604–608. https://doi.org/10.1109/TCSII.2021.3095182 doi: 10.1109/TCSII.2021.3095182
[39]	D. Sidorov, Integral dynamical models: singularities, signals and control, World Scientific, 2014. https://doi.org/10.1142/9278
[40]	Z. G. Li, C. Y. Wen, Y. C. Soh, Analysis and design of impulsive control systems, IEEE Trans. Automat. Contr., 46 (2001), 894–897. https://doi.org/10.1109/9.928590 doi: 10.1109/9.928590
[41]	V. Kumar, M. Djemai, M. Defoort, M. Malik, Total controllability results for a class of time‐varying switched dynamical systems with impulses on time scales, Asian J. Control, 24 (2022), 474–482. https://doi.org/10.1002/asjc.2457 doi: 10.1002/asjc.2457
[42]	G. Wang, Y. Ren, Stability analysis of Markovian jump systems with delayed impulses, Asian J. Control, 25 (2023), 1047–1060. https://doi.org/10.1002/asjc.2863 doi: 10.1002/asjc.2863
[43]	S. T. Zavalishchin, A. N. Sesekin, Dynamic impulse systems: theory and applications, Dordrecht: Springer, 1997. https://doi.org/10.1007/978-94-015-8893-5
[44]	Z. Yu, S. Ling, P. X. Liu, Exponential stability of time‐delay systems with flexible delayed impulse, Asian J. Control, 26 (2024), 265–279. https://doi.org/10.1002/asjc.3202 doi: 10.1002/asjc.3202
[45]	X. Li, P. Li, Q. Wang, Input/output-to-state stability of impulsive switched systems, Syst. Control Lett., 116 (2018), 1–7. https://doi.org/10.1016/j.sysconle.2018.04.001 doi: 10.1016/j.sysconle.2018.04.001
[46]	B. Jiang, J. Lou, J. Lu, K. Shi, Synchronization of chaotic neural networks: average-delay impulsive control, IEEE Trans. Neural Netw. Learn. Syst., 33 (2022), 6007–6012. https://doi.org/10.1109/TNNLS.2021.3069830 doi: 10.1109/TNNLS.2021.3069830
[47]	F. Chen, W. Zhang, LMI criteria for robust chaos synchronization of a class of chaotic systems, Nonlinear Anal. Theor., 67 (2007), 3384–3393. https://doi.org/10.1016/j.na.2006.10.020 doi: 10.1016/j.na.2006.10.020
[48]	E. E. Yaz, Linear matrix inequalities in system and control theory, Proc. IEEE, 86 (1998), 2473–2474. https://doi.org/10.1109/JPROC.1998.735454 doi: 10.1109/JPROC.1998.735454

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)