Finite Time Stabilization of Dynamical Networks Under Pinning Event-Triggered Control

ZHAO Wei; REN Fengli

doi:10.21656/1000-0887.450072

Volume 46 Issue 3

Mar. 2025

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(3): 382-393

ZHAO Wei, REN Fengli. Finite Time Stabilization of Dynamical Networks Under Pinning Event-Triggered Control[J]. Applied Mathematics and Mechanics, 2025, 46(3): 382-393. doi: 10.21656/1000-0887.450072

Citation:

ZHAO Wei, REN Fengli. Finite Time Stabilization of Dynamical Networks Under Pinning Event-Triggered Control[J]. Applied Mathematics and Mechanics, 2025, 46(3): 382-393. doi: 10.21656/1000-0887.450072

Citation:

ZHAO Wei, REN Fengli. Finite Time Stabilization of Dynamical Networks Under Pinning Event-Triggered Control[J]. Applied Mathematics and Mechanics, 2025, 46(3): 382-393. doi: 10.21656/1000-0887.450072

PDF( 951 KB)

Finite Time Stabilization of Dynamical Networks Under Pinning Event-Triggered Control

doi: 10.21656/1000-0887.450072

ZHAO Wei,
REN Fengli^,

School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, P.R.China

Received Date: 2024-03-22
Rev Recd Date: 2024-05-22
Publish Date: 2025-03-01

Abstract

Abstract

The finite time stabilization problem of dynamical directed networks under pinning adaptive event-triggered control was addressed. Unlike the existing results as for finite time stabilization with event-triggered protocol, in view of the difficulties of the control cost and the large node number, a novel pinning event-triggered protocol was designed. Given its high dimension, the analysis of the finite time stabilization under the pinning event-triggered control for dynamical networks is challenging. Based on the Lyapunov stability theory and the appropriately designed protocol, sufficient conditions were derived to guarantee the finite time stabilization. Finally, an example was given to demonstrate the effectiveness of the theoretical results.
- dynamical coupled network,
- finite time stabilization,
- pinning control,
- event-triggered scheme

FullText(HTML)

References(34)

References

[1]	CORTÉS J, BULLO F. Coordination and geometric optimization via distributed dynamical systems[J]. SIAM Journal on Control and Optimization, 2005, 44(5): 1543-1574. doi: 10.1137/S0363012903428652
[2]	REN W. Multi-vehicle consensus with a time-varying reference state[J]. Systems & Control Letters, 2007, 56(7/8): 474-483.
[3]	SMITH T R, HANSSMANN H, LEONARD N E. Orientation control of multiple underwater vehicles with symmetry-breaking potentials[C]//Proceedings of the 40 th IEEE Conference on Decision and Control. Orlando, FL, USA, 2001: 4598-4603.
[4]	BHAT S P, BERNSTEIN D S. Finite-time stability of homogeneous systems[C]//Proceedings of the 1997 American Control Conference. Albuquerque, NM, USA, 1997.
[5]	BHAT S P, BERNSTEIN D S. Nontangency-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria[J]. SIAM Journal on Control and Optimization, 2003, 42(5): 1745-1775. doi: 10.1137/S0363012902407119
[6]	LU W, LIU X, CHEN T. A note on finite-time and fixed-time stability[J]. Neural Networks, 2016, 81: 11-15. doi: 10.1016/j.neunet.2016.04.011
[7]	ZIMENKO K, EFIMOV D, POLYAKOV A. On condition for output finite-time stability and adaptive finite-time control scheme[C]// 2019 IEEE 58 th Conference on Decision and Control (CDC). Nice, France, 2019.
[8]	HADDAD W M, LEE J. Finite-time stabilization and optimal feedback control for nonlinear discrete-time systems[J]. IEEE Transactions on Automatic Control, 2023, 68(3): 1685-1691. doi: 10.1109/TAC.2022.3151195
[9]	赵玮, 任凤丽. 基于自适应控制的四元数时滞神经网络的有限时间同步[J]. 应用数学和力学, 2022, 43(1): 94-103. doi: 10.21656/1000-0887.420068 ZHAO Wei, REN Fengli. Finite time adaptive synchronization of quaternion-value neural networks with time delays[J]. Applied Mathematics and Mechanics, 2022, 43(1): 94-103. (in Chinese) doi: 10.21656/1000-0887.420068
[10]	HONG Y, WANG J, CHENG D. Adaptive finite-time control of nonlinear systems with parametric uncertainty[J]. IEEE Transactions on Automatic Control, 2006, 51(5): 858-862. doi: 10.1109/TAC.2006.875006
[11]	IERVOLINO R, AMBROSINO R. Finite-time stabilization of state dependent impulsive dynamical linear systems[J]. Nonlinear Analysis: Hybrid Systems, 2023, 47: 101305. doi: 10.1016/j.nahs.2022.101305
[12]	WU F, LI C, LIAN J. Finite-time stability of switched nonlinear systems with state jumps: a dwell-time method[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2008, 52: 6061-6072.
[13]	赵玮, 任凤丽. 基于牵制控制的多智能体系统的有限时间与固定时间一致性[J]. 应用数学和力学, 2021, 42(3): 299-307. doi: 10.21656/1000-0887.410190 ZHAO Wei, REN Fengli. Finite-time and fixed-time consensus for multi-agent systems via pinning control[J]. Applied Mathematics and Mechanics, 2021, 42(3): 299-307. (in Chinese) doi: 10.21656/1000-0887.410190
[14]	LIN X, CHEN C C. Finite-time output feedback stabilization of planar switched systems with/without an output constraint[J]. Automatica, 2021, 131: 109728. doi: 10.1016/j.automatica.2021.109728
[15]	LI S, DU H, LIN X. Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics[J]. Automatica, 2011, 47(8): 1706-1712. doi: 10.1016/j.automatica.2011.02.045
[16]	CHEN T, LU W, LIU X. Finite time convergence of pinning synchronization with a single nonlinear controller[J]. Neural Networks, 2021, 143: 246-249. doi: 10.1016/j.neunet.2021.05.036
[17]	CHEN G, LEWIS F L, XIE L. Finite-time distributed consensusvia binary control protocols[J]. Automatica, 2011, 47(9): 1962-1968. doi: 10.1016/j.automatica.2011.05.013
[18]	MATUSIK R, NOWAKOWSKI A, PLASKACZ S, et al. Finite-time stability for differential inclusions with applications to neural networks[J]. SIAM Journal on Control and Optimization, 2020, 58(5): 2854-2870. doi: 10.1137/19M1250078
[19]	CAO Y, REN W, MENG Z. Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking[J]. Systems & Control Letters, 2010, 59(9): 522-529.
[20]	HU B, GUAN Z H, FU M. Distributed event-driven control for finite-time consensus[J]. Automatica, 2019, 103: 88-95. doi: 10.1016/j.automatica.2019.01.026
[21]	WU L, LIU K, LÜ J, et al. Finite-time adaptive stability of gene regulatory networks[J]. Neurocomputing, 2019, 338: 222-232. doi: 10.1016/j.neucom.2019.02.011
[22]	HUANG J, WEN C, WANG W, et al. Adaptive finite-time consensus control of a group of uncertain nonlinear mechanical systems[J]. Automatica, 2015, 51: 292-301. doi: 10.1016/j.automatica.2014.10.093
[23]	TABUADA P. Event-triggered real-time scheduling of stabilizing control tasks[J]. IEEE Transactions on Automatic Control, 2007, 52(9): 1680-1685. doi: 10.1109/TAC.2007.904277
[24]	WANG X, LEMMON M D. Event design in event-triggered feedback control systems[C]// 2008 47 th IEEE Conference on Decision and Control. Cancun, Mexico, 2008: 2105-2110.
[25]	DIMAROGONAS D V, FRAZZOLI E, JOHANSSON K H. Distributed event-triggered control for multi-agent systems[J]. IEEE Transactions on Automatic Control, 2012, 57(5): 1291-1297. doi: 10.1109/TAC.2011.2174666
[26]	GHODRAT M, MARQUEZ H J. A new Lyapunov-based event-triggered control of linear systems[J]. IEEE Transactions on Automatic Control, 2023, 68(4): 2599-2606. doi: 10.1109/TAC.2022.3190028
[27]	LI H, LIAO X, HUANG T, et al. Event-triggering sampling based leader-following consensus in second-order multi-agent systems[J]. IEEE Transactions on Automatic Control, 2015, 60(7): 1998-2003. doi: 10.1109/TAC.2014.2365073
[28]	HE W, XU B, HAN Q L, et al. Adaptive consensus control of linear multiagent systems with dynamic event-triggered strategies[J]. IEEE Transactions on Cybernetics, 2019, 50(7): 2996-3008.
[29]	SUN Q, CHEN J, SHI Y. Event-triggered robust MPC of nonlinear cyber-physical systems against DoS attacks[J]. Science China Information Sciences, 2021, 65(1): 110202.
[30]	SHEN J, CAO J. Finite-time synchronization of coupled neural networksvia discontinuous controllers[J]. Cognitive Neurodynamics, 2011, 5(4): 373-385. doi: 10.1007/s11571-011-9163-z
[31]	LU W, CHEN T. New approach to synchronization analysis of linearly coupled ordinary differential systems[J]. Physica D: Nonlinear Phenomena, 2006, 213(2): 214-230. doi: 10.1016/j.physd.2005.11.009
[32]	HARDY G, LITTLEWOOD J, POLYA G. Inequalities[M]. Cambridge: Cambridge University Press, 1952.
[33]	YU W W, CHEN G R, LÜ J H, et al. Synchronization via pinning control on general complex networks[J]. SIAM Journal on Control and Optimization, 2013, 51(2): 21395-21416.
[34]	ZOU F, NOSSEK J A. Bifurcation and chaos in cellular neural networks[J]. IEEE Transactions on Circuits and Systems : Fundamental Theory and Applications, 1993, 40(3): 166-173.