Abstract
This paper investigates the fixed-time synchronization problem of complex networks. A novel switching controller is proposed to solve the problem. The designed controller in this paper only needs intermittently to pin a few of nodes, which could reduce the control time and save the system’s energy. Moreover, compared with the existing control methods for the fixed-time synchronization, the novel controller does not use the sign function, which could avoid the chattering behaviors. By constructing a Lyapunov function and designing a comparison system, some sufficient conditions are obtained to achieve the fixed-time synchronization. Finally, the numerical simulations could verify the effectiveness and feasibility of the proposed control approaches.
Similar content being viewed by others
References
Abdurahman A, Jiang H, and Teng Z, Finite-time synchronization for memristor-based neural networks with time-varying delays, Neural Networks, 2015, 69(3): 20–28.
Liu X, Su H, and Chen M, A switching approach to designing finite-time synchronization controllers of coupled neural networks, IEEE Transactions on Neural Networks and Learning Systems, 2016, 27(2): 471–482.
Gao J, Zhu P, Ahmed A, et al., A new switching control for finite-time synchronization of memristor-based recurrent neural networks, Neural Networks, 2017, 86(2): 1–9.
Ji G, Hu C, Yu J, et al., Finite-time and fixed-time synchronization of discontinuous complex networks: A unified control framework design, Journal of the Franklin Institute, 2018, 355(11): 4665–4685.
Liu X, Ho D, Song Q, et al., Finite/fixed-time pinning synchronization of complex networks with stochastic disturbances, IEEE Transactions on Cybernetics, 2019, 49(6): 2398–2403.
Li Q, Guo J, Sun C, et al. Finite-time synchronization for a class of dynamical complex networks with nonidentical nodes and uncertain disturbance, Journal of Systems Science & Complexity, 2019, 32(3): 818–834.
Gao J, Zhu P, Xiong W, et al., Asymptotic synchronization for stochastic memristor-based neural networks with noise disturbance, Journal of the Franklin Institute, 2016, 353(13): 3271–3289.
Wan Y, Cao J, Wen G, et al., Robust fixed-time synchronization of delayed cohen-grossberg neural networks, Neural Networks, 2016, 73(C): 86–94.
Cao J and Li R, Fixed-time synchronization of delayed memristor-based recurrent neural networks, Science China Information Sciences, 2017, 60(3): 032201.
Lu H, He W, Han Q, et al., Fixed-time synchronization for coupled delayed neural networks with discontinuous or continuous activations, Neurocomputing, 2018, 314(7): 143–153.
Parsegov S, Polyakov A, and Shcherbakov P, Fixed-time consensus algorithm for multi-agent systems with integrator dynamics, IFAC Proceedings Volumes, 2013, 46(27): 110–115.
Zuo Z and Tie L, Distributed robust finite-time nonlinear consensus protocols for multi-agent systems, International Journal of Systems Science, 2014, 47(6): 1–10.
Yang X, Ho D, Lu J, et al., Finite-time cluster synchronization of t-s fuzzy complex networks with discontious subsystems and random coupling delays, IEEE Transactions on Fuzzy Systems, 2015, 23(6): 2302–2316.
Yang X and Lu J, Finite-time synchronization of coupled networks with markovian topology and impulsive effects, IEEE Transactions on Automatic Control, 2016, 61(8): 2256–2261.
Zhang W, Yang X, Xu C, et al., Finite-time synchronization of discontinuous neural networks with delays and mismatched parameters, IEEE Transactions on Neural Networks and Learning Systems, 2018, 29(8): 3761–3771.
Yang X, Lam J, Ho D, et al., Fixed-time synchronization of complex networks with impulsive effects via non-chattering control, IEEE Transactions on Automatic Control, 2017, 62(11): 5511–5521.
Zhang W, Yang X, and Li C, Fixed-time stochastic synchronization of complex networks via continuous control, IEEE Transactions on Cybernetics, 2019, 49(8): 3099–3104.
Zhang W, Yang S, Li C, et al., Finite-time and fixed-time synchronization of complex networks with discontinuous nodes via quantized control, Neural Processing Letters, 2019, 50(3): 2073–2086.
Jing W, Lei S, Hao S, et al., Mixed H∞/passive sampled-data synchronization control of complex dynamical networks with distributed coupling delay, Journal of the Franklin Institute, 2017, 354(3): 1302–1320.
Liu Y, Guo B, Park J, et al., Nonfragile exponential synchronization of delayed complex dynamical networks with memory sampled-data control, IEEE Transactions on Neural Networks and Learning Systems, 2018, 29(1): 118–128.
Li B, Wang Z, and Ma L, An event-triggered pinning control approach to synchronization of discrete-time stochastic complex dynamical networks, IEEE Transactions on Neural Networks and Learning Systems, 2018, 29(12): 5812–5822.
Sun H, Ning L, Zhao D, et al., Synchronization of complex networks with coupling delays via adaptive pinning intermittent control, International Journal of Automation and Computing, 2013, 10(4): 312–318.
Liu X, Liu Y, and Zhou L, Quasi-synchronization of nonlinear coupled chaotic systems via aperiodically intermittent pinning control, Neurocomputing, 2015, 173(1): 759–767.
Zochowski M, Intermittent dynamical control, Physica D-Nonlinear Phenomena, 2000, 145(3): 181–190.
Li H, Hu C, Jiang H, et al., Synchronization of fractional-order complex dynamical networks via periodically intermittent pinning control, Chaos Solitons and Fractals, 2017, 103: 357–363.
Huang J, Li C, Huang T, et al., Lag quasisynchronization of coupled delayed systems with parameter mismatch by periodically intermittent control, Nonlinear Dynamics, 2013, 71(3): 469–478.
Liu X and Chen T, Synchronization of complex networks via aperiodically intermittent pinning control, IEEE Transactions on Automatic Control, 2015, 60(12): 3316–3321.
Li L, Tu Z, Mei J, et al., Finite-time synchronization of complex delayed networks via intermittent control with multiple switched periods, Nonlinear Dynamics, 2016, 85(1): 375–388.
Zuo Z and Lin T, Distributed robust finite-time nonlinear consensus protocols for multi-agent systems, International Journal of Systems Science, 2016, 47(6): 1366–1375.
Liu X and Chen T, Cluster synchronization in directed networks via intermittent pinning control, IEEE Transactions on Neural Networks, 2011, 22(7): 1009–20.
Barabasi A and Albert R, Emergence of scaling in random networks, Science, 1999, 286(5439): 509–512.
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported in part by the National Social Science Fund under Grant No. 18BTJ025, in part by the Scientific Research Starting Project of SWPU under Grant No. 2019QHZ018, and in part by the Youth Innovation Team of SWPU under Grant No. 2019CXTD08.
This paper was recommended for publication by Editor HAN Jing.
Rights and permissions
About this article
Cite this article
Gao, J., Zhao, J. Fixed-Time Synchronization of Complex Networks via Intermittent Control Without Sign Function. J Syst Sci Complex 35, 1748–1760 (2022). https://doi.org/10.1007/s11424-022-1016-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11424-022-1016-9