Abstract
This paper deals with the synchronization problem of complex dynamical networks with actuator saturation by using sampled-data control. A novel Lyapunov function taking full advantage of the information on sampling pattern is constructed for complex dynamical networks. Then, combined with free-weighting matrix approach and linear matrix inequality technique, a stability criterion is derived to guarantee the synchronization of complex dynamical networks. It is proved that the synchronization of complex dynamical networks can be achieved under some suitable conditions. In the end, the validity of the designed approach is illustrated via a numerical simulation.
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References
C.K. Ahn, Overflow oscillation elimination of 2-d digital filters in the roesser model with wiener process noise. IEEE Sig. Process. Lett. 21, 1302–1305 (2014)
C.L.P. Chen, T. Zhang, L. Chen, S.C. Tam, I-Ching divination evolutionary algorithm and its convergence analysis. IEEE Trans. Cybern. 47, 2–13 (2017)
Y. Chen, Z. Wang, B. Shen, H. Dong, Exponential synchronization for delayed dynamical networks via intermittent control: dealing with actuator saturations. IEEE Trans. Neural Netw. Learn. Syst. (2018) https://doi.org/10.1109/TNNLS.2018.2854841
F. El Haoussi, E.H. Tissir, An LMI-based approach for robust stabilization of time delay systems containing saturating actuators. IMA J. Math. Control Inf. 24, 347–356 (2018)
E. Fridman, A refined input delay approach to sampled-data control. Automatica 46, 421–427 (2010)
H. Gao, J. Wu, P. Shi, Brief paper: robust sampled-data \(H_{\infty }\) control with stochastic sampling. Automatica 45, 1729–1736 (2009)
Q. Gan, Y. Liang, Synchronization of chaotic neural networks with time delay in the leakage term and parametric uncertainties based on sampled-data control. J. Frankl. Inst. 349, 1955–1971 (2012)
G. Hu, Global synchronization for coupled lur’e dynamical networks. Circuits Syst. Signal Process. 32, 2851–2866 (2013)
T. Hu, Z. Lin, B.M. Chen, An analysis and design method for linear systems subject to actuator saturation and disturbance. Automatica 38, 351–359 (2002)
H.R. Karimi, N.A. Duffie, S. Dashkovskiy, Local capacity \(H_{\infty }\) control for production networks of autonomous work systems with time-varying delays. Eur. Control Conf. ECC 7, 849–857 (2010)
H.R. Karimi, A sliding mode approach to \(H _{\infty }\) synchronization of master–slave time-delay systems with Markovian jumping parameters and nonlinear uncertainties. J. Frankl. Inst. 349, 1480–1496 (2012)
T. Li, T. Wang, S. Fei, Pinning cluster synchronization for delayed dynamical networks via; Kronecker product. Circuits Syst. Signal Process. 32, 1907–1929 (2013)
R. Lu, W. Yu, J. Lu, A. Xue, Synchronization on complex networks of networks. IEEE Trans. Neural Netw. Learn. Syst. 25, 2110–2118 (2014)
X. Meng, L. Jia, W. Xiang, Complex network model for railway timetable stability optimisation. IET Intell. Transp. Syst. 12, 1369–1377 (2018)
Y. Su, C. Zheng, P. Mercorelli, Global finite-time stabilization of planar linear systems with actuator saturation. IEEE Trans. Circuits Syst. 64, 947–951 (2017)
P. Shi, H.R. Karimi, B. Wang, Chaos synchronization for a class of chaotic systems via \(H_{\infty }\) control technique. Asian Control Conf. ASCC (2013). https://doi.org/10.1109/ASCC.2013.6606289
B. Shen, Z. Wang, X. Liu, Sampled-data synchronization control of dynamical networks with stochastic sampling. IEEE Trans. Autom. Control 57, 2644–2650 (2012)
H. Su, M.Z.Q. Chen, X. Wang, J. Lam, Semiglobal observer-based leader-following consensus with input saturation. IEEE Trans. Ind. Electron. 61, 2842–2850 (2013)
Y. Wu, R. Lu, P. Shi, H. Su, Z.G. Wu, Sampled-data synchronization of complex networks with partial couplings and T–S fuzzy nodes. IEEE Trans. Fuzzy Syst. 26, 782–793 (2018)
Y. Wu, H. Su, P. Shi, Z. Shu, Z.G. Wu, Consensus of multiagent systems using aperiodic sampled-data control. IEEE Trans. Cybern. 46, 2132–2143 (2016)
Y. Wu, R. Lu, P. Shi, H. Su, Z.G. Wu, Analysis and design of synchronization for heterogeneous network. IEEE Trans. Cybern. 48, 1253–1262 (2018)
S. Wang, Y. Huang, S. Ren, Synchronization and robust synchronization for fractional-order coupled neural networks. IEEE Access 5, 12439–12448 (2017)
Z.G. Wu, P. Shi, H. Su, J. Chu, Sampled-data exponential synchronization of complex dynamical networks with time-varying coupling delay. IEEE Trans. Neural Netw. Learn. Syst. 24, 1177–1187 (2013)
Z. Wang, D.W.C. Ho, H. Dong, H. Gao, Robust \(H_{\infty }\) finite-horizon control for a class of stochastic nonlinear time-varying systems subject to sensor and actuator saturations. IEEE Trans. Autom. Control 55, 1716–1722 (2010)
H. Yang, Z. Yang, H. Guan, B. Zang, H. Chen, SFence-free synchronization with dynamically serialized synchronization variables. IEEE Trans. Parallel Distrib. Syst. 28, 486–500 (2017)
D. Yao, R. Lu, Y. Xu, J.W. Robust, \(H_{\infty }\) filtering for Markov jump systems with mode-dependent quantized output and partly unknown transition probabilities. Automatica 138, 328–338 (2017)
H. Ye, M. Li, C. Yan, W. Gui, Finite-time stabilization of the double integrator subject to input saturation and input delay. IEEE/CAA J. Autom. Sinica 5, 1017–1024 (2018)
T. Zhang, C.L.P. Chen, L. Chen, X. Xu, B. Hu, Design of highly nonlinear substitution boxes based on I-Ching operators. IEEE Trans. Cybern. 48, 3349–3358 (2018)
C.K. Zhang, Y. He, M. Wu, Exponential synchronization of neural networks with time-varying mixed delays and sampled-data. Neurocomputing 74, 265–273 (2010)
B. Zhou, W.X. Zheng, G.R. Duan, An improved treatment of saturation nonlinearity with its application to control of systems subject to nested saturation. Automatica 47, 306–315 (2011)
B. Zhou, H. Gao, Z. Lin, G.R. Duan, Stabilization of linear systems with distributed input delay and input saturation. Automatica 48, 712–724 (2012)
J. Zheng, B. Cui, State estimation of Chaoticl Lurie systems via communication channel with transmission delay. Circuits Syst. Signal Process. 37, 1–16 (2018)
Acknowledgements
This work was partially supported by National Key R&D Program of China (2018YFB1700400), the Innovative Int J Adv Manuf Technol Research Team Program of Guangdong Province Science Foundation (2018B030312006), the Fundamental Research Funds for the Central Universities (2017FZA5010) and the Science and Technology Planning Project of Guangdong Province (2017B010116006).
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Guan, Y., Wu, Y., Wu, H. et al. Synchronization of Complex Dynamical Networks with Actuator Saturation by Using Sampled-Data Control. Circuits Syst Signal Process 38, 5508–5527 (2019). https://doi.org/10.1007/s00034-019-01154-6
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DOI: https://doi.org/10.1007/s00034-019-01154-6