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Exponential Synchronization of Chaotic Systems with Stochastic Perturbations via Quantized Feedback control

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Abstract

In this paper, the exponential synchronization problem is investigated for chaotic systems under the quantized feedback control. The chaotic systems are represented by the unified model with time delays and stochastic perturbations. The quantized feedback control strategy is studied for the unified model with state and control quantizers, which are connected by using two dynamic scalars. The one-step control approach is put forward to make sure the exponential synchronization of drive-response systems. The corresponding control gain and two scalars are provided by solving linear matrix inequalities. Finally, the obtained results are illustrated by a numerical example.

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References

  1. X.H. Chang, G.H. Yang, New results on output feedback \({H}_{\infty }\) control for linear discrete-time systems. IEEE Trans. Autom. Control 59(5), 1355–1359 (2014)

    Article  MathSciNet  Google Scholar 

  2. W.W. Che, G.H. Yang, Quantized dynamic output feedback \({H}_{\infty }\) control for discrete-time systems with quantizer ranges consideration. Acta Autom. Sin. 34(6), 652–658 (2008)

    Article  MathSciNet  Google Scholar 

  3. N. Chen, G. Zhai, W. Gui, C. Yang, W. Liu, Decentralised \({H}_{\infty }\) quantisers design for uncertain interconnected networked systems. IET Control Theory Appl. 4(2), 177–185 (2010)

    Article  MathSciNet  Google Scholar 

  4. D.F. Coutinho, M. Fu, C.E. De Souza, Input and output quantized feedback linear systems. IEEE Trans. Autom. Control 55(3), 761–766 (2010)

    Article  MathSciNet  Google Scholar 

  5. N. Elia, S.K. Mitter, Stabilization of linear systems with limited information. IEEE Trans. Autom. Control 46(9), 1384–1400 (2002)

    Article  MathSciNet  Google Scholar 

  6. M. Fu, L. Xie, The sector bound approach to quantized feedback control. IEEE Trans. Autom. Control 50(11), 1698–1711 (2005)

    Article  MathSciNet  Google Scholar 

  7. X. Guo, J. Wang, F. Liao, D. Wang, Quantized \({H}_{\infty }\) consensus of multi-agent systems with quantization mismatch under switching weighted topologies. IEEE Trans. Control Netw. Syst. 4(99), 202–212 (2017)

    Article  MathSciNet  Google Scholar 

  8. X.G. Guo, J.L. Wang, F. Liao, S. Suresh, S. Narasimalu, Quantized insensitive consensus of Lipschitz nonlinear multi-agent systems using the incidence matrix. J. Frankl. Inst. 352(11), 4845–4863 (2015)

    Article  MathSciNet  Google Scholar 

  9. L.Y. Hao, G.H. Yang, Fault-tolerant control via sliding-mode output feedback for uncertain linear systems with quantisation. IET Control Theory Appl. 7(16), 1992–2006 (2013)

    Article  MathSciNet  Google Scholar 

  10. C. Hua, G. Chao, X. Guan, Synchronization of chaotic Lur’e systems with time delays using sampled-data control. IEEE Trans. Neural Netw. Learn. Syst. 26(6), 1214–1221 (2015)

    Article  MathSciNet  Google Scholar 

  11. S.V. Kumar, R. Sakthivel, M. Sathishkumar, S.M. Anthoni, Finite time passive reliable filtering for fuzzy systems with missing measurements. J. Dyn. Syst. Meas. Control 140(8), 081009 (2018)

    Article  Google Scholar 

  12. X. Li, C. Ding, Q. Zhu, Synchronization of stochastic perturbed chaotic neural networks with mixed delays. J. Frankl. Inst. 347(7), 1266–1280 (2010)

    Article  MathSciNet  Google Scholar 

  13. X. Li, X. Fu, Synchronization of chaotic delayed neural networks with impulsive and stochastic perturbations. Commun. Nonlinear Sci. Numer. Simul. 16(2), 885–894 (2011)

    Article  MathSciNet  Google Scholar 

  14. X. Li, X. Fu, Lag synchronization of chaotic delayed neural networks via impulsive control. IMA J. Math. Control Inf. 29(1), 133–145 (2012). (13)

    Article  MathSciNet  Google Scholar 

  15. H. Liang, Y. Zhang, T. Huang, H. Ma, Prescribed performance cooperative control for multiagent systems with input quantization. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2019.2893645

  16. H. Liang, Z. Zhang, C.K. Ahn, Event-triggered fault detection and isolation of discrete-time systems based on geometric technique. IEEE Trans. Circuits Syst. Express Briefs (2019). https://doi.org/10.1109/TCSII.2019.2907706

  17. D. Liberzon, Hybrid feedback stabilization of systems with quantized signals. Automatica 39(9), 1543–1554 (2003)

    Article  MathSciNet  Google Scholar 

  18. D. Liberzon, D. Nesic, Input-to-state stabilization of linear systems with quantized state measurements. IEEE Trans. Autom. Control 52(5), 767–781 (2007)

    Article  MathSciNet  Google Scholar 

  19. K. Liu, E. Fridman, K.H. Johansson, Y. Xia, Quantized control under round-robin communication protocol. IEEE Trans. Ind. Electron. 63(7), 4461–4471 (2016)

    Article  Google Scholar 

  20. M. Liu, H. Chen, S. Zhang, Z. Fan, Exponential synchronization of two totally different chaotic systems based on a unified model. Neural Comput. Appl. 25(7–8), 1801–1808 (2014)

    Article  Google Scholar 

  21. M. Liu, S. Zhang, Z. Fan, S. Zheng, W. Sheng, Exponential \({H}_{\infty }\) synchronization and state estimation for chaotic systems via a unified model. IEEE Trans. Neural Netw. Learn. Syst. 24(7), 1114–1126 (2013)

    Article  Google Scholar 

  22. M. Liu, S. Zhang, Y. Jin, Multi-sensor optimal \({H}_{\infty }\) fusion filters for delayed nonlinear intelligent systems based on a unified model. Neurocomputing 24(3), 280–290 (2011)

    MATH  Google Scholar 

  23. Y. Niu, D.W.C. Ho, Control strategy with adaptive quantizer’s parameters under digital communication channels. Automatica 50(10), 2665–2671 (2014)

    Article  MathSciNet  Google Scholar 

  24. J. Qiu, G. Feng, H. Gao, Observer-based piecewise affine output feedback controller synthesis of continuous-time T–S fuzzy affine dynamic systems using quantized measurements. IEEE Trans. Fuzzy Syst. 20(6), 1046–1062 (2012)

    Article  Google Scholar 

  25. S. Rathinasamy, S. Murugesan, F. Alzahrani, Y. Ren, Quantized finite-time non-fragile filtering for singular Markovian jump systems with intermittent measurements. Circuits Syst. Signal Process. (2019). https://doi.org/10.1007/s00034-019-01046-9

    Article  Google Scholar 

  26. M. Sathishkumar, R. Sakthivel, C. Wang, B. Kaviarasan, S.M. Anthoni, Non-fragile filtering for singular Markovian jump systems with missing measurements. Signal Process. 142, 125–136 (2018)

    Article  Google Scholar 

  27. A. Selivanov, A. Fradkov, D. Liberzon, Adaptive control of passifiable linear systems with quantized measurements and bounded disturbances. Syst. Control Lett. 88, 62–67 (2016)

    Article  MathSciNet  Google Scholar 

  28. H. Shen, F. Li, S. Xu, V. Sreeram, Slow state variables feedback stabilization for semi-Markov jump systems with singular perturbations. IEEE Trans. Autom. Control 63(8), 2709–2714 (2018)

    Article  MathSciNet  Google Scholar 

  29. H. Shen, Y. Men, Z.G. Wu, J. Cao, G. Lu, Network-based quantized control for fuzzy singularly perturbed semi-Markov jump systems and its application. IEEE Trans. Circuits Syst. Regul. Pap. 66(3), 1130–1140 (2019)

    Article  Google Scholar 

  30. H. Shen, T. Wang, J. Cao, G. Lu, Y. Song, T. Huang, Nonfragile dissipative synchronization for Markovian memristive neural networks: a gain-scheduled control scheme. IEEE Trans. Neural Netw. Learn. Syst. (2018). https://doi.org/10.1109/tnnls.2018.2874035

    Article  MathSciNet  Google Scholar 

  31. G. Song, S. Hao, Y. Wei, Z. Li, Quantized output feedback control of uncertain discrete-time systems with input saturation. Circuits Syst. Signal Process. 33(10), 3065–3083 (2014)

    Article  MathSciNet  Google Scholar 

  32. Q. Song, T. Huang, Stabilization and synchronization of chaotic systems with mixed time-varying delays via intermittent control with non-fixed both control period and control width. Neurocomputing 154, 61–69 (2015)

    Article  Google Scholar 

  33. D. Tong, Q. Chen, Delay and its time-derivative-dependent model reduction for neutral-type control system. Circuits Syst. Signal Process. 36(6), 2542–2557 (2017)

    Article  MathSciNet  Google Scholar 

  34. D. Tong, L. Zhang, W. Zhou, J. Zhou, Y. Xu, Asymptotical synchronization for delayed stochastic neural networks with uncertainty via adaptive control. Int. J. Control Autom. Syst. 14(3), 706–712 (2016)

    Article  Google Scholar 

  35. D. Tong, W. Zhou, X. Zhou, J. Yang, L. Zhang, Y. Xu, Exponential synchronization for stochastic neural networks with multi-delayed and Markovian switching via adaptive feedback control. Commun. Nonlinear Sci. Numer. Simul. 29(1–3), 359–371 (2015)

    Article  MathSciNet  Google Scholar 

  36. Y. Wang, X. Yang, H. Yan, Reliable fuzzy tracking control of near-space hypersonic vehicle using aperiodic measurement information. IEEE Trans. Ind. Electron. (2019). https://doi.org/10.1109/TIE.2019.2892696

    Article  Google Scholar 

  37. Z.G. Wu, P. Shi, H. Su, J. Chu, Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling. IEEE Trans. Neural Netw. Learn. Syst. 23(9), 1368–1376 (2012)

    Article  Google Scholar 

  38. Z.G. Wu, P. Shi, H. Su, J. Chu, Sampled-data synchronization of chaotic Lur’e systems with time delays. IEEE Trans. Neural Netw. Learn. Syst. 24(3), 410–421 (2013)

    Article  Google Scholar 

  39. J. Xia, Z. Jing, F. June, W. Zhen, Z. Guangming, Command filter-based adaptive fuzzy control for nonlinear systems with unknown control directions. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2911115

  40. J. Xia, Z. Jing, S. Wei, B. Zhang, W. Zhen, Finite-time adaptive fuzzy control for nonlinear systems with full state constraints. IEEE Trans. Syst. Man Cybern. Syst. (2018). https://doi.org/10.1109/TSMC.2018.2854770

    Google Scholar 

  41. C. Xu, D. Tong, Q. Chen, W. Zhou, P. Shi, Exponential stability of markovian jumping systems via adaptive sliding mode control. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2018.2884565

  42. X. Yan, D. Tong, Q. Chen, W. Zhou, Y. Xu, Adaptive state estimation of stochastic delayed neural networks with fractional Brownian motion. Neural Process. Lett. (2018). https://doi.org/10.1007/s11063-018-9960-z

    Article  Google Scholar 

  43. W. Zhang, J. Huang, P. Wei, Weak synchronization of chaotic neural networks with parameter mismatch via periodically intermittent control. Appl. Math. Model. 35(2), 612–620 (2011)

    Article  MathSciNet  Google Scholar 

  44. Z. Zhang, H. Liang, C. Wu, C.K. Ahn, Adaptive event-triggered output feedback fuzzy control for nonlinear networked systems with packet dropouts and actuator failure. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2891236

    Article  Google Scholar 

  45. B.C. Zheng, G.H. Yang, Quantized output feedback stabilization of uncertain systems with input nonlinearities via sliding mode control. Int. J. Robust. Nonlinear Control 24(2), 228–246 (2014)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work is partially supported by National Natural Science Foundation of China (61673257, 11501367, 61573095).

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Authors and Affiliations

  1. College of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201620, China

    Yao Wang & Dongbing Tong

  2. School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai, 201620, China

    Qiaoyu Chen

  3. College of Information Sciences and Technology, Donghua University, Shanghai, 200051, China

    Wuneng Zhou

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  1. Yao Wang
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  2. Dongbing Tong
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  4. Wuneng Zhou
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Correspondence to Dongbing Tong.

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Wang, Y., Tong, D., Chen, Q. et al. Exponential Synchronization of Chaotic Systems with Stochastic Perturbations via Quantized Feedback control. Circuits Syst Signal Process 39, 474–491 (2020). https://doi.org/10.1007/s00034-019-01167-1

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