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Quantized Stabilization for Highly Nonlinear Stochastic Delay Systems by Discrete-Time Control

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Abstract

In this article, some new results of quantized discrete feedback control are revealed for stochastic delay systems via discrete-time state and mode observations (DSMO). Particularly, the coefficients of considered hybrid stochastic systems do not satisfy the linear growth condition (LGC). The main emphasis is to design a quantized feedback control law that ensures \(H_\infty \) stable and exponentially stable of the integrated systems. Based on DSMO, the desired controller can be fairly constructed. Finally, the correctness of presented results is testified by a numerical case.

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All data generated or analyzed during this work are included in this paper.

References

  1. A. Ahlborn, U. Parlitz, Stabilizing unstable steady states using multiple delay deedback control. Phys. Rev. Lett. 93, 26–31 (2004)

    Article  Google Scholar 

  2. A. Bahar, X. Mao, Persistence of stochastic power law logistic model. J. Appl. Probab. Stat. 3(1), 37–43 (2008)

    MathSciNet  MATH  Google Scholar 

  3. W. Chen, S. Xu, B. Zhang, Z. Qi, Stability and stabilisation of neutral stochastic delay Markovian jump systems. IET Control Theory Appl. 10(15), 1798–1807 (2016)

    Article  MathSciNet  Google Scholar 

  4. E. Fridman, Introduction to Time-Delay Systems: Analysis and Control (Birkhauser, Basel, 2014)

    Book  MATH  Google Scholar 

  5. W. Fei, L. Hu, X. Mao, M. Shen, Delay dependent stability of highly nonlinear hybrid stochastic systems. Automatica 82, 165–170 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  6. C. Fei, M. Shen, W. Fei, X. Mao, L. Yan, Stability of highly nonlinear hybrid stochastic integro-differential delay equations. Nonlinear Anal. Hybrid Syst. 31, 180–199 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  7. W. Fei, L. Hu, X. Mao, M. Shen, Structured robust stability and boundedness of nonlinear hybrid delay systems. SIAM J. Control. Optim. 56(4), 2662–2689 (2018)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. Q. Guo, X. Mao, R. Yue, Almost sure exponential stability of stochastic differential delay equations. SIAM J. Control. Optim. 54(4), 1919–1933 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  10. M. Hua, C. Bian, J. Chen, J. Fei, Quantized \(H_\infty \) filtering for continuous-time nonhomogeneous Markov jump systems. Circuits Syst. Signal Process. 39, 3833–3857 (2020)

    MATH  Google Scholar 

  11. Y. Liu, X. Liu, Y. Jing, X. Chen, J. Qiu, Direct adaptive preassigned finite-time control with time-delay and quantized input using neural network. IEEE Trans. Neural Netw. Learn. Syst. 31(4), 1222–1231 (2020)

    Article  MathSciNet  Google Scholar 

  12. W. Liu, Y. Wang, \(H_\infty \) control of Markovian jump linear singularly perturbed systems, Circuits Syst. Signal Process., https://doi.org/10.1007/s00034-021-01676-y (2021)

  13. X. Li, X. Mao, Stabilisation of highly nonlinear hybrid stochastic differential delay equations by delay feedback control. Automatica 112, 108657 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  14. H. Li, Y. Wu, M. Chen, R. Lu, Adaptive multigradient recursive reinforcement learning event-triggered tracking control for multiagent systems. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2021.3090570

    Article  Google Scholar 

  15. H. Li, Y. Wu, M. Chen, Adaptive fault-tolerant tracking control for discrete-time multiagent systems via reinforcement learning algorithm. IEEE Trans. Cybern. 51(3), 1163–1174 (2021)

    Article  Google Scholar 

  16. M. Liu, D. Ho, Y. Niu, Robust filtering design for stochastic system with mode-dependent output quantization. IEEE Trans. Signal Process. 58(12), 6410–6416 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. R. Lu, S. Zhao, Y. Wu, Y. Xu, Finite-time bounded control for a class of stochastic nonlinear systems with randomly quantized measurements. J. Frankl. Inst. 353(17), 4368–4383 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  18. X. Mao, Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Trans. Autom. Control 47(10), 1604–1612 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  19. X. Mao, C. Yuan, Stochastic Differential Equations with Markovian Swithing (Imperial College Press, London, 2006)

    Book  Google Scholar 

  20. X. Mao, Almost sure exponential stabilization by discrete-time stochastic feedback control. IEEE Trans. Autom. Control 61(6), 1619–1624 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  21. X. Mao, Stabilization of continuous-time hybrid stochastic differential equations by discrete-time feedback control. Automatica 49(12), 3677–3681 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  22. X. Mao, W. Liu, L. Hu, Q. Luo, J. Lu, Stabilisation of hybrid stochastic differential equations by feedback control based on discrete-time state observations. Syst. Control Lett. 73, 88–95 (2014)

    Article  MATH  Google Scholar 

  23. X. Mao, Stability and stabilization of stochastic differential delay equations. IET Control Theory Appl. 1(6), 1551–1566 (2007)

    Article  Google Scholar 

  24. X. Mao, J. Lam, L. Huang, Stabilisation of hybrid stochastic differential equations by delay feedback control. Syst. Control Lett. 57(11), 927–935 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  25. C. Mei, C. Fei, W. Fei, X. Mao, Stabilisation of highly non-linear continuous-time hybrid stochastic differential delay equations by discrete-time feedback control. IET Control Theory Appl. 14(2), 313–323 (2020)

    Article  Google Scholar 

  26. Q. Ma, S. Xu, Consensus switching of second-order multiagent systems with time delay. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.3011448

    Article  Google Scholar 

  27. Q. Ma, S. Xu, Exact delay bounds of second-order multi-agent systems with input and communication delays: from algebra and geometric prospective. IEEE Trans. Circuits Syst. II Express Briefs (2021). https://doi.org/10.1109/TCSII.2021.3094185

    Article  Google Scholar 

  28. Q. Ma, S. Xu, Consensusability of first-order multiagent systems under distributed PID controller with time delay. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2021.3084366

    Article  Google Scholar 

  29. K. Pyragas, Control of chaos via extended delay feedback. Phys. Lett. A 206(5), 323–330 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  30. P. Shi, M. Liu, L. Zhang, Fault-tolerant sliding-mode-observer synthesis of Markovian jump systems using quantized measurements. IEEE Trans. Industr. Electron. 62(9), 5910–5918 (2015)

    Article  Google Scholar 

  31. X. Shangguan, Y. He, C. Zhang, L. Jin, W. Yao, L. Jiang, M. Wu, Control performance standards-oriented event-triggered load frequency control for power systems under limited communication bandwidth. IEEE Trans. Control Syst. Technol. (2021). https://doi.org/10.1109/TCST.2021.3070861

    Article  Google Scholar 

  32. G. Song, X. Mao, T. Li, Robust quantised control of hybrid stochastic systems based on discrete-time state and mode observations. Int. J. Control 92(8), 1836–1845 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  33. G. Song, B. Zheng, Q. Luo, X. Mao, Stabilisation of hybrid stochastic differential equations by feedback control based on discrete-time observations of state and mode. IET Control Theory Appl. 11(3), 301–307 (2017)

    Article  MathSciNet  Google Scholar 

  34. M. Sun, J. Lam, S. Xu, Y. Zou, Robust exponential stabilization for Markovian jump systems with mode-dependent input delay. Automatica 43(10), 1799–1807 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  35. M. Shen, W. Fei, X. Mao, Y. Liang, Stability of highly nonlinear neutral stochastic differential delay equations. Syst. Control Lett. 115, 1–8 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  36. S. Tatikonda, A. Sahai, S. Mitter, Stochastic linear control over a communication channel. IEEE Trans. Autom. Control 49, 1549–1561 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  37. L. Wu, X. Su, P. Shi, Sliding mode control with bounded \(L_2\) gain performance of Markovian jump singular time-delay systems. Automatica 48(8), 1929–1933 (2012)

    MathSciNet  MATH  Google Scholar 

  38. D. Yao, M. Liu, H. Li, H. Ma, Robust adaptive sliding mode control for nonlinear uncertain neutral Markovian jump systems. Circuits Syst. Signal Process. 35, 2741–2761 (2016)

    Article  MATH  Google Scholar 

  39. S. You, W. Liu, J. Lu, X. Mao, Q. Qiu, Stabilization of hybrid systems by feedback control based on discrete-time state observations. SIAM J. Control. Optim. 53(2), 905–925 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  40. D. Yue, Q. Han, Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching. IEEE Trans. Autom. Control 50(2), 217–222 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  41. Q. Zhu, Q. Zhang, \(P\)th moment exponential stabilisation of hybrid stochastic differential equations by feedback controls based on discrete-time state observations with a time delay. IET Control Theory Appl. 11(12), 1992–2003 (2017)

    Article  MathSciNet  Google Scholar 

  42. H. Zhang, G. Feng, H. Yan, Q. Chen, Sampled-data control of nonlinear networked systems with time-delay and quantization. Int. J. Robust Nonlinear Control 26(5), 919–933 (2016)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the following grants: National Natural Science Foundation of P.R. China (No. 61973170, 61973168), the Fundamental Research Funds for the Central Universities (No. 2020ACOCP02).

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Authors and Affiliations

  1. School of Automation, CICAEET, Nanjing University of Information Science and Technology, Nanjing, 210044, Jiangsu, China

    Gongfei Song, Haiyang Wang & Tao Li

  2. Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology, Shanghai, 200237, China

    Gongfei Song

  3. School of Information and Control Engineering, Qingdao University of Technology, Qingdao, 266520, Shandong, China

    Yanqian Wang

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  1. Gongfei Song
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Correspondence to Gongfei Song.

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Song, G., Wang, H., Li, T. et al. Quantized Stabilization for Highly Nonlinear Stochastic Delay Systems by Discrete-Time Control. Circuits Syst Signal Process 41, 2595–2613 (2022). https://doi.org/10.1007/s00034-021-01905-4

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