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Asynchronous Dynamic Output Feedback Control for Delayed Fuzzy Stochastic Markov Jump Systems Based on HMM Strategy

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Abstract

This paper addresses the asynchronous robust \(H_{\infty }\) dynamic output feedback control for Takagi–Sugeno fuzzy uncertain stochastic Markov jump systems with time-varying delays. The modes of devised fuzzy controller run asynchronously with the modes of controlled plant, which is described through a hidden Markov model. Dynamic output feedback control is that the output feedback only takes the output signal that the object can detect as the feedback signal. Because the measurement output is local information, the feedback is also local. Although it is feasible, it cannot reflect the overall situation. The fuzzy dynamic output feedback adopts parallel distribution compensation technique, which can realize global feedback, but realizing this feedback control is full of difficulties and challenges. And although introducing more variables can make the condition less conservative, it also increases the number of linear matrix inequalities and computational complexity. Improved conditions are acquired to ensure the robust exponential mean-square stability and \(H_{\infty }\) performance index for the closed-loop fuzzy uncertain stochastic Markov jump systems. Based on exponential mean-square stability, the asynchronous fuzzy dynamic output feedback controller is realized in terms of linear matrix inequalities. A numerical example and a single-link robot arm are employed to show the effectiveness and correctness of the method proposed in this paper.

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References

  1. Xu, S., Lam, J., Mao, X.: Delay-dependent \(H_{\infty }\) control and filtering for uncertain Markovian jump systems with time-varying delays. IEEE Trans. Circuits Syst. 54(9), 2070–2077 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Kwon, N.K., Park, I.S., Park, P.G.: State-feedback control for continuous-time Markovian jump fuzzy systems using a fuzzy weighting-dependent Lyapunov function. Nonlinear Dyn. 90(3), 2001–2011 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhu, Y., Zhang, L., Zheng, W.X.: Distributed \(H_{\infty }\) filtering for a class of discrete-time Markov jump Lur’e systems with redundant channels. IEEE Trans. Ind. Electron. 63(3), 1876–1885 (2016)

    Article  Google Scholar 

  4. Cheng, J., Park, J.H., Zhao, X., Karimi, H.R., Cao, J.: Quantized nonstationary filtering of network-based Markov switching RSNSs: a multiple hierarchical structure strategy. IEEE Trans. Autom. Control. 65(11), 4816–4823 (2020)

    Article  MATH  Google Scholar 

  5. Zhuang, G., Ma, Q., Zhang, B., Xu, S., Xia, J.: Admissibility and stabilization of stochastic singular Markovian jump systems with time delays. Syst. Control Lett. 114, 1–10 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  6. Shen, Y., Wu, Z., Shi, P., Su, H., Huang, T.: Asynchronous filtering for Markov jump neural networks with quantized outputs. IEEE Trans. Syst. Man Cybern. Syst. 49(2), 433–443 (2019)

  7. Zhao, D., Karimi, H.R., Sakthivel, R., Li, Y.: Non-fragile fault-tolerant control for nonlinear Markovian jump systems with intermittent actuator fault. Nonlinear Anal. Hybrid Syst. 32, 337–350 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  8. Xu, Z.H., Ni, H.J., Karimi, H.R., Zhang, D.: A Markovian jump system approach to consensus of heterogeneous multi-agent systems with partially unknown and uncertain attack strategies. Int. J. Robust Nonlinear Control. 30, 3039–3053 (2020)

    Article  MATH  Google Scholar 

  9. Sheng, L., Gao, M.: Stabilization for Markovian jump nonlinear systems with partly unknown transition probabilities via fuzzy control. Fuzzy Sets Syst. 161(21), 2780–2792 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Shi, H., Shi, L., Xu, M., Hwang, K.S.: End-to-end navigation strategy with deep reinforcement learning for mobile robots. IEEE Trans. Ind. Inf. 16(4), 2393–2402 (2020)

    Article  Google Scholar 

  11. Shi, H., Sun, G., Wang, Y., Hwang, K.S.: Adaptive image-based visual servoing with temporary loss of the visual signal. IEEE Trans. Ind. Inf. 15(4), 1956–1965 (2019)

    Article  Google Scholar 

  12. Shi, H., Hwang, K.S., Li, X., Chen, J.: A learning approach to image-based visual servoing with a bagging method of velocity calculations. Inf. Sci. 481, 244–257 (2019)

    Article  Google Scholar 

  13. Lin, H., Su, H., Shi, P., Shu, Z., Lu, R., Wu, Z.: Optimal estimation and control for lossy network: stability, convergence, and performance. IEEE Trans. Autom. Control. 62(9), 4564–4579 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  14. Li, F., Xu, S., Shen, H.: Fuzzy-model-based \(H_{\infty }\) control for Markov jump nonlinear slow sampling singularly perturbed systems with partial information. IEEE Trans. Fuzzy Syst. 27(10), 1952–1962 (2019)

    Article  Google Scholar 

  15. Zhuang, G., Xu, S., Zhang, B., Xu, H., Chu, Y.: Robust \(H_{\infty }\) deconvolution filtering for uncertain singular Markovian jump systems with time-varying delays. Int. J. Robust Nonlinear Control. 26(12), 2564–2585 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  16. Park, C., Kwon, N.K., Park, I.S., Park, P.: \(H_{\infty }\) filtering for singular Markovian jump systems with partly unknown transition rates. Automatica. 109(109), 108528 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  17. Chavezfuentes, J.R., Costa, E.F., Mayta, J.E., Terra, M.H.: Regularity and stability analysis of discrete-time Markov jump linear singular systems. Automatica 76(76), 32–40 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhuang, G., Xia, J., Feng, J., Zhang, B., Lu, J., Wang, Z.: Admissibility analysis and stabilization for neutral descriptor hybrid systems with time-varying delays. Nonlinear Anal. Hybrid Syst. 33, 311–321 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  19. Sun, W., Su, S., Wu, Y., Xia, J.: Novel adaptive fuzzy control for output constrained stochastic nonstrict feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 29(5), 1188–1197 (2021)

    Article  Google Scholar 

  20. Shen, H., Li, F., Wu, Z.G., Park, J.H., Sreeram, V.: Fuzzy-model-based non-fragile control for nonlinear singularly perturbed systems with semi-Markov jump parameters. IEEE Trans. Fuzzy Syst. 26(6), 3428–3439 (2018)

    Article  Google Scholar 

  21. Kwon, N.K., Park, I.S., Park, P., Park, C.: Dynamic output-feedback control for singular Markovian jump system: LMI approach. IEEE Trans. Autom. Control. 62(10), 5396–5400 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  22. Park, I.S., Kwon, N.K., Park, P.: Dynamic output-feedback control for singular Markovian jump systems with partly unknown transition rates. Nonlinear Dyn. 95(4), 3149–3160 (2019)

    Article  MATH  Google Scholar 

  23. Yang, F., He, J., Pan, Q.: Further improvement on delay-dependent load frequency control of power systems via truncated B-L inequality. IEEE Trans. Power Syst. 33(5), 5062–5071 (2018)

    Article  Google Scholar 

  24. Yang, F., He, J., Wang, D.: New stability criteria of delayed load frequency control systems via infinite-series-based inequality. IEEE Trans. Ind. Inf. 14(1), 231–240 (2018)

    Article  Google Scholar 

  25. Yang, F., He, J., Kang, P., Pan, Q.: Delay range-and-rate dependent stability criteria for systems with interval time-varying delay via a quasi-quadratic convex framework. Int. J. Robust Nonlinear Control. 29(8), 2494–2509 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  26. Wei, Q., Liao, Z., Yang, Z., Li, B., Liu, D.: Continuous-time time-varying policy iteration. IEEE Trans. Cybern. 50(12), 4958–4971 (2020)

    Article  Google Scholar 

  27. Wang, S., Ji, W., Jiang, Y., Liu, D.: Relaxed stability criteria for neural networks with time-varying delay using extended secondary delay partitioning and equivalent reciprocal convex combination techniques. IEEE Trans. Neural Netw. 31(10), 4157–4169 (2020)

    Article  MathSciNet  Google Scholar 

  28. Zhang, J.F., Raissi, T., Li, S.: Non-fragile saturation control of nonlinear positive Markov jump systems with time-varying delays. Nonlinear Dyn. 97(2), 1495–1513 (2019)

    Article  MATH  Google Scholar 

  29. Zhang, D., Cheng, J., Ahn, C.K., Ni, H.: A flexible terminal approach to stochastic stability and stabilization of continuous–time semi–Markovian jump systems with time–varying delay. Appl. Math. Comput. 342(1), 191–205 (2019)

  30. Shen, H., Li, F., Xu, S., Sreeram, V.: Slow state variables feedback stabilization for semi-Markov jump systems with singular perturbations. IEEE Trans. Autom. Control. 63(8), 2709–2714 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  31. Zhuang, G., Xia, J., Feng, J., Sun, W., Zhang, B.: Admissibilization for implicit jump systems with mixed retarded delays based on reciprocally convex integral inequality and barbalat’s lemma. IEEE Trans. Syst. Man, Cybern. Syst. (2020) https://doi.org/10.1109/tsmc.2020.2964057

  32. Zhuang, G., Su, S., Xia, J., Sun, W.: HMM-based asynchronous \(H_{\infty }\) filtering for fuzzy singular Markovian switching systems with retarded time-varying delays. IEEE Trans. Cybern. 51(3), 1189–1203 (2021)

    Article  Google Scholar 

  33. Jiang, B., Karimi, H.R., Yang, S., Gao, C., Kao, Y.: Observer-based adaptive sliding mode control for nonlinear stochastic Markov jump systems via T–S fuzzy Modeling: applications to robot arm model. IEEE Trans. Ind. Electron. 68(1), 466–477 (2021)

    Article  Google Scholar 

  34. Xia, J., Li, B., Su, S.F., Sun, W., Shen, H.: Finite-time command filtered event-triggered adaptive fuzzy tracking control for stochastic nonlinear systems. IEEE Trans. Fuzzy Syst. 29(7), 1815–1825 (2021)

    Article  Google Scholar 

  35. Li, X., Cao, J., Ho, D.W.: Impulsive control of nonlinear systems with time–varying delay and applications. IEEE Trans. Syst. Man, Cybern. Syst. 50(6), 2661–2673 (2020)

  36. Wu, Z.G., Shi, P., Shu, Z., Su, H., Lu, R.: Passivity-based asynchronous control for Markov jump systems. IEEE Trans. Autom. Control. 62(4), 2020–2025 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  37. Ren, H., Zong, G., Karimi, H.R.: Asynchronous finite-time filtering of Markov jump nonlinear systems and its applications. IEEE Trans. Syst. Man Cybern. 51(3), 1725–1734 (2021)

    Google Scholar 

  38. Zhuang, G., Xia, J., Sun, W., Feng, J., Ma, Q.: Asynchronous admissibility and \(H_{\infty }\) fault detection for delayed implicit Markovian switching systems under hidden Markovian model mechanism. Int. J. Robust Nonlinear Control 31(15), 7261–7279 (2021)

    Article  MathSciNet  Google Scholar 

  39. Shi, D., Elliott, R.J., Chen, T.: Event-based state estimation of discrete-state hidden Markov models. Automatica 65(65), 12–26 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  40. Chen, W., Wang, J., Shi, D., Shi, L.: Event-based state estimation of hidden Markov models through a Gilbert–Elliott channel. IEEE Trans. Autom. Control 62(7), 3626–3633 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  41. Xu, J., Ho, D.W., Li, F., Yang, W., Tang, Y.: Event-triggered risk-sensitive state estimation for hidden Markov models. IEEE Trans. Autom. Control 64(10), 4276–4283 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  42. Yang, Y., Zhao, J., Xia, J., Zhuang, G., Zhang, W.: Multiobjective optimization control for uncertain nonlinear stochastic system with state-delay. Int. J. Fuzzy Syst. 21(1), 72–83 (2019)

    Article  MathSciNet  Google Scholar 

  43. Wu, Z., Dong, S., Su, H., Li, C.: Asynchronous dissipative control for fuzzy Markov jump systems. IEEE Trans. Syst. Man Cybern. Syst. 48(8), 2426–2436 (2018)

  44. Li, Y., Deng, F., Xie, F.: Robust delay-dependent \(H_{\infty }\) filtering for uncertain Takagi-Sugeno fuzzy neutral stochastic time-delay systems. J. Franklin Inst. 356(18), 11561–11580 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  45. Ma, H., Li, H., Liang, H., Dong, G.: Adaptive fuzzy event-triggered control for stochastic nonlinear systems with full state constraints and actuator faults. IEEE Trans. Fuzzy Syst. 27(11), 2242–2254 (2019)

    Article  Google Scholar 

  46. Li, H., Zhang, Z., Yan, H., Xie, X.: Adaptive event–triggered fuzzy control for uncertain active suspension systems. IEEE Trans. Syst. Man Cybern. Syst. 49(12), 4388–4397 (2019)

  47. Dong, S., Su, H., Shi, P., Lu, R., Wu, Z.: Filtering for discrete-time switched fuzzy systems with quantization. IEEE Trans. Fuzzy Syst. 25(6), 1616–1628 (2017)

    Article  Google Scholar 

  48. Zhang, L., Yin, X., Ning, Z., Ye, D.: Robust filtering for a class of networked nonlinear systems with switching communication channels. IEEE Trans. Cybern. 47(3), 671–682 (2017)

    Article  Google Scholar 

  49. Sun, W., Wu, Y.Q., Sun, Z.Y.: Command filter-based finite-time adaptive fuzzy control for uncertain nonlinear systems with prescribed performance. IEEE Trans. Fuzzy Syst. 28(12), 3161–3170 (2020)

    Article  Google Scholar 

  50. Ding, D., Li, X., Du, X., Xie, X.: Finite-frequency model reduction of Takagi-Sugeno fuzzy systems. IEEE Trans. Fuzzy Syst. 24(6), 1464–1474 (2016)

    Article  Google Scholar 

  51. Li, C., Zhou, J., Chang, L., Huang, Z., Zhang, Y.: T–S fuzzy model identification based on a novel hyperplane-shaped membership function. IEEE Trans. Fuzzy Syst. 25(5), 1364–1370 (2017)

    Article  Google Scholar 

  52. Yuan, W., Sun, W., Liu, Z., Zhang, F.: Adaptive fuzzy tracking control of stochastic mechanical system with input saturation. Int. J. Fuzzy Syst. 21(8), 2600–2608 (2019)

    Article  MathSciNet  Google Scholar 

  53. Zhuang, G., Sun, W., Su, S.F., Xia, J.: Asynchronous feedback control for delayed fuzzy degenerate jump systems under observer-based event-driven characteristic. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.3027336

  54. Lu, R., Cheng, H., Bai, J.: Fuzzy-model-based quantized guaranteed cost control of nonlinear networked systems. IEEE Trans. Fuzzy Syst. 23(3), 567–575 (2015)

    Article  Google Scholar 

  55. Liu, Z., Wang, F., Zhang, Y., Chen, C.L.: Fuzzy adaptive quantized control for a class of stochastic nonlinear uncertain systems. IEEE Trans. Cybern. 46(2), 524–534 (2016)

    Article  Google Scholar 

  56. Liu, Y., Fang, F., Park, J.H.: Decentralized dissipative filtering for delayed nonlinear interconnected systems based on T–S fuzzy model. IEEE Trans. Fuzzy Syst. 27(4), 790–801 (2019)

    Article  Google Scholar 

  57. Dong, S., Wu, Z., Su, H., Shi, P., Karimi, H.R.: Asynchronous control of continuous-time nonlinear Markov jump systems subject to strict dissipativity. IEEE Trans. Autom. Control. 64(3), 1250–1256 (2019)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors would like to thank the Editors and the Referees for carefully reading the paper and for the comments which have helped us to greatly improve the paper. This work was supported by the National Natural Science Foundation of China under Grant Nos. 62173174, 61773191, 61973148, 62003154; Support Plan for Outstanding Youth Innovation Team in Shandong Higher Education Institutions under Grant 2019KJI010; the Natural Science Foundation of Shandong Province for Key Projects under Grant ZR2020KA010; Graduate education high-quality curriculum construction project for Shandong Province under Grant SDYKC20185.

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Authors and Affiliations

  1. School of Mathematical Sciences, Liaocheng University, Liaocheng, 252000, People’s Republic of China

    Yuqian Lin, Guangming Zhuang, Jianwei Xia, Guoliang Chen & Huasheng Zhang

  2. School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, 210094, People’s Republic of China

    Junwei Lu

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  1. Yuqian Lin
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  2. Guangming Zhuang
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  3. Jianwei Xia
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Correspondence to Guangming Zhuang.

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Lin, Y., Zhuang, G., Xia, J. et al. Asynchronous Dynamic Output Feedback Control for Delayed Fuzzy Stochastic Markov Jump Systems Based on HMM Strategy. Int. J. Fuzzy Syst. 24, 2302–2317 (2022). https://doi.org/10.1007/s40815-022-01273-4

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