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Practical prescribed time control based on high-order fully actuated system approach for strong interconnected nonlinear systems

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Abstract

This paper investigates the problem of practical prescribed time control design for strong interconnected nonlinear systems by utilizing the high-order fully actuated (HOFA) system approach. Firstly, to specify the convergence time and accuracy of the system outputs in advance regardless of initial conditions, the thought of practical prescribed time control is introduced. Then, through some recursive coordinate transformation, the considered strong interconnected nonlinear systems are transformed into the HOFA system model, and then, the controller is designed to eliminate the effect caused by nonlinearities in the system. Furthermore, with the aid of an algebraic graph theory result, all signals in the system can be ensured to be globally bounded by appropriately designing the linear part of the obtained closed-loop system. Finally, the simulation results show the effectiveness of the proposed method.

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References

  1. Wen, C.Y.: Decentralized adaptive regulation. IEEE Trans. Autom. Control 39(10), 2163–2166 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  2. Jiang, Z.P.: Decentralized and adaptive nonlinear tracking of large-scale systems via output feedback. IEEE Trans. Autom. Control 45(14), 2122–2128 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Wang, C.L., Lin, Y.: Decentralized adaptive tracking control for a class of interconnected nonlinear time-varying systems. Automatica 54, 16–24 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhang, L.L., Liu, S.S., Hua, C.C.: Truncated predictor stabilization control for interconnected nonlinear systems with time-varying input delay. Nonlinear Dyn. 107(3), 2421–2428 (2022)

    Article  Google Scholar 

  5. Jin, Z.H., Qin, Z.Y., Zhang, X.F., Guan, C.: A leader-following consensus problem via a distributed observer and fuzzy input-to-output small-gain theorem. IEEE Trans. Control. Netw. Syst. 9(1), 62–74 (2022)

    Article  MathSciNet  Google Scholar 

  6. Ma, M., Wang, T., Qiu, J.B., Karimi, H.R.: Adaptive fuzzy decentralized tracking control for large-scale interconnected nonlinear networked control systems. IEEE Trans. Fuzzy Syst. 29(10), 3186–3191 (2021)

    Article  Google Scholar 

  7. Su, H.G., Zhang, H.G., Liang, X.D., Liu, C.: Decentralized event-triggered online adaptive control of unknown large-scale systems over wireless communication networks. IEEE Trans. Neural Netw. Learn. Syst. 31(11), 4907–4919 (2020)

    Article  MathSciNet  Google Scholar 

  8. Zhang, X., Lin, Y.: Nonlinear decentralized control of large-scale systems with strong interconnections. Automatica 50(9), 2419–2423 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  9. Niu, B., Liu, J.D., Wang, D., Zhao, X.D., Wang, H.Q.: Adaptive decentralized asymptotic tracking control for large-scale nonlinear systems with unknown strong interconnections. IEEE/CAA J. Autom. Sin. 9(1), 173–186 (2022)

    Article  MathSciNet  Google Scholar 

  10. Sun, H.B., Hou, L.L., Zong, G.D., Yu, X.H.: Adaptive decentralized neural network tracking control for uncertain interconnected nonlinear systems with input quantization and time delay. IEEE Trans. Neural Netw. Learn. Syst. 31(4), 1401–1409 (2020)

    Article  MathSciNet  Google Scholar 

  11. Li, X.J., Yang, G.H.: Adaptive decentralized control for a class of interconnected nonlinear systems via backstepping approach and graph theory. Automatica 76, 87–95 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  12. Song, X.N., Man, J.T., Ahn, C.K.: Joint state and fault estimation for networked interconnected PDE systems with semi-markov fault coefficient via conjunct measurement. IEEE Trans. Circuits Syst. I Regul. Pap. 68(9), 3869–3880 (2021)

    Article  Google Scholar 

  13. Ma, H.J., Xu, L.: Decentralized adaptive fault-tolerant control for a class of strong interconnected nonlinear systems via graph theory. IEEE Trans. Autom. Control 66(7), 3227–3234 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  14. Duan, G.R.: High-order system approaches: I. Full-actuation and parametric design. Acta Autom. Sin. 41(7), 1333–1345 (2020)

    MATH  Google Scholar 

  15. Zheng, Z.W., Huang, Y.T., Xie, L.H., Zhu, B.: Adaptive trajectory tracking control of a fully actuated surface vessel with asymmetrically constrained input and output. IEEE Trans. Control Syst. Technol. 26(5), 1851–1859 (2018)

    Article  Google Scholar 

  16. Duan, G.R.: High-order fully actuated system approaches: Part I. Models and basic procedure. Int. J. Syst. Sci. 52(2), 422–435 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  17. Duan, G.R.: High-order fully actuated system approaches: Part II. Generalized strict-feedback systems. Int. J. Syst. Sci. 52(3), 437–454 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  18. Duan, G.R.: High-order fully actuated system approaches Part III. Robust control and high order backstepping. Int. J. Syst. Sci. 52(5), 952–971 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  19. Duan, G.R.: High-order fully actuated system approaches: Part V. Robust adaptive control. Int. J. Syst. Sci. 52(10), 2129–2143 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  20. Wang, A.Q., Liu, L., Qiu, J.B., Feng, G.: Event-triggered adaptive fuzzy output-feedback control for nonstrict-feedback nonlinear systems with asymmetric output constraint. IEEE Trans. Cybern. 52(1), 712–722 (2022)

    Article  Google Scholar 

  21. Li, Y.M., Tong, S.C.: Adaptive fuzzy control with prescribed performance for block-triangular-structured nonlinear systems. IEEE Trans. Fuzzy Syst. 26(3), 1153–1163 (2018)

    Article  Google Scholar 

  22. Wu, J., Sun, W., Su, S.F., Xia, J.W.: Neural-based adaptive control for nonlinear systems with quantized input and the output constraint. Appl. Math. Comput. 413, 126637 (2022)

    MathSciNet  MATH  Google Scholar 

  23. Chen, M., Wang, H.Q., Liu, X.P.: Adaptive practical fixed-time tracking control with prescribed boundary constraints. IEEE Trans. Circuits Syst. I Regul. Pap. 680(4), 1716–1726 (2021)

    Article  MathSciNet  Google Scholar 

  24. Liu, Y.L., Ma, H.J., Ma, H.: Adaptive fuzzy fault-tolerant control for uncertain nonlinear switched stochastic systems with time-varying output constraints. IEEE Trans. Fuzzy Syst. 26(5), 2487–2498 (2018)

    Article  Google Scholar 

  25. Chen, M., Liu, X.P., Wang, H.Q.: Adaptive robust fault-tolerant control for nonlinear systems with prescribed performance. Nonlinear Dyn. 81(4), 1727–1739 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  26. Zhang, L.L., Zhu, L.C., Hua, C.C., Qian, C.: Decentralised state-feedback prescribed performance control for a class of interconnected nonlinear full-state time-delay systems with strong interconnection. Int. J. Syst. Sci. 52(12), 2580–2596 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  27. Liang, H.J., Zhang, Y.H., Huang, T.W., Ma, H.: Prescribed performance cooperative control for multiagent systems with input quantization. IEEE Trans. Cybern. 50(5), 1810–1819 (2020)

    Article  Google Scholar 

  28. Xu, Z.B., Xie, N.G., Shen, H., Hu, X.L., Liu, Q.Y.: Extended state observer-based adaptive prescribed performance control for a class of nonlinear systems with full-state constraints and uncertainties. Nonlinear Dyn. 105(1), 345–358 (2021)

    Article  Google Scholar 

  29. Sun, W., Su, S.F., Wu, Y.Q., Xia, J.W.: Adaptive fuzzy event-triggered control for high-order nonlinear systems with prescribed performance. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.3025829

    Article  Google Scholar 

  30. Liu, Y., Liu, X.P., Jing, Y.W.: Adaptive fuzzy finite-time stability of uncertain nonlinear systems based on prescribed performance. Fuzzy Sets Syst. 374, 23–39 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  31. Zhou, T.Y., Liu, C.G., Liu, X.P., Wang, H.Q., Zhou, Y.C.: Finite-time prescribed performance adaptive fuzzy control for unknown nonlinear systems. Fuzzy Sets Syst. 402, 16–34 (2021)

  32. Yuan, X., Chen, B., Lin, C.: Prescribed finite-time adaptive neural tracking control for nonlinear state-constrained systems: barrier function approach. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2021.3085324

  33. Cao, Y., Cao, J.F., Song, Y.D.: Practical prescribed time tracking control over infinite time interval involving mismatched uncertainties and non-vanishing disturbances. Automatica 136, 110050 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  34. Li, M.Y., Shuai, Z.: Global-stability problem for coupled systems of differential equations on networks. J. Differ. Equ. 248(1), 1–20 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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Funding

This work was supported in part by the National Key Research and Development Program of China under Grant 2018YFB1308302; in part by the National Natural Science Foundation of China under Grant 61803326, Grant 62103353, Grant 61825304, and Grant 6182500417; in part by the Innovative Research Groups of the Natural Science Foundation of Hebei Province under Grant E2020203174; and in part by the Top Young Talents of Education Department of Hebei Province under Grant BJ2021041.

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Authors and Affiliations

  1. Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, China

    Liuliu Zhang, Lingchen Zhu & Changchun Hua

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  1. Liuliu Zhang
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  2. Lingchen Zhu
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  3. Changchun Hua
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Correspondence to Liuliu Zhang.

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Zhang, L., Zhu, L. & Hua, C. Practical prescribed time control based on high-order fully actuated system approach for strong interconnected nonlinear systems. Nonlinear Dyn 110, 3535–3545 (2022). https://doi.org/10.1007/s11071-022-07820-w

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