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Fixed-Time Fuzzy Adaptive Tracking Control of Full-State Constrained Nonlinear Systems with Unknown Virtual Control Coefficients

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Abstract

This paper studies the fixed-time fuzzy adaptive tracking control problem for a class of uncertain strict-feedback nonlinear systems with unknown virtual control coefficients (UVCCs), full state constraints and external disturbances. A novel barrier Lyapunov function is constructed to overcome the UVCCs and the state constraints simultaneously. Fuzzy-logic systems are implemented to approximate uncertain nonlinear functions of the system. Using fuzzy-logic systems and the first-order filter, the dynamic surface control is combined with backstepping design to tackle the problem of computational complexity. Based on the Lyapunov stability theory, a fixed-time fuzzy controller is designed such that not only the closed-loop system is practically fixed-time stable but also the tracking error converge to a small neighborhood of the origin. It is shown that the settling time of the proposed control method is independent of the initial conditions of the controlled system. At last, a simulation example of a single-link robot manipulator is given to demonstrate the effectiveness of the presented scheme.

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References

  1. Navabi, M., Hashkavaei, N.S., Reyhanoglu, M.: Satellite attitude control using optimal adaptive and fuzzy controllers. Acat Astronaut 204, 434–442 (2023)

    Article  ADS  Google Scholar 

  2. Canabal, A.A., Loukianov, A.G., Castaneda, J.M.C., Utkin, V.A.: Adaptive power system stabilizer with sliding mode for electric power systems. Int. J. Elec. Power 145, (2023)

  3. Sun, W., Su, S.F., Xia, J., Nguyen, V.T.: Adaptive fuzzy tracking control of flexible-joint robots with full-state constraints. IEEE Trans. Syst. Man Cybern. Syst. 49(11), 2201–2209 (2018)

    Article  Google Scholar 

  4. Xiao, P., Gu, Z.Y.: Adaptive event-triggered consensus of fractional-order nonlinear multi-agent systems. IEEE Access. 10, 213–220 (2022)

    Article  Google Scholar 

  5. Sun, W.J., Gao, M.M., Zhao, J.S.: Adaptive fuzzy finite-time control for a class of stochastic nonlinear systems with input saturation. Int. J. Fuzzy Syst. 24(1), 265–275 (2022)

    Article  Google Scholar 

  6. Zou, A., Hou, Z., Tan, M.: Adaptive control of a class of nonlinear pure-feedback systems using fuzzy backstepping approach. IEEE Trans. Fuzzy Syst. 16(4), 886–897 (2008)

    Article  Google Scholar 

  7. Xiong, Y.H., Zhai, D.H., Tavakoli, M., Xia, Y.Q.: Discrete-time control barrier function: high-order case and adaptive case. IEEE Trans. Cybern. 53(5), 3231–3239 (2023)

    Article  PubMed  Google Scholar 

  8. Hu, Y.F., Liu, W.H.: Adaptive fuzzy dynamic surface control for nonstrict-feedback nonlinear state constrained systems with input dead-zone via event-triggered sampling. Appl. Math. Comput. 450 (2023)

  9. Cui, Y., Liu, X.P.: Adaptive consensus tracking control of strict-feedback nonlinear multi-agent systems with unknown dynamic leader. Neural Comput. Appi. 34(6), 6215–6226 (2022)

    Article  Google Scholar 

  10. Yip, P., Hedrick, J.: Adaptive dynamic surface control: a simplified algorithm for adaptive backstepping control of nonlinear systems. Int. J. Control 71(5), 959–979 (1998)

    Article  MathSciNet  Google Scholar 

  11. Dong, H., Gao, S., Tang, T., Li, Y., Valavanis, K.: Error-driven nonlinear feed-back design for fuzzy adaptive dynamic surface control of nonlinear systems with prescribed tracking performance. IEEE Trans. Syst. Man Cybern. Syst. 50(3), 1013–10237 (2020)

    Article  Google Scholar 

  12. Tee, K.P., Ge, S.S., Tay, E.H.: Barrier lyapunov functions for the control of output-constrained nonlinear systems. Automatica 45(4), 918–927 (2008)

    Article  MathSciNet  Google Scholar 

  13. Zhao, K., Song, Y., Meng, W., Philip, C.L., Chen, L.: Low-cost approximation-based adaptive tracking control of output-constrained nonlinear systems. IEEE Trans. Neural Netw. Learn. Syst. 32(11), 4890–4900 (2021)

    Article  MathSciNet  PubMed  Google Scholar 

  14. Sun, W., Su, S.F., Wu, Y., Xia, J., Nguyen, V.T.: Adaptive fuzzy control with high-order barrier Lyapunov functions for high-order uncertain nonlinear systems with full-state constraints. IEEE Trans. Cybern. 50(8), 3424–3432 (2020)

    Article  PubMed  Google Scholar 

  15. Sun, W., Su, S., Dong, G., Bai, W.: Reduced adaptive fuzzy tracking control for high-order stochastic nonstrict feedback nonlinear system with full-state constraints. IEEE Trans. Syst. Man Cybern. Syst. 51(3), 1496–1506 (2021)

    Google Scholar 

  16. Liu, Y., Lu, S., Li, D., Tong, S.: Adaptive controller design-based ABLF for a class of nonlinear time-varying state constraint systems. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1546–1553 (2017)

    Article  Google Scholar 

  17. Polyakov, A.: Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans. Autom. Control 57(8), 2106–2110 (2012)

    Article  MathSciNet  Google Scholar 

  18. Lai, G.Y., Huang, K., Li, L., Liu, Z., Zhang, Y., Chen, C.L.P.: Fixed-time adaptive fuzzy control scheme with prescribed tracking accuracy for uncertain nonlinear hysteretic systems. J. Franklin I. 360(9), 5969–5995 (2023)

    Article  MathSciNet  Google Scholar 

  19. Shao, K.Y., Feng, A., Wang, T.T.: Fixed-time sliding mode synchronization of uncertain fractional-order hyperchaotic systems by using a novel non-singleton-interval type-2 probabilistic fuzzy neural network. Fractal Frct. 7(3) (2023)

  20. Chen, C.Y., Han, Y.Y., Zhu, S., Zeng, Z.G.: Neural network-based fixed-time tracking and containment control of second-order heterogeneous nonlinear multiagent systems. IEEE Trans. Neural Netw. Learn. Syst. (2023)

  21. Chen, L., Wang, Q.: Prescribed performance-barrier Lyapunov function for the adaptive control of unknown pure-feedback systems with full-state constraints. Nonlinear Dyn. 95(3), 2443–2459 (2019)

    Article  Google Scholar 

  22. Jing, Y., Yang, G.: Fuzzy adaptive quantized fault-tolerant control of strict-feedback nonlinear systems with mismatched external disturbances. IEEE Trans. Syst. Man Cybern. Syst. 50(9), 3424–3434 (2020)

    Article  Google Scholar 

  23. Wang, H., Shi, P., Li, H., Zhou, Q.: Adaptive neural tracking control for a class of nonlinear systems with dynamic uncertainties. IEEE Trans. Cybern. 47(10), 3075–3087 (2017)

    Article  PubMed  Google Scholar 

  24. Jia, T., Pan, Y., Liang, H., Lam, H.: Event-based adaptive fixed-time fuzzy control for active vehicle suspension systems with time-varying displacement constraint. IEEE Trans. Fuzzy Syst. 30(8), 2813–2821 (2022)

    Article  Google Scholar 

  25. Wang, F., Gao, H., Wang, K., Zhu, C., Zong, Q., Hua, C.: Disturbance observer-based finite-time control design for a quadrotor uav with external disturbance. IEEE T. Aero. Elec. Sys. 57(2), 834–847 (2021)

    Article  Google Scholar 

  26. Zhou, Q., Zhao, S., Li, H., Lu, R.: Adaptive neural network tracking control for robotic manipulators with dead zone. IEEE Trans. Neural Netw. Learn. Syst. 30(12), 611–3620 (2019)

    Article  MathSciNet  CAS  Google Scholar 

  27. Zuo, Z., Tie, L.: Distributed robust finite-time nonlinear consensus protocols for multi-agent systems. Int. J. Syst. Sci. 47(6), 1366–1375 (2016)

    Article  MathSciNet  Google Scholar 

  28. Sun, Y., Chen, B., Lin, C., Wang, H.: Finite-time adaptive control for a class of nonlinear systems with nonstrict feedback structure. IEEE Trans. Cybern. 48(10), 2774–2782 (2018)

    Article  Google Scholar 

  29. Wang, C., Lin, Y.: Decentralized adaptive tracking control for a class of interconnected nonlinear time-varying systems. Automatica 54(4), 16–24 (2015)

    Article  MathSciNet  Google Scholar 

  30. Li, Z.M., Chang, X.H., Xiong, J.: Event-based fuzzy tracking control for nonlinear networked systems subject to dynamic quantization. IEEE Trans. Fuzzy Syst. 31(3), 941–954 (2023)

    Article  Google Scholar 

  31. Hu, X., Li, Y., Hou, Z.: Event-triggered fuzzy adaptive fixed-time tracking control for nonlinear systems. IEEE Trans. Cybern. 52(7), 7206–7217 (2022)

    Article  PubMed  Google Scholar 

  32. Song, X.N., Sun, P., Ahn, C.K., Song, S.: Observer-based neural adaptive fixed-time tracking control for multi-input multi-output nonlinear systems with actuator faults. Int. J. Robust Nonlin. (2023)

  33. Ren, B., Ge, S., Tee, K., Lee, T.: Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function. IEEE Trans. Neural Netw. 21(8), 1339–1345 (2010)

    Article  PubMed  Google Scholar 

  34. Yang, W., Pan, Y., Liang, H.: Event-triggered adaptive fixed-time NN control for constrained nonstrict-feedback nonlinear systems with prescribed performance. Neurocomputing 422(6), 332–344 (2021)

    Article  Google Scholar 

  35. Shi, W.R., Hou, M.Z., Hao, M.R.: Adaptive robust dynamic surface asymptotic tracking for uncertain strict-feedback nonlinear systems with unknown control direction. ISA Trans. 121, 95–104 (2022)

    Article  PubMed  Google Scholar 

  36. Liu, D.C., Liu, Z., Chen, C.L.P., Zhang, Y.: Distributed adaptive fuzzy control approach for prescribed-time containment of uncertain nonlinear multi-agent systems with unknown hysteresis. Nonlinear Dynam. 105, 257–275 (2021)

    Article  Google Scholar 

  37. Zhao, L., Liu, G.Q., Yu, J.P.: Finite-time adaptive fuzzy tracking control for a class of nonlinear systems with full-State constraints. IEEE Trans. Fuzzy Syst. 29, 2246–2255 (2021)

    Article  Google Scholar 

  38. Xing, L., Wen, C., Liu, Z., Su, H., Cai, J.: Event-triggered adaptive control for a class of uncertain nonlinear systems. IEEE Trans. Autom. Control 62(4), 2071–2076 (2017)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant on. 12171124); and the Science Research Foundation for Introduced Talents, Fujian Provience of China (Grant on. GY-Z21215, GY-Z21216).

Funding

National Natural Science Foundation of China,12171124,Yujing Shi,Science Research Foundation for Introduced Talents,Fujian Provience of China,GY -Z21215,Yujing Shi,GY—Z21216,Yujing Shi.

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Authors and Affiliations

  1. Department of Heilongjiang Provincial Key Laboratory of Optimization Control and Intelligent Analysis for Complex Systems, Harbin University of Science and Technology, Harbin, 150080, China

    Chen Wang

  2. Department of Computer Science and Mathematics, Fujian University of Technology, Fuzhou, 350118, China

    Yujing Shi

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  1. Chen Wang
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Correspondence to Chen Wang.

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Wang, C., Shi, Y. Fixed-Time Fuzzy Adaptive Tracking Control of Full-State Constrained Nonlinear Systems with Unknown Virtual Control Coefficients. Int. J. Fuzzy Syst. 26, 196–211 (2024). https://doi.org/10.1007/s40815-023-01588-w

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  • DOI: https://doi.org/10.1007/s40815-023-01588-w

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