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Finite-time adaptive neural resilient DSC for fractional-order nonlinear large-scale systems against sensor-actuator faults

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Abstract

The aim of this paper is to study an adaptive neural finite-time resilient dynamic surface control (DSC) strategy for a category of nonlinear fractional-order large-scale systems (FOLSSs). First, a novelty fractional-order Nussbaum function and a coordinate transformation method are formulated to overcome the compound unknown control coefficients induced by the unknown severe faults and false data injection attacks. Then, an enhanced fractional-order DSC technology is employed, which can tactfully surmount the deficiency of explosive calculations exposed in the backstepping framework. Furthermore, the radial basis function neural network is applied to address the unknown items related to the nonlinear FOLSSs. Based on the fractional Lyapunov stability criterion, a decentralized finite-time control approach is developed, which can ensure that all states of the closed-loop system are bounded and that the stabilization errors of each subsystem tend toward a small area in finite time. At last, two simulation examples are given to confirm the put-forward control algorithm’s effectiveness.

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References

  1. Chen, K., Tang, R.N., Li, C., Wei, P.N.: Robust adaptive fractional-order observer for a class of fractional-order nonlinear systems with unknown parameters. Nonlinear Dyn. 94, 415–427 (2018)

    Article  MATH  Google Scholar 

  2. Li, X.Y., He, J.S., Wen, C.Y., Liu, X.K.: Backstepping-based adaptive control of a class of uncertain incommensurate fractional-order nonlinear systems with external disturbance. IEEE Trans. Ind. Electron. 69(4), 4087–4095 (2022)

    Article  Google Scholar 

  3. Song, S., Park, J.H., Zhang, B.Y., Song, X.N., Zhang, Z.Q.: Adaptive command filtered neuro-fuzzy control design for fractional-order nonlinear systems with unknown control directions and input quantization. IEEE Trans. Syst. Man Cybern. Syst. 51(11), 7238–7249 (2021)

    Article  Google Scholar 

  4. Zhang, Y.L., Tong, S.C.: Adaptive fuzzy output-feedback decentralized control for fractional-order nonlinear large-scale systems. IEEE Trans. Cybern. 52(12), 12795–12804 (2022)

    Article  Google Scholar 

  5. Tong, S.C., Li, Y.M., Liu, Y.J.: Observer-based adaptive neural networks control for large-scale interconnected systems with nonconstant control gains. IEEE Trans. Neural Netw. Learn. Syst. 32(4), 1575–1585 (2021)

    Article  MathSciNet  Google Scholar 

  6. Zhang, J., Li, S., Ahn, C.K., Xiang, Z.R.: Decentralized event-triggered adaptive fuzzy control for nonlinear switched large-scale systems with input delay via command-filtered backstepping. IEEE Trans. Fuzzy Syst. 30(6), 2118–2123 (2022)

    Article  Google Scholar 

  7. Liang, B.Y., Zheng, S.Q., Ahn, C.K., Liu, F.: Adaptive fuzzy control for fractional-order interconnected systems with unknown control directions. IEEE Trans. Fuzzy Syst. 30(1), 75–87 (2022)

    Article  Google Scholar 

  8. Wu, L.B., Park, J.H., Xie, X.P., Ren, Y.W., Yang, Z.C.: Distributed adaptive neural network consensus for a class of uncertain nonaffine nonlinear multi-agent systems. Nonlinear Dyn. 100, 1243–1255 (2020)

    Article  MATH  Google Scholar 

  9. Yan, B.C., Niu, B., Zhao, X.D., Wang, H.Q., Chen, W.D., Liu, X.M.: Neural-network-based adaptive event-triggered asymptotically consensus tracking control for nonlinear nonstrict-feedback MASs: an improved dynamic surface approach. IEEE Trans. Neural Netw. Learn. Syst. (2022). https://doi.org/10.1109/TNNLS.2022.3175956

    Article  Google Scholar 

  10. Li, Y.M., Li, K.W., Tong, S.C.: Adaptive neural network finite-time control for multi-input and multi-output nonlinear systems with positive powers of odd rational numbers. IEEE Trans. Neural Netw. Learn. Syst. 31(7), 2532–2543 (2020)

    MathSciNet  Google Scholar 

  11. Swaroop, D., Hedrick, J.K., Yip, P.P., Gerdes, J.C.: Dynamic surface control for a class of nonlinear systems. IEEE Trans. Autom. Control 45(10), 1893–1899 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wang, D., Huang, J.: Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form. IEEE Trans. Neural Netw. Learn. Syst. 16(1), 195–202 (2005)

    Article  Google Scholar 

  13. Zhan, Y.L., Li, X.M., Tong, S.C.: Observer-based decentralized control for non-strict-feedback fractional-order nonlinear large-scale systems with unknown dead zones. IEEE Trans. Neural Netw. Learn. Syst. (2022). https://doi.org/10.1109/TNNLS.2022.3143901

    Article  Google Scholar 

  14. Zhan, Y.L., Sui, S., Tong, S.T.: Adaptive fuzzy decentralized dynamic surface control for fractional-order nonlinear large-scale systems. IEEE Trans. Fuzzy Syst. 30(8), 3373–3383 (2022)

    Article  Google Scholar 

  15. Bhat, S.P., Bernstein, D.S.: Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Autom. Control 43(5), 678–682 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  16. Ma, J.L., Park, J.H., Xu, S.Y.: Global adaptive finite-time control for uncertain nonlinear systems with actuator faults and unknown control directions. Nonlinear Dyn. 97, 2533–2545 (2019)

    Article  MATH  Google Scholar 

  17. Li, Y.X., Wei, M., Tong, S.C.: Event-triggered adaptive neural control for fractional-order nonlinear systems based on finite-time scheme. IEEE Trans. Cybern. 52(9), 9481–9489 (2022)

    Article  Google Scholar 

  18. You, X.X., Dian, S.Y., Liu, K., Guo, B., Xiang, G.F., Zhu, Y.Q.: Command filter-based adaptive fuzzy finite-time tracking control for uncertain fractional-order nonlinear systems. IEEE Trans. Fuzzy Syst. 31(1), 226–240 (2023)

    Article  Google Scholar 

  19. Zhang, X., Tan, J.Q., Wu, J., Chen, W.S.: Event-triggered-based fixed-time adaptive neural fault-tolerant control for stochastic nonlinear systems under actuator and sensor faults. Nonlinear Dyn. 108, 2279–2296 (2022)

  20. Zhang, L.L., Yang, G.H.: Observer-based adaptive decentralized fault-tolerant control of nonlinear large-scale systems with sensor and actuator faults. IEEE Trans. Ind. Electron. 66(10), 8019–8029 (2019)

    Article  Google Scholar 

  21. Zhang, X.L., Zheng, S.Q., Ahn, C.K., Xie, Y.L.: Adaptive neural consensus for fractional-order multi-agent systems with faults and delays. IEEE Trans. Neural Netw. Learn. Syst. (2022). https://doi.org/10.1109/TNNLS.2022.3146889

    Article  Google Scholar 

  22. Wu, L.B., Park, J.H.: Adaptive fault-tolerant control of uncertain switched nonaffine nonlinear systems with actuator faults and time delays. IEEE Trans. Syst. Man Cybern. Syst. 50(9), 3470–3480 (2020)

    Article  Google Scholar 

  23. Yoo, S.J.: Neural-network-based adaptive resilient dynamic surface control against unknown deception attacks of uncertain nonlinear time-delay cyberphysical systems. IEEE Trans. Neural Netw. Learn. Syst. 31(10), 4341–4353 (2020)

    Article  MathSciNet  Google Scholar 

  24. Jiang, X.Y., Mu, X.W., Hu, Z.H.: Decentralized adaptive fuzzy tracking control for a class of nonlinear uncertain interconnected systems with multiple faults and denial-of-service attack. IEEE Trans. Fuzzy Syst. 29(10), 3130–3141 (2021)

    Article  Google Scholar 

  25. Huang, J.S., Zhao, L., Wang, Q.G.: Adaptive control of a class of strict feedback nonlinear systems under replay attacks. ISA Trans. 107, 134–142 (2020)

    Article  Google Scholar 

  26. Zhang, H.G., Guo, X.Y., Sun, J.Y., Zhou, Y.: Event-triggered cooperative adaptive fuzzy control for stochastic nonlinear systems with measurement sensitivity and deception attacks. IEEE Trans. Fuzzy Syst. 31(3), 774–785 (2023).

  27. Song, S., Park, J.H., Zhang, B.Y., Song, X.N.: Adaptive NN finite-time resilient control for nonlinear time-delay systems with unknown false data injection and actuator faults. IEEE Trans. Neural Netw. Learn. Syst. 33(10), 5416–5428 (2022)

    Article  MathSciNet  Google Scholar 

  28. Song, S., Park, J.H., Zhang, B.Y., Song, X.N.: Event-based adaptive fuzzy fixed-time secure control for nonlinear CPSs against unknown false data injection and backlash-like hysteresis. IEEE Trans. Fuzzy Syst. 30(6), 1939–1951 (2022)

    Article  Google Scholar 

  29. Yang, Z.C., Zheng, S.Q., Liu, F., Xie, Y.L.: Adaptive output feedback control for fractional-order multi-agent systems. ISA Trans. 96, 195–209 (2020)

    Article  Google Scholar 

  30. Li, Z.J., Zhao, J.: Resilient adaptive control of switched nonlinear cyber-physical systems under uncertain deception attacks. Inf. Sci. 543(8), 398–409 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  31. Cheng, T.T., Niu, B., Zhang, J.M., Wang, D., Wang, Z.H.: Time-/event-triggered adaptive neural asymptotic tracking control of nonlinear interconnected systems with unmodeled dynamics and prescribed performance. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2021.3129228

    Article  Google Scholar 

  32. 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 

  33. Sui, S., Tong, S.C.: Finite-time fuzzy adaptive PPC for nonstrict-feedback nonlinear MIMO systems. IEEE Trans. Cybern. 53(2), 732–742 (2023)

    Article  Google Scholar 

  34. Yang, W.G., Zheng, W.X., Yu, W.W.: Observer-based event-triggered adaptive fuzzy control for fractional-order time-varying delayed MIMO systems against actuator faults. IEEE Trans. Fuzzy Syst. 30(12), 5445–5459 (2022)

    Article  Google Scholar 

  35. Li, Y.X., Yang, G.H.: Adaptive asymptotic tracking control of uncertain nonlinear systems with input quantization and actuator faults. Automatica 72, 177–185 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  36. Yoo, S. J.: Neural-network-based adaptive resilient dynamic surface control against unknown deception attacks of uncertain nonlinear time-delay cyberphysical systems. IEEE Trans. Neural Netw. Learn. Syst 31(10), 4341–4353 (2020)

  37. Podlubny, I.: Fractional Differential Equations. Academic, New York (1998)

    MATH  Google Scholar 

  38. Li, Y., Chen, Y.Q., Podlubny, I.: MittagCLeffler stability of fractional order nonlinear dynamic systems. Automatica 45(8), 1965–1969 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  39. Nussbaum, R.D.: Some remarks on a conjecture in parameter adaptive control. Syst. Control Lett. 3(5), 243–246 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  40. Huang, J.S., Wang, W., Wen, C.Y., Zhou, J.: Adaptive control of a class of strict-feedback time-varying nonlinear systems with unknown control coefficients. Automatica 93, 98–105 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  41. Jin, X., Haddad, W.M., Yucelen, T.: An adaptive control architecture for mitigating sensor and actuator attacks in cyber-physical systems. IEEE Trans. Autom. Control 62(11), 6058–6064 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  42. Y.M, Li., S.C, Tong: Adaptive neural networks decentralized FTC design for nonstrict-feedback nonlinear interconnected large-scale systems against actuator faults. IEEE Trans. Neural Netw. Learn. Syst. 28(11), 2541–2554 (2017)

    Article  MathSciNet  Google Scholar 

  43. Hilfer, R., Butzer, P.L., Westphal, U.: An introduction to fractional calculus. In: Appl. Fract. Calc. Phys., pp. 1–85. World Scientific (2010)

  44. Wang, L.X.: Stable adaptive fuzzy control of nonlinear systems. IEEE Trans. Fuzzy Syst. 1(2), 146–155 (1993)

    Article  Google Scholar 

  45. Wu, G.C., Baleanu, D., Luo, W.H.: Lyapunov functions for Riemann-Liouville-like fractional difference equations. Appl. Math. Comput. 314(1), 228–236 (2017)

    MathSciNet  MATH  Google Scholar 

  46. Ma, Z.Y., Ma, H.J.: Adaptive fuzzy backstepping dynamic surface control of strict-feedback fractional-order uncertain nonlinear systems. IEEE Trans. Fuzzy Syst. 28(1), 122–133 (2020)

    Article  Google Scholar 

  47. Qian, C.J., Lin, W.: Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Syst. Control Lett. 42(3), 185–200 (2001)

  48. Hardy, G.H., Littlewood, J.E., Polya, G.: Inequalities. Cambridge Univ. Press, London (1952)

    MATH  Google Scholar 

  49. Mani, P., Rajan, R., Shanmugam, L., Joo, Y.H.: Adaptive fractional fuzzy integral sliding mode control for PMSM model. IEEE Trans. Fuzzy Syst. 27(8), 1674–1686 (2019)

    Article  Google Scholar 

  50. Li, Y.M., Li, Y.X., Tong, S.C.: Event-based finite-time control for nonlinear multi-agent systems with asymptotic tracking. IEEE Trans. Autom. Control (2022). https://doi.org/10.1109/TAC.2022.3197562

    Article  Google Scholar 

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 62203153, in part by the Natural Science Fund for Excellent Young Scholars of Henan Province under Grant 202300410127, and in part by the Serbian Ministry of Education, Science and Technological Development (No. 451-03-68/2022-14/200108).

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Authors and Affiliations

  1. School of Information Engineering, Henan University of Science and Technology, Luoyang, 471023, China

    Xiaona Song, Peng Sun & Shuai Song

  2. Department of Automatic Control, Robotics and Fluid Technique, Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac, Dositejeva 19, Kraljevo, 36000, Serbia

    Vladimir Stojanovic

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  1. Xiaona Song
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Correspondence to Shuai Song.

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Song, X., Sun, P., Song, S. et al. Finite-time adaptive neural resilient DSC for fractional-order nonlinear large-scale systems against sensor-actuator faults. Nonlinear Dyn 111, 12181–12196 (2023). https://doi.org/10.1007/s11071-023-08456-0

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