This paper studies the issue of adaptive fuzzy output-feedback event-triggered control (ETC) for a fractional-order nonlinear system (FONS). The considered fractional-order system is subject to unmeasurable states. Fuzzy-logic systems (FLSs) are used to approximate unknown nonlinear functions, and a fuzzy state observer is founded to estimate the unmeasurable states. By constructing appropriate Lyapunov functions and utilizing the backstepping dynamic surface control (DSC) design technique, an adaptive fuzzy output-feedback ETC scheme is developed to reduce the usage of communication resources. It is proved that the controlled fractional-order system is stable, the tracking and observer errors are able to converge to a neighborhood of zero, and the Zeno phenomenon is excluded. A simulation example is given to verify the availability of the proposed ETC algorithm.
Citation: Chaoyue Wang, Zhiyao Ma, Shaocheng Tong. Adaptive fuzzy output-feedback event-triggered control for fractional-order nonlinear system[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 12334-12352. doi: 10.3934/mbe.2022575
This paper studies the issue of adaptive fuzzy output-feedback event-triggered control (ETC) for a fractional-order nonlinear system (FONS). The considered fractional-order system is subject to unmeasurable states. Fuzzy-logic systems (FLSs) are used to approximate unknown nonlinear functions, and a fuzzy state observer is founded to estimate the unmeasurable states. By constructing appropriate Lyapunov functions and utilizing the backstepping dynamic surface control (DSC) design technique, an adaptive fuzzy output-feedback ETC scheme is developed to reduce the usage of communication resources. It is proved that the controlled fractional-order system is stable, the tracking and observer errors are able to converge to a neighborhood of zero, and the Zeno phenomenon is excluded. A simulation example is given to verify the availability of the proposed ETC algorithm.
[1] |
S. Qureshi, A. Yusuf, A. A. Shaikh, M. Inc, D. Baleanu, Fractional modeling of blood ethanol concentration system with real data application, Chaos, 29 (2019), 013143. https://doi.org/10.1063/1.5082907 doi: 10.1063/1.5082907
![]() |
[2] |
S. Ullah, M. A. Khan, M. Farooq, A fractional model for the dynamics of TB virus, Chaos Solitons Fractals, 29 (2019), 63–71. https://doi.org/10.1016/j.chaos.2018.09.001 doi: 10.1016/j.chaos.2018.09.001
![]() |
[3] |
R. M. Jena, S. Chakraverty, H. Rezazadeh, D. D. Ganji, On the solution of time-fractional dynamical model of Brusselator reaction-diffusion system arising in chemical reactions, Math. Methods Appl. Sci., 43 (2020), 3903–3913. https://doi.org/10.1002/mma.6141 doi: 10.1002/mma.6141
![]() |
[4] |
H. Liu, S. G. Li, Y. G. Sun, H. X. Wang, Prescribed performance synchronization for fractional-order chaotic systems, Chin. Phys. B, 24 (2015). https://doi.org/10.1088/1674-1056/24/9/090505 doi: 10.1088/1674-1056/24/9/090505
![]() |
[5] |
Y. H. Wei, Y. Q. Chen, S. Liang, Y. Wang, A novel algorithm on adaptive backstepping control of fractional order system, Neurocomputing, 116 (2018), 63–71. https://doi.org/10.1016/j.neucom.2015.03.029 doi: 10.1016/j.neucom.2015.03.029
![]() |
[6] |
X. Y. Li, C. Y. Wen, Y. Zou, Adaptive backstepping control for fractional-order nonlinear systems with external disturbance and uncertain parameters using smooth control, IEEE Trans. Syst. Man, Cybern. Syst., 51 (2021), 7860–7869. https://doi.org/10.1109/TSMC.2020.2987335 doi: 10.1109/TSMC.2020.2987335
![]() |
[7] |
H. Liu, Y. P. Pan, S. G. Li, Y. Chen, Adaptive fuzzy backstepping control of fractional-order nonlinear systems, IEEE Trans. Syst. Man, Cybern., Syst., 47 (2017), 2209–2217. https://doi.org/10.1109/TSMC.2016.2640950 doi: 10.1109/TSMC.2016.2640950
![]() |
[8] |
C. H. Wang, M. Liang, Adaptive NN tracking control for nonlinear fractional order systems with uncertainty and input saturation, IEEE Access, 6 (2018), 70035–70044. https://doi.org/10.1109/ACCESS.2018.2878772 doi: 10.1109/ACCESS.2018.2878772
![]() |
[9] |
Y. X. Li, Q. Y. Wang, S. C. Tong, Fuzzy adaptive fault-tolerant control of fractional-order nonlinear systems, IEEE Trans. Syst. Man, Cybern. Syst., 51 (2021), 1372–1379. https://doi.org/10.1109/TSMC.2019.2894663 doi: 10.1109/TSMC.2019.2894663
![]() |
[10] |
Z. Y. Ma, H. J. Ma, Adaptive fuzzy backstepping dynamic surface control of strict-feedback fractional-order uncertain nonlinear systems, IEEE Trans. Fuzzy Syst., 28 (2020), 122–133. https://doi.org/10.1109/TFUZZ.2019.2900602 doi: 10.1109/TFUZZ.2019.2900602
![]() |
[11] |
S. Sui, C. L. P. Chen, S. C. Tong, Neural-network-based adaptive DSC design for switched fractional-order nonlinear systems, IEEE Trans. Neural Network Learn. Syst., 32 (2021), 4703–4712. https://doi.org/10.1109/TNNLS.2020.3027339 doi: 10.1109/TNNLS.2020.3027339
![]() |
[12] |
Z. Y. Ma, H. J. Ma, Reduced-order observer-based adaptive backstepping control for fractional-order uncertain nonlinear systems, IEEE Trans. Fuzzy Syst., 28 (2020), 3287–3301. https://doi.org/10.1109/TFUZZ.2019.2949760 doi: 10.1109/TFUZZ.2019.2949760
![]() |
[13] |
S. Song, J. H. Park, B. Y. Zhang, X. N. Song, Observer-based adaptive hybrid fuzzy resilient control for fractional-order nonlinear systems with time-varying delays and actuator failures, IEEE Trans. Fuzzy Syst., 29 (2021), 471–485. https://doi.org/10.1109/TFUZZ.2019.2955051 doi: 10.1109/TFUZZ.2019.2955051
![]() |
[14] |
W. G. Yang, W. W. Yu, Y. Z. Lv, L. Zhu, T. Hayat, Adaptive fuzzy tracking control design for a class of uncertain nonstrict-feedback fractional-order nonlinear SISO systems, IEEE Trans. Cybern., 51 (2021), 3039–3053. https://doi.org/10.1109/TCYB.2019.2931401 doi: 10.1109/TCYB.2019.2931401
![]() |
[15] |
X. D. Li, D. X. Peng, J. D. Cao, Lyapunov stability for impulsive systems via event-triggered impulsive control, IEEE Trans. Autom. Control., 65 (2020), 4908–4913. https://doi.org/10.1109/TAC.2020.2964558 doi: 10.1109/TAC.2020.2964558
![]() |
[16] |
S. Sui, C. L. P. Chen, S. C. Tong, Event-trigger-based finite-time fuzzy adaptive control for stochastic nonlinear system with unmodeled dynamics, IEEE Trans. Fuzzy Syst., 29 (2021), 1914–1926. https://doi.org/10.1109/TFUZZ.2020.2988849 doi: 10.1109/TFUZZ.2020.2988849
![]() |
[17] |
W. Wang, Y. M. Li, S. C, Tong, Neural-network-based adaptive event-triggered consensus control of nonstrict-feedback nonlinear systems, IEEE Trans. Neural Network Learn. Syst., 32 (2021), 1750–1764. https://doi.org/10.1109/TNNLS.2020.2991015 doi: 10.1109/TNNLS.2020.2991015
![]() |
[18] |
M. Wei, Y. X. Li, S. C. Tong, Event-triggered adaptive neural control of fractional-order nonlinear systems with full-state constraints, Neurocomputing, 412 (2020), 320–326. https://doi.org/10.1016/j.neucom.2020.06.082 doi: 10.1016/j.neucom.2020.06.082
![]() |
[19] |
B. Q. Cao, X. B. Nie, Event-triggered adaptive neural networks control for fractional-order nonstrict-feedback nonlinear systems with unmodeled dynamics and input saturation, Neural Networks, 142 (2021), 288–302. https://doi.org/10.1016/j.neunet.2021.05.014 doi: 10.1016/j.neunet.2021.05.014
![]() |
[20] |
Y. X. Li, M. Wei, S. C. Tong, Event-triggered adaptive neural control for fractional-order nonlinear systems based on finite-time scheme, IEEE Trans. Cybern., 2021 (2021), 1–9. https://doi.org/10.1109/TCYB.2021.3056990 doi: 10.1109/TCYB.2021.3056990
![]() |
[21] | I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999. |
[22] |
P. Gong, W. Y. Lan, Adaptive robust tracking control for uncertain nonlinear fractional-order multi-agent systems with directed topologies, Automatica, 92 (2018), 92–99. https://doi.org/10.1016/j.automatica.2018.02.010 doi: 10.1016/j.automatica.2018.02.010
![]() |
[23] |
X. D. Li, D. W. C. Ho J. D. Cao, Finite-time stability and settling estimation of nonlinear impulsive systems, Automatica, 99 (2019), 361–368. https://doi.org/10.1016/j.automatica.2018.10.024 doi: 10.1016/j.automatica.2018.10.024
![]() |
[24] |
X. D. Li, S. J. Song, J. H. Wu, Exponential stability of nonlinear systems with delayed impulses and applications, IEEE Trans. Autom. Control, 64 (2019), 4024–4034. https://doi.org/10.1109/TAC.2019.2905271 doi: 10.1109/TAC.2019.2905271
![]() |