Echo state network-based adaptive control for nonstrict-feedback nonlinear systems with input dead-zone and external disturbance

Hadil Alhazmi; Mohamed Kharrat; Hadil Alhazmi; Mohamed Kharrat

doi:10.3934/math.20241008

AIMS Mathematics

2024, Volume 9, Issue 8: 20742-20762. doi: 10.3934/math.20241008

Previous Article Next Article

Research article

Echo state network-based adaptive control for nonstrict-feedback nonlinear systems with input dead-zone and external disturbance

Hadil Alhazmi ¹,
Mohamed Kharrat ^{2
,
,}

1.
Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka, Saudi Arabia

Received: 23 April 2024 Revised: 02 June 2024 Accepted: 12 June 2024 Published: 26 June 2024
MSC : 92B20, 93C10, 93C40

This paper addressed the adaptive control problem for non-strict-feedback nonlinear systems with dead-zone and external disturbances. The design methodology integrated the backstepping technique with the approximation of unknown functions using an echo state network (ESN), enabling real-time adjustments. A comprehensive Lyapunov stability study was conducted to confirm the semi-globally uniformly ultimately boundedness (SGUUB) of all signals in the closed-loop system, ensuring that the tracking error converged to a small neighborhood of the origin. The effectiveness of the proposed method was further demonstrated through two examples, and error assessment criteria were utilized for comparisons with existing controllers.
- adaptive control,
- Lyapunov function,
- nonlinear systems,
- dead-zone,
- external disturbance,
- echo state network,
- error assessment criteria
Citation: Hadil Alhazmi, Mohamed Kharrat. Echo state network-based adaptive control for nonstrict-feedback nonlinear systems with input dead-zone and external disturbance[J]. AIMS Mathematics, 2024, 9(8): 20742-20762. doi: 10.3934/math.20241008

Related Papers:

Abstract

This paper addressed the adaptive control problem for non-strict-feedback nonlinear systems with dead-zone and external disturbances. The design methodology integrated the backstepping technique with the approximation of unknown functions using an echo state network (ESN), enabling real-time adjustments. A comprehensive Lyapunov stability study was conducted to confirm the semi-globally uniformly ultimately boundedness (SGUUB) of all signals in the closed-loop system, ensuring that the tracking error converged to a small neighborhood of the origin. The effectiveness of the proposed method was further demonstrated through two examples, and error assessment criteria were utilized for comparisons with existing controllers.

References

[1]	B. Ren, S. S. Ge, K. P. Tee, T. H. Lee, Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function, IEEE Trans. Neural Netw., 21 (2010), 1339–1345. https://doi.org/10.1109/TNN.2010.2047115 doi: 10.1109/TNN.2010.2047115
[2]	A. Kamalifar, M. B. Menhaj, M. N. Monfared, A. Fakharian, Design of robust model reference adaptive controller for a wider class of nonlinear systems, Iran. J. Sci. Technol. Trans. Electr. Eng., 46 (2022), 127–139. https://doi.org/10.1007/s40998-021-00451-8 doi: 10.1007/s40998-021-00451-8
[3]	B. Chen, H. Zhang, C. Lin, Observer-based adaptive neural network control for nonlinear systems in nonstrict-feedback form, IEEE Trans. Neural Netw. Learn. Syst., 27 (2016), 89–98. https://doi.org/10.1109/TNNLS.2015.2412121 doi: 10.1109/TNNLS.2015.2412121
[4]	M. Kharrat, M. Krichen, L. Alkhalifa, K. Gasmi, Neural networks-based adaptive command filter control for nonlinear systems with unknown backlash-like hysteresis and its application to single link robot manipulator, AIMS Math., 9 (2024), 959–973. https://doi.org/10.3934/math.2024048 doi: 10.3934/math.2024048
[5]	C. Wang, M. Liang, Y. Chai, An adaptive control of fractional-order nonlinear uncertain systems with input saturation, Complexity, 2019 (2019), 5643298. https://doi.org/10.1155/2019/5643298 doi: 10.1155/2019/5643298
[6]	M. Wang, X. Liu, P. Shi, Adaptive neural control of pure-feedback nonlinear time-delay systems via dynamic surface technique, IEEE Trans. Syst. Man Cybern. B, 41 (2011), 1681–1692. https://doi.org/10.1109/TSMCB.2011.2159111 doi: 10.1109/TSMCB.2011.2159111
[7]	M. Kharrat, M. Krichen, L. Alkhalifa, K. Gasmi, Neural-networks-based adaptive fault-tolerant control of nonlinear systems with actuator faults and input quantization, IEEE Access, 11 (2023), 137680–137687. https://doi.org/10.1109/ACCESS.2023.3338376 doi: 10.1109/ACCESS.2023.3338376
[8]	J. An, W. Yang, X. Xu, T. Chen, B. Du, Y. Tang, et al., Decentralized adaptive control for quasi-consensus in heterogeneous nonlinear multiagent systems, Discrete Dyn. Nat. Soc., 2021 (2021), 2230805. https://doi.org/10.1155/2021/2230805 doi: 10.1155/2021/2230805
[9]	S. Tong, T. Wang, Y. Li, H. Zhang, Adaptive neural network output feedback control for stochastic nonlinear systems with unknown dead-zone and unmodeled dynamics, IEEE Trans. Cybern., 44 (2014), 910–921. https://doi.org/10.1109/TCYB.2013.2276043 doi: 10.1109/TCYB.2013.2276043
[10]	J. Luo, H. Liu, Adaptive fractional fuzzy sliding mode control for multivariable nonlinear systems, Discrete Dyn. Nat. Soc., 2014 (2014), 541918. https://doi.org/10.1155/2014/541918 doi: 10.1155/2014/541918
[11]	Q. Zhou, H. Li, C. Wu, L. Wang, C. K. Ahn, Adaptive fuzzy control of nonlinear systems with unmodeled dynamics and input saturation using small-gain approach, IEEE Trans. Syst. Man Cybern.: Syst., 47 (2017), 1979–1989. https://doi.org/10.1109/TSMC.2016.2586108 doi: 10.1109/TSMC.2016.2586108
[12]	B. Chen, X. Liu, K. Liu, C. Lin, Fuzzy approximation-based adaptive control of nonlinear delayed systems with unknown dead zone, IEEE Trans. Fuzzy Syst., 22 (2014), 237–248. https://doi.org/10.1109/TFUZZ.2013.2250507 doi: 10.1109/TFUZZ.2013.2250507
[13]	G. Chen, J. Dong, Approximate optimal adaptive prescribed performance control for uncertain nonlinear systems with feature information, IEEE Trans. Syst. Man Cybern.: Syst., 54 (2024), 2298–2308. https://doi.org/10.1109/TSMC.2023.3342854 doi: 10.1109/TSMC.2023.3342854
[14]	Y. Deng, X. Zhang, G. Zhang, X. Han, Adaptive neural tracking control of strict-feedback nonlinear systems with event-triggered state measurement, ISA Trans., 117 (2021), 28–39. https://doi.org/10.1016/j.isatra.2021.01.049 doi: 10.1016/j.isatra.2021.01.049
[15]	S. Tong, X. Min, Y. Li, Observer-based adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown control gain functions, IEEE Trans. Cybern., 50 (2020), 3903–3913. https://doi.org/10.1109/TCYB.2020.2977175 doi: 10.1109/TCYB.2020.2977175
[16]	G. Yang, J. Yao, Multilayer neurocontrol of high‐order uncertain nonlinear systems with active disturbance rejection, Int. J. Robust Nonlinear Control, 34 (2024), 2972–2987. https://doi.org/10.1002/rnc.7118 doi: 10.1002/rnc.7118
[17]	G. Yang, Asymptotic tracking with novel integral robust schemes for mismatched uncertain nonlinear systems, Int. J. Robust Nonlinear Control, 33 (2023), 1988–2002. https://doi.org/10.1002/rnc.6499 doi: 10.1002/rnc.6499
[18]	C. C. Ku, K. Y. Lee, Diagonal recurrent neural networks for dynamic systems control, IEEE Trans. Neural Netw., 6 (1995), 144–156. https://doi.org/10.1109/72.363441 doi: 10.1109/72.363441
[19]	S. Lun, M. Wu, X. Lu, M. Li, Fixed‐time adaptive tracking control for MIMO nonlinear system with input delay saturation based on echo state network, IET Control Theory Appl., 18 (2024), 374–383. https://doi.org/10.1049/cth2.12559 doi: 10.1049/cth2.12559
[20]	S. I. Han, J. M. Lee, Precise positioning of nonsmooth dynamic systems using fuzzy wavelet echo state networks and dynamic surface sliding mode control, IEEE Trans. Ind. Electron., 60 (2013), 5124–5136. https://doi.org/10.1109/TIE.2012.2218560 doi: 10.1109/TIE.2012.2218560
[21]	Y. Wang, G. Zong, D. Yang, K. Shi, Finite‐time adaptive tracking control for a class of nonstrict feedback nonlinear systems with full state constraints, Int. J. Robust Nonlinear Control, 32 (2022), 2551–2569. https://doi.org/10.1002/rnc.5777 doi: 10.1002/rnc.5777
[22]	N. Xu, X. Zhao, G. Zong, Y. Wang, Adaptive control design for uncertain switched nonstrict-feedback nonlinear systems to achieve asymptotic tracking performance, Appl. Math. Comput., 408 (2021), 126344. https://doi.org/10.1016/j.amc.2021.126344 doi: 10.1016/j.amc.2021.126344
[23]	J. Wu, Y. Hu, Y. Huang, Indirect adaptive robust control of nonstrict feedback nonlinear systems by a fuzzy approximation strategy, ISA Trans., 108 (2021), 10–17. https://doi.org/10.1016/j.isatra.2020.08.038 doi: 10.1016/j.isatra.2020.08.038
[24]	Y. Li, S. Tong, Command-filtered-based fuzzy adaptive control design for MIMO-switched nonstrict-feedback nonlinear systems, IEEE Trans. Fuzzy Syst., 25 (2017), 668–681. https://doi.org/10.1109/TFUZZ.2016.2574913 doi: 10.1109/TFUZZ.2016.2574913
[25]	M. Kharrat, Neural networks-based adaptive fault-tolerant control for stochastic nonlinear systems with unknown backlash-like hysteresis and actuator faults, J. Appl. Math. Comput., 70 (2024), 1995–2018. https://doi.org/10.1007/s12190-024-02042-2 doi: 10.1007/s12190-024-02042-2
[26]	S. Sui, C. P. Chen, S. 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
[27]	Y. Alruwaily, M. Kharrat, Funnel-based adaptive neural fault-tolerant control for nonlinear systems with dead-zone and actuator faults: application to rigid robot manipulator and inverted pendulum systems, Complexity, in press. https://doi.org/10.1155/2024/5344619
[28]	T. Gao, T. Li, Y. J. Liu, S. Tong, F. Sun, Observer-based adaptive fuzzy control of non-strict feedback nonlinear systems with function constraints, IEEE Trans. Fuzzy Syst., 31 (2023), 2556–2567. https://doi.org/10.1109/TFUZZ.2022.3228319 doi: 10.1109/TFUZZ.2022.3228319
[29]	Y. Liang, Y. X. Li, W. W. Che, Z. Hou, Adaptive fuzzy asymptotic tracking for nonlinear systems with nonstrict-feedback structure, IEEE Trans. Cybern., 51 (2021), 853–861. https://doi.org/10.1109/TCYB.2020.3002242 doi: 10.1109/TCYB.2020.3002242
[30]	X. Zhao, P. Shi, X. Zheng, L. Zhang, Adaptive tracking control for switched stochastic nonlinear systems with unknown actuator dead-zone, Automatica, 60 (2015), 193–200. https://doi.org/10.1016/j.automatica.2015.07.022 doi: 10.1016/j.automatica.2015.07.022
[31]	M. Cai, P. Shi, J. Yu, Adaptive neural finite-Time control of non-strict feedback nonlinear systems with non-symmetrical dead-zone, IEEE Trans. Neural Netw. Learn. Syst., 35 (2024), 1409–1414. https://doi.org/10.1109/TNNLS.2022.3178366 doi: 10.1109/TNNLS.2022.3178366
[32]	K. Li, S. Tong, Observer-based finite-time fuzzy adaptive control for MIMO non-strict feedback nonlinear systems with errors constraint, Neurocomputing, 341 (2019), 135–148. https://doi.org/10.1016/j.neucom.2019.02.022 doi: 10.1016/j.neucom.2019.02.022
[33]	H. Wang, H. R. Karimi, P. X. Liu, H. Yang, Adaptive neural control of nonlinear systems with unknown control directions and input dead-zone, IEEE Trans. Syst. Man Cybern.: Syst., 48 (2018), 1897–1907. https://doi.org/10.1109/TSMC.2017.2709813 doi: 10.1109/TSMC.2017.2709813
[34]	J. Ni, Z. Wu, L. Liu, C. Liu, Fixed-time adaptive neural network control for nonstrict-feedback nonlinear systems with deadzone and output constraint, ISA Trans., 97 (2020), 458–473. https://doi.org/10.1016/j.isatra.2019.07.013 doi: 10.1016/j.isatra.2019.07.013
[35]	J. Zhang, S. Li, Z. Xiang, Adaptive fuzzy output feedback event-triggered control for a class of switched nonlinear systems with sensor failures, IEEE Trans. Circuits Syst. I, 67 (2020), 5336–5346. https://doi.org/10.1109/TCSI.2020.2994547 doi: 10.1109/TCSI.2020.2994547
[36]	Y. Sun, B. Mao, H. Liu, S. Zhou, Output feedback adaptive control for stochastic non-strict-feedback system with dead-zone, Int. J. Control Autom. Syst., 18 (2020), 2621–2629. https://doi.org/10.1007/s12555-019-0876-9 doi: 10.1007/s12555-019-0876-9
[37]	Y. Zhan, X. Li, S. Tong, Observer-based decentralized control for non-strict-feedback fractional-order nonlinear large-scale systems with unknown dead zones, IEEE Trans. Neural Netw. Learn. Syst., 34 (2023), 7479–7490. https://doi.org/10.1109/TNNLS.2022.3143901 doi: 10.1109/TNNLS.2022.3143901
[38]	S. Zhu, L. Chu, M. Wang, Y. Han, S. Yang, Multi-dimensional Taylor network-based adaptive output-feedback tracking control for a class of nonlinear systems, IEEE Access, 8 (2020), 77298–77307. https://doi.org/10.1109/ACCESS.2020.2989523 doi: 10.1109/ACCESS.2020.2989523
[39]	J. Liu, Q. G. Wang, J. Yu, Convex optimization-based adaptive fuzzy control for uncertain nonlinear systems with input saturation using command filtered backstepping, IEEE Trans. Fuzzy Syst., 31 (2023), 2086–2091. https://doi.org/10.1109/TFUZZ.2022.3216103 doi: 10.1109/TFUZZ.2022.3216103
[40]	J. Liu, Q. G. Wang, J. Yu, Event-triggered adaptive neural network tracking control for uncertain systems with unknown input saturation based on command filters, IEEE Trans. Neural Netw. Learn. Syst., 35 (2024), 8702–8707. https://doi.org/10.1109/TNNLS.2022.3224065 doi: 10.1109/TNNLS.2022.3224065
[41]	X. Shi, C. C. Lim, P. Shi, S. Xu, Adaptive neural dynamic surface control for nonstrict-feedback systems with output dead zone, IEEE Trans. Neural Netw. Learn. Syst., 29 (2018), 5200–5213. https://doi.org/10.1109/TNNLS.2018.2793968 doi: 10.1109/TNNLS.2018.2793968

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)