On asymptotic fixed-time controller design for uncertain nonlinear systems with pure state constraints

Yebin Li; Dongshu Wang; Zuowei Cai; Yebin Li; Dongshu Wang; Zuowei Cai

doi:10.3934/math.20231389

AIMS Mathematics

2023, Volume 8, Issue 11: 27151-27174. doi: 10.3934/math.20231389

Previous Article Next Article

Research article Special Issues

On asymptotic fixed-time controller design for uncertain nonlinear systems with pure state constraints

1.
School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, China
2.
School of Information Science and Engineering, Hunan Women's University, Changsha, Hunan 410000, China

Received: 02 August 2023 Revised: 10 September 2023 Accepted: 13 September 2023 Published: 25 September 2023
MSC : 93B52, 93D05, 93D40

This study investigates the problem of asymptotic fixed-time tracking control (AFXTTC) for uncertain nonlinear systems (UNS) subject to pure state constraints. To study this problem, we define asymptotic fixed-time stability (AFXTS) and thus a criterion for determining AFXTS. Dynamic surface control (DSC) is combined with fuzzy logic systems (FLSs) to construct a new adaptive fuzzy asymptotic fixed-time controller. A barrier Lyapunov function (BLF) is introduced to ensure that constraints on all states are satisfied. The proposed criterion is used to analyze the AFXTS of the system, and the effectiveness and superiority of the theoretical analysis results are verified through simulations.
- asymptotic fixed-time stability,
- uncertain nonlinear system,
- pure state constraints,
- adaptive fuzzy control,
- backstepping
Citation: Yebin Li, Dongshu Wang, Zuowei Cai. On asymptotic fixed-time controller design for uncertain nonlinear systems with pure state constraints[J]. AIMS Mathematics, 2023, 8(11): 27151-27174. doi: 10.3934/math.20231389

Related Papers:

Abstract

This study investigates the problem of asymptotic fixed-time tracking control (AFXTTC) for uncertain nonlinear systems (UNS) subject to pure state constraints. To study this problem, we define asymptotic fixed-time stability (AFXTS) and thus a criterion for determining AFXTS. Dynamic surface control (DSC) is combined with fuzzy logic systems (FLSs) to construct a new adaptive fuzzy asymptotic fixed-time controller. A barrier Lyapunov function (BLF) is introduced to ensure that constraints on all states are satisfied. The proposed criterion is used to analyze the AFXTS of the system, and the effectiveness and superiority of the theoretical analysis results are verified through simulations.

References

[1]	M. Krstić, I. Kanellakopoulos, P. V. Kokotović, Nonlinear and adaptive control design, New York: Wiley, 1995.
[2]	H. Khalilć, Nonlinear systems, Englewood Cliffs, NJ, USA: Prentice-Hall, 2000.
[3]	P. A. Ioannou, B. Fidan, Adaptive control tutorial, Philadelphia, PA: Society for Industrial and Applied Mathematics, 2006. https://doi.org/10.1137/1.9780898718652
[4]	B. Xu, D. Wang, Y. Zhang, Z. Shi, DOB-based neural control of flexible hypersonic flight vehicle considering wind effects, IEEE T. Ind. Electron., 64 (2017), 8676–8685. https://doi.org/10.1109/TIE.2017.2703678 doi: 10.1109/TIE.2017.2703678
[5]	L. Tang, X. Wu, J. Lü, J. Lu, R. M. D'Souza, Master stability functions for complete, intralayer, and interlayer synchronization in multiplex networks of coupled Rössler oscillators, Phys. Rev. E, 99 (2019), 012304.
[6]	J. Zhuang, J. Cao, L. Tang, Y. Xia, M. Perc, Synchronization analysis for stochastic delayed multilayer network with additive couplings, IEEE T. Syst. Man Cy-S., 50 (2020), 4807–4816. https://doi.org/10.1109/TSMC.2018.2866704 doi: 10.1109/TSMC.2018.2866704
[7]	W. Zhang, W. Yi, Fuzzy observer-based dynamic surface control for input-saturated nonlinear systems and its application to missile guidance, IEEE Access, 8 (2020), 121285–121298. https://doi.org/10.1109/ACCESS.2020.3006489 doi: 10.1109/ACCESS.2020.3006489
[8]	M. Lv, D. Wang, Z. Peng, L. Liu, H. Wang, Event-triggered neural network control of autonomous surface vehicles over wireless network, Sci. China Inform. Sci., 63 (2020), 150205.
[9]	B. Zhang, X. Sun, M. Lv, S. G. Liu, L. Li, Distributed adaptive fixed-time fault-tolerant control for multiple 6-DOF uavs with full-state constraints guarantee, IEEE Syst. J., 16 (2022), 4792–4803. https://doi.org/10.1109/JSYST.2021.3128973 doi: 10.1109/JSYST.2021.3128973
[10]	Y. Wu, Z. Zheng, L. Tang, C. Xu, Synchronization dynamics of phase oscillator populations with generalized heterogeneous coupling, Chaos Soliton. Fract., 164 (2022), 112680. https://doi.org/10.1016/j.chaos.2022.112680 doi: 10.1016/j.chaos.2022.112680
[11]	L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X doi: 10.1016/S0019-9958(65)90241-X
[12]	L. Wang, Fuzzy systems are universal approximators, IEEE International Conference on Fuzzy Systems, 1992, 1163–1170.
[13]	G. Wen, B. Li, B. Niu, Optimized backstepping control using reinforcement learning of observer-critic-actor architecture based on the fuzzy system for a class of nonlinear strict-feedback systems, IEEE T. Fuzzy Syst., 30 (2022), 4322–4335. https://doi.org/10.1109/TFUZZ.2022.3148865 doi: 10.1109/TFUZZ.2022.3148865
[14]	J. Zhang, S. Tong, Y. Li, Adaptive fuzzy finite-time output-feedback fault-tolerant control of nonstrict-feedback systems against actuator faults, IEEE T. Syst. Man Cy-S., 52 (2022), 1276–1287. https://doi.org/10.1109/TSMC.2020.3011702 doi: 10.1109/TSMC.2020.3011702
[15]	G. Lai, Y. Zhang, Z. Liu, J. W. Wang, K. R. Chen, C. L. P. Chen, Direct adaptive fuzzy control scheme with guaranteed tracking performances for uncertain canonical nonlinear systems, IEEE T. Fuzzy Syst., 30 (2022), 818–829. https://doi.org/10.1109/TFUZZ.2021.3049902 doi: 10.1109/TFUZZ.2021.3049902
[16]	G. Cui, J. Yu, P. Shi, Observer-based finite-time adaptive fuzzy control with prescribed performance for nonstrict-feedback nonlinear systems, IEEE T. Fuzzy Syst., 30 (2022), 767–778. https://doi.org/10.1109/TFUZZ.2020.3048518 doi: 10.1109/TFUZZ.2020.3048518
[17]	G. Liu, J. H. Park, H. Xu, C. C. Hua, Reduced-order observer-based output-feedback tracking control for nonlinear time-delay systems with global prescribed performance, IEEE T. Cybernetics, 53 (2023), 5560–5571. https://doi.org/10.1109/TCYB.2022.3158932 doi: 10.1109/TCYB.2022.3158932
[18]	S. Sui, H. Xu, S. Tong, C. L. P. Chen, A novel prescribed performance fuzzy adaptive output feedback control for nonlinear MIMO systems in finite-time, IEEE T. Fuzzy Syst., 30 (2021), 3633–3644. https://doi.org/10.1109/TFUZZ.2021.3119750 doi: 10.1109/TFUZZ.2021.3119750
[19]	H. Wang, K. Xu, P. X. Liu, J. F. Qiao, Adaptive fuzzy fast finite-time dynamic surface tracking control for nonlinear systems, IEEE T. Circuits-Ⅰ, 68 (2021), 4337–4348. https://doi.org/10.1109/TCSI.2021.3098830 doi: 10.1109/TCSI.2021.3098830
[20]	W. M. Haddad, J. Lee, Finite-time stabilization and optimal feedback control for nonlinear discrete-time systems, IEEE T. Automat. Contr., 68 (2023), 1685–1691. https://doi.org/10.1109/TAC.2022.3151195 doi: 10.1109/TAC.2022.3151195
[21]	D. Jin, B. Niu, H. Wang, D. Yang, A new adaptive DS-based finite-time neural tracking control scheme for nonstrict-feedback nonlinear systems, IEEE T. Syst. Man Cy-S., 52 (2022), 1014–1018. https://doi.org/10.1109/TSMC.2020.3009405 doi: 10.1109/TSMC.2020.3009405
[22]	J. Zhu, Y. Yang, T. Zhang, Z. Q. Cao, Finite-time stability control of uncertain nonlinear systems with self-limiting control terms, IEEE T. Neur. Net. Lear., 2022, 35235522. https://doi.org/10.1109/TNNLS.2022.3149894 doi: 10.1109/TNNLS.2022.3149894
[23]	Y. Li, Z. Hou, W. Che, Z. G. Wu, Event-based design of finite-time adaptive control of uncertain nonlinear systems, IEEE T. Neur. Net. Lear., 33 (2021), 3804–3813. https://doi.org/10.1109/TNNLS.2021.3054579 doi: 10.1109/TNNLS.2021.3054579
[24]	A. Polyakov, Nonlinear feedback design for fixed-time stabilization of linear control systems, IEEE T. Automat. Contr., 57 (2012), 2106–2110. https://doi.org/10.1109/TAC.2011.2179869 doi: 10.1109/TAC.2011.2179869
[25]	K. Lu, Z. Liu, H. Yu, C. L. P. Chen, Y. Zhang, Adaptive fuzzy inverse optimal fixed-time control of uncertain nonlinear systems, IEEE T. Fuzzy Syst., 30 (2021), 3857–3868. https://doi.org/10.1109/TFUZZ.2021.3132151 doi: 10.1109/TFUZZ.2021.3132151
[26]	J. Sun, J. Yi, Z. Pu, Fixed-time adaptive fuzzy control for uncertain nonstrict-feedback systems with time-varying constraints and input saturations, IEEE T. Fuzzy Syst., 30 (2022), 1114–1128. https://doi.org/10.1109/TFUZZ.2021.3052610 doi: 10.1109/TFUZZ.2021.3052610
[27]	L. Zhang, B. Chen, C. Lin, Y. Shang, Fuzzy adaptive fixed-time consensus tracking control of high-order multiagent systems, IEEE T. Fuzzy Syst., 30 (2022), 567–578. https://doi.org/10.1590/s0104-40362022003000001 doi: 10.1590/s0104-40362022003000001
[28]	F. Kong, Q. Zhu, T. Huang, Fixed-time stability for discontinuous uncertain inertial neural networks with time-varying delays, IEEE T. Syst. Man, Cy-Syst., 52 (2021), 4507–4517. https://doi.org/10.1109/TSMC.2021.3096261 doi: 10.1109/TSMC.2021.3096261
[29]	X. Jin, Y. Shi, Y. Tang, H. Werner, J. Kurths, Event-triggered fixed-time attitude consensus with fixed and switching topologies, IEEE T. Automat. Contr., 67 (2021), 4138–4145. https://doi.org/10.1109/TAC.2021.3108514 doi: 10.1109/TAC.2021.3108514
[30]	C. Huang, Z. Liu, C. L. P. Chen, Y. Zhang, Adaptive fixed-time neural control for uncertain nonlinear multiagent systems, IEEE T. Neur. Net. Lear., 2022, 35482688. https://doi.org/10.1109/TNNLS.2022.3165836 doi: 10.1109/TNNLS.2022.3165836
[31]	W. Sun, S. Diao, S. Su, Z. Y. Sun, Fixed-time adaptive neural network control for nonlinear systems with input saturation, IEEE T. Neur. Net. Lear., 34 (2023), 1911–1920. https://doi.org/10.1109/TNNLS.2021.3105664 doi: 10.1109/TNNLS.2021.3105664
[32]	X. Hu, Y. Li, S. Tong, Z. S. Hou, Event-triggered adaptive fuzzy asymptotic tracking control of nonlinear pure-feedback systems with prescribed performance, IEEE T. Cybernetics, 53 (2023), 2380–2390. https://doi.org/10.1109/TCYB.2021.3118835 doi: 10.1109/TCYB.2021.3118835
[33]	Y. Li, S. Liang, B. Xu, M. S. Hou, Predefined-time asymptotic tracking control for hypersonic flight vehicles with input quantization and faults, IEEE T. Aero. Elec. Sys., 57 (2021), 2826–2837. https://doi.org/10.1109/TAES.2021.3068442 doi: 10.1109/TAES.2021.3068442
[34]	Z. Liu, G. Lai, Y. Zhang, C. L. P. Chen, Adaptive neural output feedback control of output-constrained nonlinear systems with unknown output nonlinearity, IEEE T. Neur. Net. Lear., 26 (2015), 1789–1802. https://doi.org/10.1109/TNNLS.2015.2420661 doi: 10.1109/TNNLS.2015.2420661
[35]	Y. Liu, M. Gong, S. Tong, C. L. P. Chen, Adaptive fuzzy output feedback control for a class of nonlinear systems with full state constraints, IEEE T. Fuzzy Syst., 26 (2018), 2607–2617. https://doi.org/10.1109/TFUZZ.2018.2798577 doi: 10.1109/TFUZZ.2018.2798577
[36]	D. Li, Y. Liu, S. Tong, C. L. P. Chen, D. J. Li, Neural networks-based adaptive control for nonlinear state constrained systems with input delay, IEEE T. Cybernetics, 49 (2019), 1249–1258. https://doi.org/10.1109/TCYB.2018.2799683 doi: 10.1109/TCYB.2018.2799683
[37]	A. Liu, H. Li, Stabilization of delayed boolean control networks with state constraints: A barrier Lyapunov function method, IEEE T. Circuits-Ⅱ, 68 (2021), 2553–2557. https://doi.org/10.1109/TCSII.2021.3053081 doi: 10.1109/TCSII.2021.3053081
[38]	M. Wang, Y. Zou, C. Yang, System transformation-based neural control for full-state-constrained pure-feedback systems via disturbance Observer, IEEE T. Cybernetics, 52 (2022), 1479–1489. https://doi.org/10.1109/TCYB.2020.2988897 doi: 10.1109/TCYB.2020.2988897
[39]	L. Zhao, J. Yu, P. Shi, Adaptive finite-time command filtered backstepping control for markov jumping nonlinear systems with full-state constraints, IEEE T. Circuits-Ⅱ, 69 (2022), 3244–3248. https://doi.org/10.1109/TCSII.2022.3152851 doi: 10.1109/TCSII.2022.3152851
[40]	J. Yu, L. Zhao, H. Yu, Barrier Lyapunov functions-based command filtered output feedback control for full-state constrained nonlinear systems, Automatica, 105 (2019), 71–79. https://doi.org/10.1016/j.diff.2019.02.001 doi: 10.1016/j.diff.2019.02.001
[41]	K. P. Tee, B. Ren, S. S. Ge, Control of nonlinear systems with time-varying output constraints, Automatica, 47 (2011), 2511–2516. https://doi.org/10.1016/j.automatica.2011.08.044 doi: 10.1016/j.automatica.2011.08.044
[42]	T. Gao, Y. Liu, D. Li, S. Tong, T. Li, Adaptive neural control using tangent time-varying blfs for a class of uncertain stochastic nonlinear systems with full state constraints, IEEE T. Cybernetics, 51 (2021), 1943–1953. https://doi.org/10.1109/TCYB.2019.2906118 doi: 10.1109/TCYB.2019.2906118
[43]	C. Xin, Y. Li, C. K. Ahn, Adaptive neural asymptotic tracking of uncertain non-strict feedback systems with full-state constraints via command filtered technique, IEEE T. Neur. Net. Lear., 2022, 35044923. https://doi.org/10.1109/TNNLS.2022.3141091 doi: 10.1109/TNNLS.2022.3141091
[44]	Y. Zhang, J. Guo, Z. Xiang, Finite-time adaptive neural control for a class of nonlinear systems with asymmetric time-varying full-state constraints, IEEE T. Neur. Net. Lear., 2022, 35044923. https://doi.org/10.1109/TNNLS.2022.3164948 doi: 10.1109/TNNLS.2022.3164948
[45]	P. K. Mishra, N. K. Verma, On controller design for nonlinear systems with pure state constraints, IEEE T. Circuits-Ⅱ, 69 (2022), 2236–2240. https://doi.org/10.1109/TCSII.2021.3129254 doi: 10.1109/TCSII.2021.3129254
[46]	T. Yu, Y. Liu, L. Liu, S. C. Tong, Adaptive fuzzy control of nonlinear systems with function constraints based on time-varying IBLFs, IEEE T. Fuzzy Syst., 30 (2022), 4939–4952. https://doi.org/10.1109/TFUZZ.2022.3164536 doi: 10.1109/TFUZZ.2022.3164536
[47]	B. Mao, X. Wu, J. Lü, et al. Predefined-time bounded consensus of multiagent systems with unknown nonlinearity via distributed adaptive fuzzy control, IEEE T. Cybernetics, 53 (2023), 2622–2635. https://doi.org/10.1109/TCYB.2022.3163755 doi: 10.1109/TCYB.2022.3163755
[48]	L. Wu, J. H. Park, X. Xie, Y. F. Li, Adaptive asymptotic tracking control of uncertain nonlinear systems based on taylor decoupling and event-trigger, IEEE T. Syst. Man Cy.-S., 52 (2022), 2053–2060. https://doi.org/10.1109/TSMC.2020.3034579 doi: 10.1109/TSMC.2020.3034579
[49]	K. Zhao, Y. Song, C. L. P. Chen, L. Chen, Adaptive asymptotic tracking with global performance for nonlinear systems with unknown control directions, IEEE T. Automat. Contr., 67 (2022), 1566–1573. https://doi.org/10.1109/TAC.2021.3074899 doi: 10.1109/TAC.2021.3074899
[50]	H. Cheng, X. Huang, H. Cao, Asymptotic tracking control for uncertain nonlinear strict-feedback systems with unknown time-varying delays, IEEE T. Neur. Net. Lear., 2022, 35349457. https://doi.org/10.1109/TNNLS.2022.3160803 doi: 10.1109/TNNLS.2022.3160803
[51]	X. Ding, J. Lu, H. Li, Stability of logical dynamic systems with a class of constrained switching, IEEE T. Circuits-Ⅰ, 69 (2022), 4248–4257. https://doi.org/10.1109/TCSI.2022.3190479 doi: 10.1109/TCSI.2022.3190479

Reader Comments

Your name:*

Email:*
© 2023 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)