IEEE/CAA Journal of Automatica Sinica
Citation:  H. R. Ren, H. Ma, H. Y. Li, and Z. Y. Wang, “Adaptive fixedtime control of nonlinear MASs with actuator faults,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 5, pp. 1252–1262, May 2023. doi: 10.1109/JAS.2023.123558 
The adaptive fixedtime consensus problem for a class of nonlinear multiagent systems (MASs) with actuator faults is considered in this paper. To approximate the unknown nonlinear functions in MASs, radial basis function neural networks are used. In addition, the first order sliding mode differentiator is utilized to solve the “explosion of complexity” problem, and a filter error compensation method is proposed to ensure the convergence of filter error in fixed time. With the help of the Nussbaum function, the actuator failure compensation mechanism is constructed. By designing the adaptive fixedtime controller, all signals in MASs are bounded, and the consensus errors between the leader and all followers converge to a small area of origin. Finally, the effectiveness of the proposed control method is verified by simulation examples.
[1] 
Z. Li, L. Gao, W. Chen, and Y. Xu, “Distributed adaptive cooperative tracking of uncertain nonlinear fractionalorder multiagent systems,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 1, pp. 292–300, 2020. doi: 10.1109/JAS.2019.1911858

[2] 
C. Deng, W. Gao, and W. Che, “Distributed adaptive faulttolerant output regulation of heterogeneous multiagent systems with coupling uncertainties and actuator faults,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 4, pp. 1098–1106, 2020. doi: 10.1109/JAS.2020.1003258

[3] 
Q. Wei, X. Wang, X. Zhong, and N. Wu, “Consensus control of leaderfollowing multiagent systems in directed topology with heterogeneous disturbances,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 2, pp. 423–431, 2021. doi: 10.1109/JAS.2021.1003838

[4] 
Z. Liu, W. Lin, X. Yu, J. J. RodríguezAndina, and H. Gao, “Approximationfree robust synchronization control for duallinearmotorsdriven systems with uncertainties and disturbances,” IEEE Trans. Industrial Electronics, vol. 69, no. 10, pp. 10500–10509, 2022. doi: 10.1109/TIE.2021.3137619

[5] 
J.X. Zhang and T. Chai, “Singularityfree continuous adaptive control of uncertain underactuated surface vessels with prescribed performance,” IEEE Trans. Syst.,Man,and Cyber.: Syst., vol. 52, no. 9, pp. 5646–5655, 2022. doi: 10.1109/TSMC.2021.3129798

[6] 
G. Lin, H. Li, C. K. Ahn, and D. Yao, “Eventbased finitetime neural control for humanintheloop UAV attitude systems,” IEEE Trans. Neural Networks and Learning Systems, 2022. DOI: 10.1109/TNNLS.2022.3166531

[7] 
H. Ren, Y. Wang, M. Liu, and H. Li, “An optimal estimation framework of multiagent systems with random transport protocol,” IEEE Trans. Signal Processing, vol. 70, pp. 2548–2559, 2022. doi: 10.1109/TSP.2022.3175020

[8] 
T. Liu, Z. Qin, Y. Hong, and Z.P. Jiang, “Distributed optimization of nonlinear multiagent systems: A smallgain approach,” IEEE Trans. Automatic Control, vol. 67, no. 2, pp. 676–691, 2022. doi: 10.1109/TAC.2021.3053549

[9] 
Zhang, T. Liu, and Z.P. Jiang, “Tracking control of unicycle mobile robots with eventtriggered and selftriggered feedback,” IEEE Trans. Automatic Control, 2022. DOI: 10.1109/TAC.2022.3173932

[10] 
H. Li, Y. Wu, M. Chen, and R. Lu, “Adaptive multigradient recursive reinforcement learning eventtriggered tracking control for multiagent systems,” IEEE Trans. Neural Networks and Learning Systems, vol. 34, no. 1, pp. 144–156, 2023. doi: 10.1109/TNNLS.2021.3090570

[11] 
Z. Jin, X. Sun, Z. Qin, and C. K. Ahn, “Fuzzy smallgain approach for the distributed optimization of TS fuzzy cyberphysical systems,” IEEE Trans. Cybernetics, 2022. DOI: 10.1109/TCYB.2022.3202576

[12] 
Z. Jin, C. K. Ahn, and J. Li, “Momentumbased distributed continuoustime nonconvex optimization of nonlinear multiagent systems via timescale separation,” IEEE Trans. Network Science and Engineering, vol. 10, no. 2, pp. 980–989, 2023. doi: 10.1109/TNSE.2022.3225409

[13] 
Z. Jin, Z. Qin, X. Zhang, and C. Guan, “A leaderfollowing consensus problem via a distributed observer and fuzzy inputtooutput smallgain theorem,” IEEE Trans. Control Network Syst., vol. 9, no. 1, pp. 62–74, 2022. doi: 10.1109/TCNS.2022.3141690

[14] 
J. Ni, S hi, Y. Zhao, and Z. Wu, “Fixedtime output consensus tracking for highorder multiagent systems with directed network topology and packet dropout,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 4, pp. 817–836, 2021. doi: 10.1109/JAS.2021.1003916

[15] 
X. Zheng, H. Li, C. K. Ahn, and D. Yao, “NNbased fixedtime attitude tracking control for multiple unmanned aerial vehicles with nonlinear faults,” IEEE Trans. Aerospace Electronic Systems, 2022. DOI: 10.1109/TAES.2022.3205566

[16] 
Y. Pan, Q. Li, H. Liang, and H.K. Lam, “A novel mixed control approach for fuzzy systems via membership functions online learning policy,” IEEE Trans. Fuzzy Systems, vol. 30, no. 9, pp. 3812–3822, 2022. doi: 10.1109/TFUZZ.2021.3130201

[17] 
H. Ma, H. Ren, Q. Zhou, H. Li, and Z. Wang, “Observerbased neural control of Nlink flexiblejoint robots,” IEEE Trans. Neural Networks Learning Syst., 2022. DOI: 10.1109/TNNLS.2022.3203074

[18] 
L. Cao, D. Yao, H. Li, W. Meng, and R. Lu, “Fuzzybased dynamic event triggering formation control for nonstrictfeedback nonlinear MASs,” Fuzzy Sets and Systems, vol. 452, pp. 1–22, 2023. doi: 10.1016/j.fss.2022.03.005

[19] 
Y. Pan, Y. Wu, and H.K. Lam, “Securitybased fuzzy control for nonlinear networked control systems with DoS attacks via a resilient eventtriggered scheme,” IEEE Trans. Fuzzy Systems, vol. 30, no. 10, pp. 4359–4368, 2022. doi: 10.1109/TFUZZ.2022.3148875

[20] 
H. Ren, H. Ma, H. Li, and R. Lu, “A disturbance observer based intelligent control for nonstrictfeedback nonlinear systems,” SCIENCE CHINA—Technological Sciences, vol. 66, no. 2, pp. 456–467, 2023. doi: 10.1007/s1143102221267

[21] 
H. Zhou, S. Sui, and S. Tong, “Fuzzy adaptive finitetime consensus control for highorder nonlinear multiagent systems based on eventtriggered,” IEEE Trans. Fuzzy Systems, vol. 30, no. 11, pp. 4891–4904, 2022. doi: 10.1109/TFUZZ.2022.3163907

[22] 
Z. Liu, X. Dong, J. Xue, H. Li, and Y. Chen, “Adaptive neural control for a class of purefeedback nonlinear systems via dynamic surface technique,” IEEE Trans. Neural Networks Learning Syst., vol. 27, no. 9, pp. 1969–1975, 2016. doi: 10.1109/TNNLS.2015.2462127

[23] 
M. Chen and S. S. Ge, “Adaptive neural output feedback control of uncertain nonlinear systems with unknown hysteresis using disturbance observer,” IEEE Trans. Industrial Electronics, vol. 62, no. 12, pp. 7706–7716, 2015. doi: 10.1109/TIE.2015.2455053

[24] 
L. Wang and C. L. Chen, “Adaptive fuzzy dynamic surface control of nonlinear constrained systems with unknown virtual control coefficients,” IEEE Trans. Fuzzy Systems, vol. 28, no. 8, pp. 1737–1747, 2020. doi: 10.1109/TFUZZ.2019.2921277

[25] 
S.L. Dai, K. Lu, and J. Fu, “Adaptive finitetime tracking control of nonholonomic multirobot formation systems with limited fieldofview sensors,” IEEE Trans. Cybernetics, vol. 52, no. 10, pp. 10695–10708, 2022. doi: 10.1109/TCYB.2021.3063481

[26] 
K. Li, S. Tong, and Y. Li, “Finitetime adaptive fuzzy decentralized control for nonstrictfeedback nonlinear systems with outputconstraint,” IEEE Trans. Syst.,Man,Cybernetics: Syst., vol. 50, no. 12, pp. 5271–5284, 2020. doi: 10.1109/TSMC.2018.2870698

[27] 
F. Wang, B. Chen, Y. Sun, Y. Gao, and C. Lin, “Finitetime fuzzy control of stochastic nonlinear systems,” IEEE Trans. Cybernetics, vol. 50, no. 6, pp. 2617–2626, 2020. doi: 10.1109/TCYB.2019.2925573

[28] 
S.L. Dai, S. He, X. Chen, and X. Jin, “Adaptive leaderfollower formation control of nonholonomic mobile robots with prescribed transient and steadystate performance,” IEEE Trans. Industrial Informatics, vol. 16, no. 6, pp. 3662–3671, 2020. doi: 10.1109/TII.2019.2939263

[29] 
Y. Liu, H. Li, Z. Zuo, X. Li, and R. Lu, “An overview of finite/fixedtime control and its application in engineering systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 12, pp. 2106–2120, 2022. doi: 10.1109/JAS.2022.105413

[30] 
Y. Li, F. Qu, and S. Tong, “Observerbased fuzzy adaptive finitetime containment control of nonlinear multiagent systems with input delay,” IEEE Trans. Cybernetics, vol. 51, no. 1, pp. 126–137, 2021. doi: 10.1109/TCYB.2020.2970454

[31] 
L. Wang, H. Wang, X. Liu, S. Ling, and S. Liu, “Fuzzy finitetime command filtering output feedback control of nonlinear systems,” IEEE Trans. Fuzzy Systems, vol. 30, no. 1, pp. 97–107, 2022. doi: 10.1109/TFUZZ.2020.3032784

[32] 
A. Polyakov, D. Efimov, and W. Perruquetti, “Finitetime and fixedtime stabilization: Implicit Lyapunov function approach,” Automatica, vol. 51, pp. 332–340, 2015. doi: 10.1016/j.automatica.2014.10.082

[33] 
J. Liu, Y. Zhang, Y. Yu, and C. Sun, “Fixedtime eventtriggered consensus for nonlinear multiagent systems without continuous communications,” IEEE Trans. Syst.,Man,Cybernetics: Syst., vol. 49, no. 11, pp. 2221–2229, 2019. doi: 10.1109/TSMC.2018.2876334

[34] 
L. Zhang, B. Chen, C. Lin, and Y. Shang, “Fuzzy adaptive fixedtime consensus tracking control of highorder multiagent systems,” IEEE Trans. Fuzzy Systems, vol. 30, no. 2, pp. 567–578, 2022. doi: 10.1109/TFUZZ.2020.3042239

[35] 
Z. Liu, F. Wang, Y. Zhang, X. Chen, and C. L. Chen, “Adaptive tracking control for a class of nonlinear systems with a fuzzy deadzone input,” IEEE Trans. Fuzzy Systems, vol. 23, no. 1, pp. 193–204, 2015. doi: 10.1109/TFUZZ.2014.2310491

[36] 
Y.J. Liu, J. Li, S. Tong, and C. L. Chen, “Neural network controlbased adaptive learning design for nonlinear systems with fullstate constraints,” IEEE Trans. Neural Networks Learning Syst., vol. 27, no. 7, pp. 1562–1571, 2016. doi: 10.1109/TNNLS.2015.2508926

[37] 
B. Chen, H. Zhang, X. Liu, and C. Lin, “Neural observer and adaptive neural control design for a class of nonlinear systems,” IEEE Trans. Neural Networks Learning Syst., vol. 29, no. 9, pp. 4261–4271, 2018. doi: 10.1109/TNNLS.2017.2760903

[38] 
J. Xia, J. Zhang, J. Feng, Z. Wang, and G. Zhuang, “Command filterbased adaptive fuzzy control for nonlinear systems with unknown control directions,” IEEE Trans. Syst.,Man,Cybernetics: Syst., vol. 51, no. 3, pp. 1945–1953, 2021.

[39] 
Y. Li and S. Tong, “Adaptive neural networks decentralized FTC design for nonstrictfeedback nonlinear interconnected largescale systems against actuator faults,” IEEE Trans. Neural Networks Learning Systems, vol. 28, no. 11, pp. 2541–2554, 2017. doi: 10.1109/TNNLS.2016.2598580

[40] 
Y. Wang, Y. Song, M. Krstic, and C. Wen, “Adaptive finite time coordinated consensus for highorder multiagent systems: Adjustable fraction power feedback approach,” Information Sciences, vol. 372, pp. 392–406, 2016. doi: 10.1016/j.ins.2016.08.054

[41] 
J.X. Zhang, Q.G. Wang, and W. Ding, “Global outputfeedback prescribed performance control of nonlinear systems with unknown virtual control coefficients,” IEEE Trans. Automatic Control, vol. 67, no. 12, pp. 6904–6911, 2022. doi: 10.1109/TAC.2021.3137103

[42] 
X. Lin, Y. Yu, and C. Sun, “A decoupling control for quadrotor UAV using dynamic surface control and sliding mode disturbance observer,” Nonlinear Dynamics, vol. 97, no. 1, pp. 781–795, 2019. doi: 10.1007/s11071019050136

[43] 
H.B. Zeng, Y. He, and K. L. Teo, “Monotonedelayintervalbased lyapunov functionals for stability analysis of systems with a periodically varying delay,” Automatica, vol. 138, p. 110030, 2022. doi: 10.1016/j.automatica.2021.110030

[44] 
X.C. Shangguan, C.K. Zhang, Y. He, L. Jin, L. Jiang, J. W. Spencer, and M. Wu, “Robust load frequency control for power system considering transmission delay and sampling period,” IEEE Trans. Industrial Informatics, vol. 17, no. 8, pp. 5292–5303, 2021. doi: 10.1109/TII.2020.3026336

[45] 
Z. Li, X. Yu, J. Qiu, and H. Gao, “Cell division genetic algorithm for component allocation optimization in multifunctional placers,” IEEE Trans. Industrial Informatics, vol. 18, no. 1, pp. 559–570, 2022. doi: 10.1109/TII.2021.3069459

[46] 
H. Gao, Z. Li, X. Yu, and J. Qiu, “Hierarchical multiobjective heuristic for PCB assembly optimization in a beamhead surface mounter,” IEEE Trans. Cybernetics, vol. 52, no. 7, pp. 6911–6924, 2022. doi: 10.1109/TCYB.2020.3040788

[47] 
Z. Li, K. Zhao, L. Zhang, X. Wu, T. Zhang, Q. Li, X. Li, and C.Y. Su, “Humanintheloop control of a wearable lower limb exoskeleton for stable dynamic walking,” IEEE/ASME Trans. Mechatronics, vol. 26, no. 5, pp. 2700–2711, 2021. doi: 10.1109/TMECH.2020.3044289

[48] 
Z. Li, C. Deng, and K. Zhao, “Humancooperative control of a wearable walking exoskeleton for enhancing climbing stair activities,” IEEE Trans. Industrial Electronics, vol. 67, no. 4, pp. 3086–3095, 2020. doi: 10.1109/TIE.2019.2914573

[49] 
Z. Li, Z. Ren, K. Zhao, C. Deng, and Y. Feng, “Humancooperative control design of a walking exoskeleton for body weight support,” IEEE Trans. Industrial Informatics, vol. 16, no. 5, pp. 2985–2996, 2020. doi: 10.1109/TII.2019.2900121
