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Event-trigger-based Fault-tolerant Control of Uncertain Non-affine Systems with Predefined Performance

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  • Control Theory and Applications
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Abstract

Fault-tolerant control (FTC) of a non-affine system with uncertainties is one of critical issues in nonlinear control. In this paper, in the presence of unknown actuator failures, an event-trigger-based FTC scheme is proposed for such a nonlinear system with predefined performance. For actuator failures, a compensation mechanism is designed to alleviate their impacts. By utilizing a predefined performance function, higher tracking accuracy can be obtained. Meanwhile, an event-triggered mechanism with a time-varying threshold, depending on tracking error, reduces the number of communications for a controller-to-actuator channel. An adaptive event-triggered function is then proposed with the compensation mechanism to improve the self-adjusting ability of the triggered function. Also, extended state observers and tracking differentiators are utilized to reconstruct unknown dynamics of the system and to simplify high-order derivation of virtual control laws, respectively. The stability of the closed-loop system is analyzed by input-to-state practically stability. Finally, two simulation results are supplied to verify the effectiveness of the proposed control method.

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References

  1. Y. Yang, Y. Xiao, and T. Li, “A survey of autonomous underwater vehicle formation: Performance, formation control, and communication capability,” IEEE Communications Surveys & Tutorials, vol. 23, no. 2, pp. 815–841, 2021.

    Article  Google Scholar 

  2. X. Bu, “Air-breathing hypersonic vehicles funnel control using neural approximation of non-affine dynamics,” IEEE/ASME Transactions on Mechatronics, vol. 23, no. 5, pp. 2099–2108, 2018.

    Article  Google Scholar 

  3. T. Li, W. Bai, Q. Liu, Y. Long, and C. Chen, “Distributed fault-tolerant containment control protocols for the discrete-time multiagent systems via reinforcement learning method,” IEEE Transactions on Neural Networks and Learning Systems, pp. 1–13, 2021, DOI: https://doi.org/10.1109/TNNLS.2021.3121403

  4. H. Ma, H. Li, H. Liang, and G. Dong, “Adaptive fuzzy event-triggered control for stochastic nonlinear systems with full state constraints and actuator faults,” IEEE Transactions on Fuzzy Systems, vol. 27, no. 11, pp. 2242–2254, 2019.

    Article  Google Scholar 

  5. Y. Liang, H. Zhang, J. Duan, and S. Sun, “Event-triggered reinforcement learning H∞ control design for constrained-input nonlinear systems subject to actuator failures,” Information Sciences, vol. 543, pp. 273–295, 2021.

    Article  MATH  Google Scholar 

  6. D. Ye, M. Chen, and H. Yang, “Distributed adaptive event-triggered fault-tolerant consensus of multiagent systems with general linear dynamics,” IEEE Transactions on Cybernetics, vol. 49, no. 3, pp. 757–767, 2019.

    Article  Google Scholar 

  7. Z. Li, J. Dong, and C. Xi, “Event-triggered adaptive reliable guaranteed performance control for uncertain nonlinear systems with abrupt non-affine faults,” Applied Mathematics and Computation, vol. 380, pp. 1–14, 2020.

    Article  MATH  Google Scholar 

  8. C. Zhu, C. Li, X. Chen, K. Zhang, X. Xin, and H. Wei, “Event-triggered adaptive fault tolerant control for a class of uncertain nonlinear systems,” Entropy, vol. 9, no. 2, pp. 235–245, 2022.

    Google Scholar 

  9. X. Shao and D. Ye, “Fuzzy adaptive event-triggered secure control for stochastic nonlinear high-order mass subject to DoS attacks and actuator faults,” IEEE Transactions on Fuzzy Systems, vol. 29, no. 12, pp. 3812–3821, 2021.

    Article  Google Scholar 

  10. K. Lu, Z. Liu, and Y. Zhang, “Event-triggered neural control of nonlinear systems with rate-dependent hysteresis input based on a new filter,” IEEE Transactions on Neural Networks and Learning Systems, vol. 31, no. 4, pp. 1270–1284, 2020.

    Article  Google Scholar 

  11. C. Wang and L. Guo, “Adaptive compensation for infinite number of actuator failures with an application to flight control,” International Journal of Adaptive Control and Signal Processing, vol. 30, no. 3, pp. 443–455, 2016.

    Article  MATH  Google Scholar 

  12. J. Wang, Z. Liu, C. Chen, and Y. Zhang, “Fuzzy adaptive compensation control of uncertain stochastic nonlinear systems with actuator failures and input hysteresis,” IEEE Transactions on Cybernetics, vol. 49, no. 1, pp. 2–13, 2019.

    Article  Google Scholar 

  13. G. Lai, C. Wen, Z. Liu, Y. Zhang, C. Chen, and S. Xie, “Adaptive compensation for infinite number of actuator failures/faults using output feedback control,” Information Sciences, vol. 399, pp. 1–12, 2017.

    Article  MATH  Google Scholar 

  14. G. Lai, Z. Liu, C. Chen, Y. Zhang, and X. Chen, “Adaptive compensation for infinite number of time-varying actuator failures in fuzzy tracking control of uncertain nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 2, pp. 474–486, 2018.

    Article  Google Scholar 

  15. J. Han, “From PID to active disturbance rejection control,” IEEE Transactions on Industrial Electronics, vol. 56, no. 3, pp. 900–906, 2009.

    Article  Google Scholar 

  16. B. Guo and Z. Zhao, “On convergence of the nonlinear active disturbance rejection control for MIMO systems,” SIAM Journal on Control and Optimization, vol. 51, no. 2, pp. 1727–1757, 2013.

    Article  MATH  Google Scholar 

  17. B. Guo and Z. Zhao, “On the convergence of an extended state observer for nonlinear systems with uncertainty,” Systems & Control Letters, vol. 60, no. 6, pp. 420–430, 2011.

    Article  MATH  Google Scholar 

  18. Z. Zhao and B. Guo, “On active disturbance rejection control for nonlinear systems using time-varying gain,” European Journal of Control, vol. 23, pp. 62–70, 2015.

    Article  MATH  Google Scholar 

  19. B. Guo, Z. Wu, and H. Zhou, “Active disturbance rejection control approach to output-feedback stabilization of a class of uncertain nonlinear systems subject to stochastic disturbance,” IEEE Transactions on Automatic Control, vol. 61, no. 6, pp. 1613–1618, 2016.

    Article  MATH  Google Scholar 

  20. X. Ma, Y. Guo, and L. Chen, “Active disturbance rejection control for electric power steering system with assist motor variable mode,” Journal of the Franklin Institute, vol. 355, no. 3, pp. 1139–1155, 2018.

    Article  MATH  Google Scholar 

  21. Z. Chu, Y. Sun, C. Wu, and N. Sepehri, “Active disturbance rejection control applied to automated steering for lane keeping in autonomous vehicles,” Control Engineering Practice, vol. 74, pp. 13–21, 2018.

    Article  Google Scholar 

  22. N. Zhang, W. Gai, G. Zhang, and J. Zhang, “An active disturbance rejection control guidance law based collision avoidance for unmanned aerial vehicles,” Aerospace Science and Technology, vol. 77, pp. 658–669, 2018.

    Article  Google Scholar 

  23. Z. Jun, Y. Cheng, H. Du, D. Wu, M. Zhu, and X. Lin, “Active finite-time disturbance rejection control for attitude tracking of quad-rotor under input saturation,” Journal of the Franklin Institute, vol. 357, no. 16, pp. 11153–11170, 2020.

    Article  MATH  Google Scholar 

  24. Y. Xu, S. Tong, and Y. Li, “Prescribed performance fuzzy adaptive fault-tolerant control of non-linear systems with actuator faults,” IET Control Theory & Applications, vol. 8, no. 6, pp. 420–431, 2014.

    Article  Google Scholar 

  25. W. Wang, D. Wang, Z. Peng, and T. Li, “Prescribed performance consensus of uncertain nonlinear strict-feedback systems with unknown control directions,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 46, no. 9, pp. 1279–1286, 2016.

    Article  Google Scholar 

  26. X. Wang, X. Yin, and F. Shen, “Disturbance observer based adaptive neural prescribed performance control for a class of uncertain nonlinear systems with unknown backlashlike hysteresis,” Neurocomputing, vol. 299, pp. 10–19, 2018.

    Article  Google Scholar 

  27. J. Zhang and G. Yang, “Fuzzy adaptive output feedback control of uncertain nonlinear systems with prescribed performance,” IEEE Transactions on Cybernetics, vol. 48, no. 5, pp. 1342–1354, 2018.

    Article  Google Scholar 

  28. K. Zhao, Y. Song, and Y. Wang, “Regular error feedback based adaptive practical prescribed time tracking control of normal-form nonaffine systems,” Journal of the Franklin Institute, vol. 356, no. 5, pp. 2759–2779, 2019.

    Article  MATH  Google Scholar 

  29. Y. Yang, J. Tan, and D. Yue, “Prescribed performance tracking control of a class of uncertain pure-feedback nonlinear systems with input saturation,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 50, no. 5, pp. 1733–1745, 2020.

    Article  Google Scholar 

  30. X. Wang and M. Lemmon, “Event-triggering in distributed networked control systems,” IEEE Transactions on Automatic Control, vol. 56, no. 3, pp. 586–601, 2011.

    Article  MATH  Google Scholar 

  31. D. Dimarogonas, E. Frazzoli, and K. Johansson, “Distributed event-triggered control for multi-agent systems,” IEEE Transactions on Automatic Control, vol. 57, no. 5, pp. 1291–1297, 2012.

    Article  MATH  Google Scholar 

  32. C. Wang, C. Wen, and Y. Lin, “Decentralized adaptive backstepping control for a class of interconnected nonlinear systems with unknown actuator failures,” Journal of the Franklin Institute, vol. 352, no. 3, pp. 835–850, 2015.

    Article  MATH  Google Scholar 

  33. C. Wang, C. Wen, and Y. Lin, “Adaptive actuator failure compensation for a class of nonlinear systems with unknown control direction,” IEEE Transactions on Automatic Control, vol. 62, no. 1, pp. 385–392, 2016.

    Article  MATH  Google Scholar 

  34. Y. Choi and S. Yoo, “Event-triggered decentralized adaptive fault-tolerant control of uncertain interconnected nonlinear systems with actuator failures,” ISA Transactions, vol. 77, pp. 77–89, 2018.

    Article  Google Scholar 

  35. L. Xing, C. Wen, Z. Liu, H. Su, and J. Cai, “Adaptive compensation for actuator failures with event-triggered input,” Automatica, vol. 85, pp. 129–136, 2017.

    Article  MATH  Google Scholar 

  36. Y. Li and G. Yang, “Adaptive neural control of pure-feedback nonlinear systems with event-triggered communications,” IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 12, pp. 6242–6251, 2018.

    Article  Google Scholar 

  37. X. Yang and H. He, “Adaptive critic designs for event-triggered robust control of nonlinear systems with unknown dynamics,” IEEE Transactions on Cybernetics, vol. 49, no. 6, pp. 2255–2267, 2018.

    Article  Google Scholar 

  38. C. Zhang and G. Yang, “Event-triggered adaptive output feedback control for a class of uncertain nonlinear systems with actuator failures,” IEEE Transactions on Cybernetics, vol. 50, no. 1, pp. 201–210, 2018.

    Article  Google Scholar 

  39. L. Xing, C. Wen, Z. Liu, H. Su, and J. Cai, “Event-triggered output feedback control for a class of uncertain nonlinear systems,” IEEE Transactions on Automatic Control, vol. 64, no. 1, pp. 290–297, 2018.

    Article  MATH  Google Scholar 

  40. L. Wang, M. Basin, H. Li, and R. Lu, “Observer-based composite adaptive fuzzy control for nonstrict-feedback systems with actuator failures,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 4, pp. 2336–2347, 2018.

    Article  Google Scholar 

  41. H. Pan, H. Li, W. Sun, and Z. Wang, “Adaptive fault-tolerant compensation control and its application to nonlinear suspension systems,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 50, no. 5, pp. 1766–1776, 2020.

    Article  Google Scholar 

  42. Y. Liu and W. Wang, “Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems,” Information Sciences, vol. 177, no. 18, pp. 3901–3917, 2007.

    Article  MATH  Google Scholar 

  43. M. Wang, X. Liu, and P. Shi, “Adaptive neural control of pure-feedback nonlinear time-delay systems via dynamic surface technique,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 41, no. 6, pp. 1681–1692, 2011.

    Article  Google Scholar 

  44. W. Zhang and W. Wei, “Disturbance-observer-based finite-time adaptive fuzzy control for non-triangular switched nonlinear systems with input saturation,” Information Sciences, vol. 561, pp. 152–167, 2021.

    Article  Google Scholar 

  45. Z. Li, J. Dong, and C. Xi, “Event-triggered adaptive reliable guaranteed performance control for uncertain nonlinear systems with abrupt non-affine faults,” Applied Mathematics and Computation, vol. 380, 125256, 2020.

    Article  MATH  Google Scholar 

  46. J. Yu, P. Shi, and L. Zhao, “Finite-time command filtered backstepping control for a class of nonlinear systems,” Automatica, vol. 92, pp. 173–180, 2018.

    Article  MATH  Google Scholar 

  47. J. Yu, P. Shi, W. Dong, and C. Lin, “Adaptive fuzzy control of nonlinear systems with unknown dead zones based on command filtering,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 1, pp. 46–55, 2016.

    Article  Google Scholar 

  48. M. Chen, H. Wang, X. Liu, T. Hayat, and F. Alsaadi, “Adaptive finite-time dynamic surface tracking control of nonaffine nonlinear systems with dead zone,” Neurocomputing, vol. 366, pp. 66–73, 2019.

    Article  Google Scholar 

  49. D. Swaroop, J. Hedrick, P. Yip, and J. Gerdes, “Dynamic surface control for a class of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 45, no. 10, pp. 1893–1899, 2000.

    Article  MATH  Google Scholar 

  50. C. Ren, Y. Ding, and S. Ma, “A structure-improved extended state observer based control with application to an omnidirectional mobile robot,” ISA Transactions, vol. 101, pp. 335–345, 2020.

    Article  Google Scholar 

  51. S. Diao, W. Sun, and S. Su, “Neural-based adaptive event-triggered tracking control for flexible-joint robots with random noises,” International Journal of Robust and Nonlinear Control, vol. 32, no. 5, pp. 2722–2740, 2022.

    Article  Google Scholar 

  52. S. Diao, W. Sun, S. Su, and J. Xia, “Adaptive fuzzy event-triggered control for single-link flexible-joint robots with actuator failures,” IEEE Transactions on Cybernetics, vol. 52, no. 8, pp. 7231–7241, 2022.

    Article  Google Scholar 

  53. Y. Li, F. Qu, and S. Tong, “Observer-based fuzzy adaptive finite-time containment control of nonlinear multiagent systems with input delay,” IEEE Transactions on Cybernetics, vol. 51, no. 1, pp. 126–137, 2020.

    Article  Google Scholar 

  54. Y. Li, X. Shao, and S. Tong, “Adaptive fuzzy prescribed performance control of nontriangular structure nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 28, no. 10, pp. 2416–2426, 2019.

    Article  Google Scholar 

  55. Y. Yang, X. Si, and D. Yue, “Trigger-based tracking control for a class of uncertain nonlinear systems via an event-triggered extended state observer,” International Journal of Robust and Nonlinear Control, vol. 31, no. 1, pp. 287–305, 2021.

    Article  Google Scholar 

  56. A. González, A. Cuenca, V. Balaguer, and P. García, “Event-triggered predictor-based control with gain-scheduling and extended state observer for networked control systems,” Information Sciences, vol. 491, pp. 90–108, 2019.

    Article  MATH  Google Scholar 

  57. L. Liu, W. Zhang, D. Wang, and Z. Peng, “Event-triggered extended state observers design for dynamic positioning vessels subject to unknown sea loads,” Ocean Engineering, vol. 209, 107242, 2020.

    Article  Google Scholar 

  58. D. Ran, X. Chen, A. Ruiter, and B. Xiao, “Adaptive extended-state observer-based fault tolerant attitude control for spacecraft with reaction wheels,” Acta Astronautica, vol. 145, pp. 501–514, 2018.

    Article  Google Scholar 

  59. B. Li, K. Qin, B. Xiao, and Y. Yang, “Finite-time extended state observer based fault tolerant output feedback control for attitude stabilization,” ISA Transactions, vol. 91, pp. 11–20, 2019.

    Article  Google Scholar 

  60. Y. Huang and J. Han, “Analysis and design for the second order nonlinear continuous extended states observer,” Chinese Science Bulletin, vol. 45, no. 21, pp. 1938–1944, 2000.

    Article  Google Scholar 

  61. J. Han, Active Disturbance Rejection Control Technique-The Technique for Estimating and Compensating the Uncertainties, National Defense Industry Press, Beijing, 2008.

    Google Scholar 

  62. B. Guo and Z. Zhao, “Weak convergence of nonlinear high-gain racking differentiator,” IEEE Transactions on Automatic Control, vol. 58, no. 4, pp. 1074–1080, 2013.

    Article  MATH  Google Scholar 

  63. E. Sontag, “Further results about input-state stabilization,” IEEE Transactions on Automatic Control, vol. 35, no. 4, pp. 473–476, 1990.

    Article  MATH  Google Scholar 

  64. E. Sontag, “On the input-to-state stability property,” European Journal of Control, vol. 1, no. 1, pp. 24–36, 1995.

    Article  MATH  Google Scholar 

  65. J. Ma, Z. Zheng, and P. Li, “Adaptive dynamic surface control of a class of nonlinear systems with unknown direction control gains and input saturation,” IEEE Transactions on Cybernetics, vol. 45, no. 4, pp. 728–741, 2014.

    Article  Google Scholar 

  66. Z. Shen, Y. Bi, Y. Wang, and C. Guo, “MLP neural network-based recursive sliding mode dynamic surface control for trajectory tracking of fully actuated surface vessel subject to unknown dynamics and input saturation,” Neurocomputing, vol. 377, pp. 103–112, 2020.

    Article  Google Scholar 

  67. C. Chen, Y. Hu, and J. Wu, “Active disturbance rejection control for non-affine pure feedback nonlinear systems,” Acta Automatica Sinica, vol. 40, no. 7, pp. 1528–1536, 2014.

    Google Scholar 

  68. Y. Li, Y. Liu, and S. Tong, “Observer-based neuro-adaptive optimized control of strict-feedback nonlinear systems with state constraints,” IEEE Transactions on Neural Networks and Learning Systems, vol. 33, no. 7, pp. 3131–3145, 2022.

    Article  Google Scholar 

  69. L. Xing, C. Wen, Z. Liu, H. Su, and J. Cai, “Adaptive compensation for actuator failures with event-triggered input,” Automatica, vol. 85, pp. 129–136, 2017.

    Article  MATH  Google Scholar 

  70. J. Chen, S. Hara, and G. Chen, “Best tracking and regulation performance under control energy constraint,” IEEE Transactions on Automatic Control, vol. 48, no. 8, pp. 1320–1336, 2003.

    Article  MATH  Google Scholar 

  71. T. Shen, Robot Robust Control Foundation, Tsinghua University Press, Beijing, 2000.

    Google Scholar 

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Authors and Affiliations

  1. College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China

    Yang Yang, Yuwei Zhang, Zijin Wang & Xuefeng Si

  2. Key Laboratory of Industrial Internet of Things and Networked Control, Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Yang Yang

  3. School of Mathematical Sciences, Queensland University of Technology, Brisbane, 4001, Australia

    Jinran Wu

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Correspondence to Yang Yang.

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This work was supported in part by National Natural Science Foundation of China under Grant 61873130, in part by Natural Science Foundation of Jiangsu Province under Grant BK20191377, in part by Key projects of Natural Science Foundation of Hebei Province under Grant E2020203139, in part by the 1311 Talent Project of Nanjing University of Posts and Telecommunications, in part by Natural Science Foundation of Nanjing University of Posts and Telecommunications under Grant NY220194, NY221082 and NY222144, and in part by the foundation from Key Laboratory of Industrial Internet of Things and Networked Control of the Ministry of Education of China under Grant 2021FF01.

Yang Yang received his B.E., M.E., and Ph.D. degrees in automatic control from Dalian Maritime University, Dalian, China, in 2008, 2010, and 2013, respectively. From 2018 to 2019, he held a visiting research fellow position at the School of Electrical Engineering and Computer Science, Queensland University of Technology, Brisbane QLD, Australia. He is currently an Associate Professor with the College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications (NJUPT), Nanjing, China. His research interests include nonlinear control theory and intelligent control. Dr. Yang was a recipient of the National Scholarship for Ph.D. candidates, the HOSCO Special Award, the Jiangsu Government Scholarship for Overseas Studies, the IET CSR Best Paper Award of 2019 Chinese Automation Congress, the Excellent Postdoctoral Research Fellow Award of NJUPT, and the 1311 Talent Project at NJUPT. He serves as a reviewer for various peer-reviewed journals.

Yuwei Zhang is currently pursuing her master’s degree in control theory and control engineering at Nanjing University of Posts and Telecommunications, Nanjing, China. Her current research interests include nonlinear control theory.

Zijin Wang is currently pursuing a master’s degree in control theory and control engineering at Nanjing University of Posts and Telecommunications, Nanjing, China. His current research interests include nonlinear control theory.

Jinran Wu is pursuing a Ph.D. degree in statistics at the School of Mathematical Sciences and the ARC Centre of Excellence for Mathematical & Statistical Frontiers, Queensland University of Technology, Brisbane QLD, Australia. He was awarded his bachelor’s degree from Anhui University, China in 2014, and his master’s degree from Lanzhou University, China in 2017. He is interested in the robust statistical learning and engineering optimisations. He was awarded the Australian Government Research Training Program (RTP) Stipend (International), 2018.

Xuefeng Si is currently pursuing a master’s degree in control theory and control engineering at Nanjing University of Posts and Telecommunications, Nanjing, China. His current research interests include smart grid control.

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Yang, Y., Zhang, Y., Wang, Z. et al. Event-trigger-based Fault-tolerant Control of Uncertain Non-affine Systems with Predefined Performance. Int. J. Control Autom. Syst. 21, 519–535 (2023). https://doi.org/10.1007/s12555-021-1007-y

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