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Event-triggered tracking control for a class of nonholonomic systems in chained form

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Abstract

In this study, the event-triggered asymptotic tracking control problem is considered for a class of nonholonomic systems in chained form for the time-varying reference input. First, to eliminate the ripple phenomenon caused by the imprecise compensation of the time-varying reference input, a novel time-varying event-triggered piecewise continuous control law and a triggering mechanism with a time-varying triggering function are developed. Second, an explicit integral input-to-state stable Lyapunov function is constructed for the time-varying closed-loop system regarding the sampling error as the external input. The origin of the closed-loop system is shown to be uniformly globally asymptotically stable for any global exponential decaying threshold signals, which in turn rules out the Zeno behavior. Moreover, infinitely fast sampling can be avoided by appropriately tuning the exponential convergence rate of the threshold signal. A numerical simulation example is provided to illustrate the proposed control approach.

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References

  1. Shen D B, Sun Z D, Sun W J. Leader-follower formation control without leader’s velocity information. Sci China Inf Sci, 2014, 57: 092202

    Article  MATH  Google Scholar 

  2. Guo X, Ma S G, Li B, et al. Modeling and optimal torque control of a snake-like robot based on the fiber bundle theory. Sci China Inf Sci, 2015, 58: 032205

    Article  MATH  Google Scholar 

  3. He X D, Geng Z Y. Leader-follower formation control of underactuated surface vessels. Sci China Inf Sci, 2022, 65: 209201

    Article  MathSciNet  Google Scholar 

  4. Wang J, Wang T, Yao C, et al. Active tension optimal control for WT wheelchair robot by using a novel control law for holonomic or nonholonomic systems. Sci China Inf Sci, 2014, 57: 112203

    Article  Google Scholar 

  5. Qu Z. Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles. London: Springer-Verlag, 2009

    MATH  Google Scholar 

  6. Brockett R W. Asymptomtic stability and feedback stabilization. In: Differential Geometric Control Theory. Boston: Birkhauser, 1983. 181–191

    Google Scholar 

  7. Kolmanovsky I, McClamroch N H. Developments in nonholonomic control problems. IEEE Control Syst Mag, 1995, 15: 20–36

    Article  Google Scholar 

  8. Astolfi A. Discontinuous control of nonholonomic systems. Syst Control Lett, 1996, 27: 37–45

    Article  MathSciNet  MATH  Google Scholar 

  9. Morin P, Samson C. Application of backstepping techniques to the time-varying exponential stabilisation of chained form systems. Eur J Control, 1997, 3: 15–36

    Article  MATH  Google Scholar 

  10. Marchand N, Alamir M. Discontinuous exponential stabilization of chained form systems. Automatica, 2003, 39: 343–348

    Article  MathSciNet  MATH  Google Scholar 

  11. Wang J, Qu Z H, Hull R A, et al. Cascaded feedback linearization and its application to stabilization of nonholonomic systems. Syst Control Lett, 2007, 56: 285–295

    Article  MathSciNet  MATH  Google Scholar 

  12. Wu K, Su J Y, Sun C Y. Output feedback control for mobile robot systems with significant external disturbances. Sci China Inf Sci, 2020, 63: 199201

    Article  Google Scholar 

  13. Kanayama Y, Kimura Y, Miyazaki F, et al. A stable tracking control method for an autonomous mobile robot. In: Proceedings of IEEE International Conference on Robotics and Automation, Cincinnati, 1990. 384–389

  14. Jiang Z P, Nijmeijer H. Tracking control of mobile robots: a case study in backstepping. Automatica, 1997, 33: 1393–1399

    MathSciNet  MATH  Google Scholar 

  15. Jiang Z P, Nijmeijer H. A recursive technique for tracking control of nonholonomic systems in chained form. IEEE Trans Automat Contr, 1999, 44: 265–279

    Article  MathSciNet  MATH  Google Scholar 

  16. Lefeber E, Robertsson A, Nijmeijer H. Linear controllers for exponential tracking of systems in chained-form. Int J Robust Nonlinear Control, 2000, 10: 243–263

    Article  MathSciNet  MATH  Google Scholar 

  17. Fu J, Chai T Y, Su C Y, et al. Motion/force tracking control of nonholonomic mechanical systems via combining cascaded design and backstepping. Automatica, 2013, 49: 3682–3686

    Article  MathSciNet  MATH  Google Scholar 

  18. Maghenem M, Loría A, Panteley E. A cascades approach to formation-tracking stabilization of force-controlled autonomous vehicles. IEEE Trans Automat Contr, 2018, 63: 2662–2669

    Article  MathSciNet  MATH  Google Scholar 

  19. Yu X, Liu L. Leader-follower formation of vehicles with velocity constraints and local coordinate frames. Sci China Inf Sci, 2017, 60: 070206

    Article  Google Scholar 

  20. Fu J J, Lv Y Z, Yu W W. Robust adaptive time-varying region tracking control of multi-robot systems. Sci China Inf Sci, 2023, 66: 159202

    Article  Google Scholar 

  21. Zhang P P, Liu T F, Jiang Z P. Systematic design of robust event-triggered state and output feedback controllers for uncertain nonholonomic systems. IEEE Trans Automat Contr, 2020, 66: 213–228

    Article  MathSciNet  MATH  Google Scholar 

  22. Postoyan R, Bragagnolo M C, Galbrun E, et al. Event-triggered tracking control of unicycle mobile robots. Automatica, 2015, 52: 302–308

    Article  MathSciNet  MATH  Google Scholar 

  23. Sun Z Q, Dai L, Xia Y Q, et al. Event-based model predictive tracking control of nonholonomic systems with coupled input constraint and bounded disturbances. IEEE Trans Automat Contr, 2018, 63: 608–615

    Article  MathSciNet  MATH  Google Scholar 

  24. Zhang P P, Liu T F, Jiang Z P. Tracking control of unicycle mobile robots with event-triggered and self-triggered feedback. IEEE Trans Automat Contr, 2022. doi: https://doi.org/10.1109/TAC.2022.3173932

  25. Chen X, Hao F, Ma B L. Periodic event-triggered cooperative control of multiple non-holonomic wheeled mobile robots. IET Control Theor Appl, 2017, 11: 890–899

    Article  MathSciNet  Google Scholar 

  26. Liu Z X, Wang L, Wang J H, et al. Distributed sampled-data control of nonholonomic multi-robot systems with proximity networks. Automatica, 2017, 77: 170–179

    Article  MathSciNet  MATH  Google Scholar 

  27. Chu X, Peng Z X, Wen G G, et al. Distributed formation tracking of nonholonomic autonomous vehicles via event-triggered and sampled-data method. Int J Control, 2019, 92: 2243–2254

    Article  MathSciNet  MATH  Google Scholar 

  28. Yang J Y, Xiao F, Chen T W. Event-triggered formation tracking control of nonholonomic mobile robots without velocity measurements. Automatica, 2020, 112: 108671

    Article  MathSciNet  MATH  Google Scholar 

  29. Franklin G, Emami-Naeini A. Design of ripple-free multivariable robust servomechanisms. IEEE Trans Automat Contr, 1986, 31: 661–664

    Article  MATH  Google Scholar 

  30. Xu L, Su Y F, Cai H. Event-based tracking of nonholonomic systems in chained form. In: Proceedings of the 41st Chinese Control Conference, Hefei, 2022. 728–733

  31. Wang Y, Miao Z Q, Cheng Y. Simultaneous stabilization and tracking of wheeled mobile robots via chained form. In: Proceedings of the 11th IEEE International Conference on Control & Automation, Taiwan, 2014. 643–648

  32. Liu W, Huang J. Output regulation of linear systems via sampled-data control. Automatica, 2020, 113: 108684

    Article  MathSciNet  MATH  Google Scholar 

  33. Liu T F, Jiang Z P. Event-based control of nonlinear systems with partial state and output feedback. Automatica, 2015, 53: 10–22

    Article  MathSciNet  MATH  Google Scholar 

  34. Malisoff M, Mazenc F. Constructions of Strict Lyapunov Functions. London: Springer-Verlag, 2009

    Book  MATH  Google Scholar 

  35. Maghenem M, Loría A, Panteley E. A robust δ-persistently exciting controller for leader-follower tracking-agreement of multiple vehicles. Eur J Control, 2018, 40: 1–12

    Article  MathSciNet  MATH  Google Scholar 

  36. Lin Y, Sontag E D, Wang Y. A smooth converse Lyapunov theorem for robust stability. SIAM J Control Optim, 1996, 34: 124–160

    Article  MathSciNet  MATH  Google Scholar 

  37. Yu H, Hao F, Chen X. On event-triggered control for integral input-to-state stable systems. Syst Control Lett, 2019, 123: 24–32

    Article  MathSciNet  MATH  Google Scholar 

  38. Spong M W, Hutchinson S, Vidyasagar M. Robot Modeling and Control. New York: Wiley, 2006

    Google Scholar 

  39. Zhang Y, Su Y F. Consensus of hybrid linear multi-agent systems with periodic jumps. Sci China Inf Sci, 2023, 66: 179204

    Article  Google Scholar 

  40. Zhang G Q, Yao M Q, Shan Q H, et al. Observer-based asynchronous self-triggered control for a dynamic positioning ship with the hysteresis input. Sci China Inf Sci, 2022, 65: 212206

    Article  MathSciNet  Google Scholar 

  41. Lee T C, Tsai C Y, Song K T. Fast parking control of mobile robots: a motion planning approach with experimental validation. IEEE Trans Contr Syst Technol, 2004, 12: 661–676

    Article  Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 62173092, 62173149).

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Authors and Affiliations

  1. Center for Discrete Mathematics and Theoretical Computer Science, Fuzhou University, Fuzhou, 350116, China

    Liang Xu

  2. College of Computer and Data Science, Fuzhou University, Fuzhou, 350116, China

    Youfeng Su

  3. School of Automation Science and Engineering, South China University of Technology, Guangzhou, 510641, China

    He Cai

Authors
  1. Liang Xu
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  2. Youfeng Su
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  3. He Cai
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Correspondence to Youfeng Su.

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Xu, L., Su, Y. & Cai, H. Event-triggered tracking control for a class of nonholonomic systems in chained form. Sci. China Inf. Sci. 66, 172201 (2023). https://doi.org/10.1007/s11432-022-3648-8

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  • DOI: https://doi.org/10.1007/s11432-022-3648-8

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