Predictor control for wave PDE / nonlinear ODE cascaded system with boundary value-dependent propagation speed

Xiushan Cai; Yuhang Lin; Junfeng Zhang; Cong Lin

Kybernetika (2022)

  • Volume: 58, Issue: 3, page 400-425
  • ISSN: 0023-5954

Abstract

top
This paper investigates predictor control for wave partial differential equation (PDE) and nonlinear ordinary differential equation (ODE) cascaded system with boundary value-dependent propagation speed. A predictor control is designed first. A two-step backstepping transformation and a new time variable are employed to derive a target system whose stability is established using Lyapunov arguments. The equivalence between stability of the target and the original system is provided using the invertibility of the backstepping transformations. Stability of the closed-loop system is established by Lyapunov arguments.

How to cite

top

Cai, Xiushan, et al. "Predictor control for wave PDE / nonlinear ODE cascaded system with boundary value-dependent propagation speed." Kybernetika 58.3 (2022): 400-425. <http://eudml.org/doc/298881>.

@article{Cai2022,
abstract = {This paper investigates predictor control for wave partial differential equation (PDE) and nonlinear ordinary differential equation (ODE) cascaded system with boundary value-dependent propagation speed. A predictor control is designed first. A two-step backstepping transformation and a new time variable are employed to derive a target system whose stability is established using Lyapunov arguments. The equivalence between stability of the target and the original system is provided using the invertibility of the backstepping transformations. Stability of the closed-loop system is established by Lyapunov arguments.},
author = {Cai, Xiushan, Lin, Yuhang, Zhang, Junfeng, Lin, Cong},
journal = {Kybernetika},
keywords = {cascaded system; wave dynamics; boundary value-dependent; predictor control; backstepping transformation},
language = {eng},
number = {3},
pages = {400-425},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Predictor control for wave PDE / nonlinear ODE cascaded system with boundary value-dependent propagation speed},
url = {http://eudml.org/doc/298881},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Cai, Xiushan
AU - Lin, Yuhang
AU - Zhang, Junfeng
AU - Lin, Cong
TI - Predictor control for wave PDE / nonlinear ODE cascaded system with boundary value-dependent propagation speed
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 3
SP - 400
EP - 425
AB - This paper investigates predictor control for wave partial differential equation (PDE) and nonlinear ordinary differential equation (ODE) cascaded system with boundary value-dependent propagation speed. A predictor control is designed first. A two-step backstepping transformation and a new time variable are employed to derive a target system whose stability is established using Lyapunov arguments. The equivalence between stability of the target and the original system is provided using the invertibility of the backstepping transformations. Stability of the closed-loop system is established by Lyapunov arguments.
LA - eng
KW - cascaded system; wave dynamics; boundary value-dependent; predictor control; backstepping transformation
UR - http://eudml.org/doc/298881
ER -

References

top
  1. Bekiaris-Liberis, N., Krstic, M., , IEEE Trans. Automat. Control 59 (2014), 1555-1570. MR3225229DOI
  2. Bresch-Pietri, D., Krstic, M., , Automatica 50 (2014), 1407-1415. MR3198779DOI
  3. Cai, X., Yang, J., Liu, L., Zhang, J., , Asian J. Control (2021). DOI
  4. Cai, X., Wu, J., Zhan, X., Zhang, X., , Kybernetika 55 (2019), 727-739. MR4043545DOI
  5. Cai, X., Liao, L., Zhang, J., Zhang, W., Observer design for a class of nonlinear system in cascade with counter-conveting transport dynamics., Kybernetika 52 (2016), 76-88. MR3482612
  6. Cai, X., Krstic, M., , Int. J. Robust. Nonlinear Control 25 (2015), 222-251. Zbl1305.93167MR3293094DOI
  7. Cai, X., Krstic, M., , Automatica 68 (2016), 27-38. MR3483665DOI
  8. Cai, X., Diagne, M., , IEEE Trans. Automat. Control 66 (2021), 4401-4408. MR4308496DOI
  9. Diagne, M., Bekiaris-Liberis, N., Krstic, M., , Automatica 85 (2017), 362-373. MR3712879DOI
  10. Jansen, J., Nonlinear Dynamics of Oilwell Drillstrings., Ph.D. Thesis, Delfh University of Technology, 1993. 
  11. Krstic, M., , IEEE Trans. Automat. Control 55 (2010), 287-303. MR2604408DOI
  12. Lin, C., Cai, X., , IEEE Access 10 (2022), 35653-35664. DOI
  13. Meglio, F. Di, Argomedo, F. Bribiesca, Hu, L., Krstic, M., , Automatica 87 (2018), 281-289. MR3733925DOI
  14. Su, L., Wang, J., Krstic, M., , IEEE Trans. Automat. Control 63 (2018), 2633-2640. MR3845992DOI
  15. Su, L., Chen, S., Wang, J., Krstic, M., , Automatica 120 (2020), 109147(1-14). MR4130471DOI
  16. Saldivar, M., Mondie, S., Loiseau, J., Rasvan, V., Stick-slip oscillations in oilwell drillstrings: distributed parameter and neutral type retarded model approaches., In: Proc. 18th IFAC World Congress, Milano 2011, pp. 284-289. 
  17. Sagert, C., Meglio, F., Krstic, M., Rouchon, P., , In: IFAC Sympositium on System Structure and Control, France 2013, pp. 779-784. DOI
  18. Sontag, E., , IEEE Trans. Automat. Control 34 (1989), 435-443. MR0987806DOI

NotesEmbed ?

top

You must be logged in to post comments.