Modelling and optimal control of networked systems with stochastic communication protocols

Chaoqun Zhu; Bin Yang; Xiang Zhu

Kybernetika (2020)

  • Volume: 56, Issue: 2, page 239-260
  • ISSN: 0023-5954

Abstract

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This paper is concerned with the finite and infinite horizon optimal control issue for a class of networked control systems with stochastic communication protocols. Due to the limitation of networked bandwidth, only the limited number of sensors and actuators are allowed to get access to network mediums according to stochastic access protocols. A discrete-time Markov chain with a known transition probability matrix is employed to describe the scheduling behaviors of the stochastic access protocols, and the networked systems are modeled as a Markov jump system based on the augmenting technique. In such a framework, both the approaches of stochastic analysis and dynamic programming are utilized to derive the optimal control sequences satisfying the quadratic performance index. Moreover, the optimal controller gains are characterized by solving the solutions to coupled algebraic Riccati equations. Finally, a numerical example is provided to demonstrate the correctness and effectiveness of the proposed results.

How to cite

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Zhu, Chaoqun, Yang, Bin, and Zhu, Xiang. "Modelling and optimal control of networked systems with stochastic communication protocols." Kybernetika 56.2 (2020): 239-260. <http://eudml.org/doc/297354>.

@article{Zhu2020,
abstract = {This paper is concerned with the finite and infinite horizon optimal control issue for a class of networked control systems with stochastic communication protocols. Due to the limitation of networked bandwidth, only the limited number of sensors and actuators are allowed to get access to network mediums according to stochastic access protocols. A discrete-time Markov chain with a known transition probability matrix is employed to describe the scheduling behaviors of the stochastic access protocols, and the networked systems are modeled as a Markov jump system based on the augmenting technique. In such a framework, both the approaches of stochastic analysis and dynamic programming are utilized to derive the optimal control sequences satisfying the quadratic performance index. Moreover, the optimal controller gains are characterized by solving the solutions to coupled algebraic Riccati equations. Finally, a numerical example is provided to demonstrate the correctness and effectiveness of the proposed results.},
author = {Zhu, Chaoqun, Yang, Bin, Zhu, Xiang},
journal = {Kybernetika},
keywords = {networked control systems; optimal control; stochastic communication protocol; markov chain},
language = {eng},
number = {2},
pages = {239-260},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Modelling and optimal control of networked systems with stochastic communication protocols},
url = {http://eudml.org/doc/297354},
volume = {56},
year = {2020},
}

TY - JOUR
AU - Zhu, Chaoqun
AU - Yang, Bin
AU - Zhu, Xiang
TI - Modelling and optimal control of networked systems with stochastic communication protocols
JO - Kybernetika
PY - 2020
PB - Institute of Information Theory and Automation AS CR
VL - 56
IS - 2
SP - 239
EP - 260
AB - This paper is concerned with the finite and infinite horizon optimal control issue for a class of networked control systems with stochastic communication protocols. Due to the limitation of networked bandwidth, only the limited number of sensors and actuators are allowed to get access to network mediums according to stochastic access protocols. A discrete-time Markov chain with a known transition probability matrix is employed to describe the scheduling behaviors of the stochastic access protocols, and the networked systems are modeled as a Markov jump system based on the augmenting technique. In such a framework, both the approaches of stochastic analysis and dynamic programming are utilized to derive the optimal control sequences satisfying the quadratic performance index. Moreover, the optimal controller gains are characterized by solving the solutions to coupled algebraic Riccati equations. Finally, a numerical example is provided to demonstrate the correctness and effectiveness of the proposed results.
LA - eng
KW - networked control systems; optimal control; stochastic communication protocol; markov chain
UR - http://eudml.org/doc/297354
ER -

References

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  1. Hespanha, J. P., Naghshtabrizi, P., Xu, Y., , Proc. IEEE 95 (2007), 138-162. DOI
  2. Zhang, X.-M., Han, Q.-L., Ge, X., Ding, D., Ding, L., Yue, D., Peng, C., , IEEE/CAA J. Automat. Sinica (2019). MR3841465DOI
  3. Ding, D., Han, Q.-L., Wang, Z., Ge, X., , IEEE Trans. Industr. Inform. 15 (2019), 2483-2499. DOI
  4. Ding, L., Han, Q.-L., Zhang, X.-M., , IEEE Trans. Industr. Inform. 15 (2019), 3910-3922. DOI
  5. Shu, S., Lin, F., , IEEE Trans. Automat. Control 62 (2017), 190-205. MR3598003DOI
  6. Ge, X., Han, Q.-L., Zhang, X.-M., Ding, L., Yang, F., , IEEE Trans. Cybernet. (2019). DOI
  7. Song, H., and, S.-C. Chen, Yam, Y., , IEEE Trans. Cybernet. 47 (2017), 3669-3679. DOI
  8. Okano, K., Wakaiki, M., Yang, G., Hespanha, J. P., , IEEE Trans. Automat. Control 63 (2018), 1708-1723. MR3805143DOI
  9. Ding, L., Han, Q.-L., Ge, X., Zhang, X.-M., , IEEE Trans. Cybernet. 48 (2018), 1110-1123. MR3554944DOI
  10. Han, Q.-L., Liu, Y., Yang, F., , IEEE Trans. Neural Networks Learning Syst. 27 (2016), 426-434. MR3463952DOI
  11. Xue, B., Li, N., Li, S., Zhu, Q., , IEEE Trans. Industr. Electron. 60 (2013), 3318-3327. DOI
  12. Liu, K., Fridman, E., Hetel, L., , Systems Control Lett. 61 (2012), 666-675. MR2913495DOI
  13. Zhang, L., Hristu-Varsakelis, D., , Automatica 42 (2006), 953-958. MR2227598DOI
  14. Longo, S., Herrmann, G., Barber, P., , IEEE Trans. Control Systems Technol. 20 (2012), 1613-1621. DOI
  15. Hristu-Varsakelis, D., Zhang, L., , Int. J. Control 81 (2008), 1266-1280. MR2424496DOI
  16. Zhang, W.-A., Yu, L., Feng, G., , Automatica 47 (2011), 1992-2000. MR2886812DOI
  17. Walsh, G. C., Ye, H., Bushnell, L. G., , IEEE Trans. Control Systems Technol. 10 (2002), 438-446. DOI
  18. Guo, G., Jin, H., , Int. J. Robust Nonlinear Control 20 (2010), 140-1426. MR2680715DOI
  19. Guo, G., , Int. J. Control 84 (2011), 78-93. MR2773880DOI
  20. Zhang, W.-A., Yu, L., Feng, G., , Int. J. Robust Nonlinear Control 25 (2015), 3072-3085. MR3415520DOI
  21. Zou, L., Wang, Z., Han, Q.-L., Zhou, D., , IEEE Trans. Automat. Control 62 (2017), 6582-6588. MR3743543DOI
  22. Guo, G., Lu, Z., Han, Q.-L., , IEEE Trans. Automat. Control 57 (2012), 1799-1804. MR2945943DOI
  23. Zou, L., Wang, Z., Han, Q.-L., Zhou, D., , IEEE Trans. Automat. Control 64 (2019), 720-727. MR3912120DOI
  24. Zhu, C., Guo, G., Yang, B., Wang, Z., , Math. Problems Engrg. 2015 (2015), 1-11. MR3319209DOI
  25. Zou, L., Wang, Z., Gao, H., , Automatica 63 (2016), 366-373. MR3430004DOI
  26. Zhang, J., Peng, C., Fei, M.-R., Tian, Y.-C., , J. Franklin Inst. 354 (2017), 3838-3853. MR3649255DOI
  27. Ding, D., Wang, Z., Han, Q.-L., , Automatica 106 (2019), 221-229. MR3952583DOI
  28. Long, Y., Liu, S., Xie, L., , IEEE Control Systems Lett. 1 (2017), 176-181. DOI
  29. Donkers, M. C. F., Heemels, W. P. M. H., Bernardini, D., Bemporad, A., Shneer, V., , Automatica 48 (2012), 917-925. MR2912818DOI
  30. Xu, Y., Su, H., Pan, Y.-J., Wu, Z.-G., Xu, W., , J. Franklin Inst. 350 (2013), 2013-2027. MR3084055DOI
  31. Yaz, E., , IEEE Trans. Automat. Control 33 (1988), 407-410. DOI
  32. Running, K. D., Martins, N. C., , IEEE Trans. Automat. Control 54 (2009), 2260-2266. MR2568681DOI
  33. Costa, O. L. V., Marques, R. P., , Math. Control Signals Syst. 12 (1999), 167-195. MR1692164DOI
  34. Yang, F., Wang, Z., Hung, Y. S., Gani, M., , IEEE Trans. Automat. Control 51 (2006), 511-518. MR2205692DOI
  35. Guo, G., Lu, Z., , Euroup. J. Control 18 (2012), 323-330. MR3012037DOI

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