Decentralized control for large-scale systems with time-varying delay and unmatched uncertainties

Wen-Jeng Liu

Kybernetika (2011)

  • Volume: 47, Issue: 2, page 285-299
  • ISSN: 0023-5954

Abstract

top
Many real-world systems contain uncertainties and with time-varying delays, also, they have become larger and more complicated. Hence, a new decentralized variable structure control law is proposed for a class of uncertain large-scale system with time varying delay in the interconnection and time varying unmatched uncertainties in the state matrix. The proposed decentralized control law for the large-scale time-varying delay system is realized independently through the delayed terms and it can drive the trajectories of the investigated systems onto the sliding mode. Further, the proposed control law can be successfully applied to stabilize a class of uncertain large-scale time-varying delay system with matched and unmatched uncertainties. The so-called sliding coefficient matching condition can be extended for the decentralized variable structure control of the uncertain large-scale time-varying delay systems. Furthermore, in the sliding mode, the investigated system with matched and unmatched uncertainties still bears the insensitivity to the uncertainties and disturbances, which is the same as the systems with just matched uncertainties do. Finally, an illustrative example is given to verify the validity of the proposed decentralized variable structure control law. It has been shown that the proposed decentralized control law is effective for all subsystems of the investigated system. However, the traditional decentralized variable structure control law is not applicable to the investigated system with unmatched uncertainties. It is worth noting that the traditional large-scale system is only a special case in this work.

How to cite

top

Liu, Wen-Jeng. "Decentralized control for large-scale systems with time-varying delay and unmatched uncertainties." Kybernetika 47.2 (2011): 285-299. <http://eudml.org/doc/197038>.

@article{Liu2011,
abstract = {Many real-world systems contain uncertainties and with time-varying delays, also, they have become larger and more complicated. Hence, a new decentralized variable structure control law is proposed for a class of uncertain large-scale system with time varying delay in the interconnection and time varying unmatched uncertainties in the state matrix. The proposed decentralized control law for the large-scale time-varying delay system is realized independently through the delayed terms and it can drive the trajectories of the investigated systems onto the sliding mode. Further, the proposed control law can be successfully applied to stabilize a class of uncertain large-scale time-varying delay system with matched and unmatched uncertainties. The so-called sliding coefficient matching condition can be extended for the decentralized variable structure control of the uncertain large-scale time-varying delay systems. Furthermore, in the sliding mode, the investigated system with matched and unmatched uncertainties still bears the insensitivity to the uncertainties and disturbances, which is the same as the systems with just matched uncertainties do. Finally, an illustrative example is given to verify the validity of the proposed decentralized variable structure control law. It has been shown that the proposed decentralized control law is effective for all subsystems of the investigated system. However, the traditional decentralized variable structure control law is not applicable to the investigated system with unmatched uncertainties. It is worth noting that the traditional large-scale system is only a special case in this work.},
author = {Liu, Wen-Jeng},
journal = {Kybernetika},
keywords = {decentralized variable structure control; uncertain large-scale systems; time-delayed systems; unmatched uncertainty; decentralized variable structure control; uncertain large-scale systems; time-delayed systems; unmatched uncertainty},
language = {eng},
number = {2},
pages = {285-299},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Decentralized control for large-scale systems with time-varying delay and unmatched uncertainties},
url = {http://eudml.org/doc/197038},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Liu, Wen-Jeng
TI - Decentralized control for large-scale systems with time-varying delay and unmatched uncertainties
JO - Kybernetika
PY - 2011
PB - Institute of Information Theory and Automation AS CR
VL - 47
IS - 2
SP - 285
EP - 299
AB - Many real-world systems contain uncertainties and with time-varying delays, also, they have become larger and more complicated. Hence, a new decentralized variable structure control law is proposed for a class of uncertain large-scale system with time varying delay in the interconnection and time varying unmatched uncertainties in the state matrix. The proposed decentralized control law for the large-scale time-varying delay system is realized independently through the delayed terms and it can drive the trajectories of the investigated systems onto the sliding mode. Further, the proposed control law can be successfully applied to stabilize a class of uncertain large-scale time-varying delay system with matched and unmatched uncertainties. The so-called sliding coefficient matching condition can be extended for the decentralized variable structure control of the uncertain large-scale time-varying delay systems. Furthermore, in the sliding mode, the investigated system with matched and unmatched uncertainties still bears the insensitivity to the uncertainties and disturbances, which is the same as the systems with just matched uncertainties do. Finally, an illustrative example is given to verify the validity of the proposed decentralized variable structure control law. It has been shown that the proposed decentralized control law is effective for all subsystems of the investigated system. However, the traditional decentralized variable structure control law is not applicable to the investigated system with unmatched uncertainties. It is worth noting that the traditional large-scale system is only a special case in this work.
LA - eng
KW - decentralized variable structure control; uncertain large-scale systems; time-delayed systems; unmatched uncertainty; decentralized variable structure control; uncertain large-scale systems; time-delayed systems; unmatched uncertainty
UR - http://eudml.org/doc/197038
ER -

References

top
  1. Chou, C. H., Cheng, C. C., 10.1016/S0016-0032(00)00070-3, J. Franklin Inst. 338 (2001), 35–46. (2001) Zbl0966.93101MR1815709DOI10.1016/S0016-0032(00)00070-3
  2. Chou, C. H., Cheng, C. C., 10.1109/TAC.2003.814263, IEEE Trans. Automat. Control 48 (2003), 1213–1217. (2003) MR1988091DOI10.1109/TAC.2003.814263
  3. Chen, W., Li, J., 10.1109/TSMCB.2007.904544, IEEE Trans. Systems Man Cybernet. 38 (2008), 258–266. (2008) DOI10.1109/TSMCB.2007.904544
  4. Ding, Z., Decentralized output regulation of large scale nonlinear systems with delay, Kybernetika 45 (2009), 33–48. (2009) Zbl1158.93303MR2489579
  5. Fridman, E., Shaked, U., 10.1109/TAC.2002.804462, IEEE Trans. Automat. Control 47 (2002), 1931–1937. (2002) MR1937712DOI10.1109/TAC.2002.804462
  6. Hsu, K. C., 10.1080/00207729808929529, Internat. J. Systems Sci. 29 (1998), 365–372. (1998) DOI10.1080/00207729808929529
  7. Hsu, K. C., 10.1023/A:1008256611126, Dynamics and Control 8 (1998), 341–354. (1998) MR1644236DOI10.1023/A:1008256611126
  8. Hsu, K. C., 10.1115/1.2802539, ASME J. Dynamic Systems, Measurement, and Control 121 (1999), 708–713. (1999) DOI10.1115/1.2802539
  9. Hua, C., Wang, Q., Guan, X., 10.1109/TAC.2008.917658, IEEE Trans. Automat. Control 53 (2008), 801–807. (2008) MR2401033DOI10.1109/TAC.2008.917658
  10. Hung, J. Y., Gao, W. B., Hung, J. C., 10.1109/41.184817, IEEE Trans. Ind. Electronics 40 (1993), 2–22. (1993) DOI10.1109/41.184817
  11. Luo, N., Sen, M. Dela, 10.1049/ip-d.1993.0035, IEE Proc. Part D – Control Theory Appl. 140 (1993), 261–274. (1993) DOI10.1049/ip-d.1993.0035
  12. Mahmoud, M. S., 10.1109/9.362842, IEEE Trans. Automat. Control 39 (1994), 2484–2488. (1994) Zbl0825.93628MR1337577DOI10.1109/9.362842
  13. Petersen, I. R., Robust H ∞ control of an uncertain system via a stable decentralized output feedback controller, Kybernetika 45 (2009), 101–120. (2009) Zbl1158.93328MR2489583
  14. Petersen, I. R., 10.1016/0167-6911(87)90102-2, Systems Control Lett. 8 (1987), 351–357. (1987) Zbl0618.93056MR0884885DOI10.1016/0167-6911(87)90102-2
  15. Shyu, K. K., Chen, Y. C., 10.1080/00207179508921558, Internat. J. Control 62 (1995), 589–600. (1995) Zbl0830.93026MR1619686DOI10.1080/00207179508921558
  16. Shyu, K. K., Liu, W. J., Hsu, K. C., 10.1049/ip-cta:20030758, IEE Proc. Part D – Control Theory Appl. 150 (2003), 467–475. (2003) DOI10.1049/ip-cta:20030758
  17. Shyu, K. K., Liu, W. J., Hsu, K. C., 10.1016/j.automatica.2005.03.004, Automatica 41 (2005), 1239–1246. (2005) Zbl1080.93003MR2160123DOI10.1016/j.automatica.2005.03.004
  18. Siljak, D. D., Decentralized Control of Complex Systems, Academic, San Diego 1991. (1991) MR1086632
  19. Sun, X. M., Wang, W., Liu, G. P., Zhao, J., 10.1109/TSMCB.2007.912078, IEEE Trans. Systems Man Cybernet. 38 (2008), 528–533. (2008) DOI10.1109/TSMCB.2007.912078
  20. Tao, C. W., Wang, W. Y., Chan, M. L., 10.1109/TSMCB.2002.805805, IEEE Trans. Systems Man Cybernet. 34 (2004), 639–645. (2004) DOI10.1109/TSMCB.2002.805805
  21. Wu, J., Weng, Z., Tian, Z., Shi, S., Fault tolerant control for uncertain time-delay systems based on sliding mode control, Kybernetika 44 (2008), 617–632. (2008) Zbl1180.93087MR2479308
  22. Xu, S., Lam, J., 10.1109/TAC.2006.886495, IEEE Trans. Automat. Control 52 (2007), 95–101. (2007) MR2286766DOI10.1109/TAC.2006.886495
  23. Yan, J., Tsai, J. S., Kung, F., 10.1115/1.2801253, ASME J. Dynamic Systems, Measurement, and Control 119 (1997), 307–312. (1997) Zbl0882.93002DOI10.1115/1.2801253
  24. Young, K. D., Utkin, V. I., Özgüner, Ü., 10.1109/87.761053, IEEE Trans. Control Systems Technology 7 (1999), 328–342. (1999) DOI10.1109/87.761053
  25. Zheng, F., Wang, Q.-G., Lee, T. H., 10.1016/j.automatica.2005.03.014, Automatica 41 (2005), 1375–1383. (2005) Zbl1086.93029MR2160482DOI10.1016/j.automatica.2005.03.014

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.