Decentralized design of interconnected feedback control systems with quantized signals

Guisheng Zhai; Ning Chen; Weihua Gui

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 2, page 317-325
  • ISSN: 1641-876X

Abstract

top
In this paper, we consider the design of interconnected feedback control systems with quantized signals. We assume that a decentralized dynamic output feedback has been designed for an interconnected continuous-time LTI system so that the closed-loop system is stable and a desired disturbance attenuation level is achieved, and that the subsystem measurement outputs are quantized before they are passed to the local controllers. We propose a local-output-dependent strategy for updating the parameters of the quantizers, so that the overall closed-loop system is asymptotically stable and achieves the same disturbance attenuation level. Both the pre-designed controllers and the parameters of the quantizers are constructed in a decentralized manner, depending on local measurement outputs.

How to cite

top

Guisheng Zhai, Ning Chen, and Weihua Gui. "Decentralized design of interconnected $H_∞$ feedback control systems with quantized signals." International Journal of Applied Mathematics and Computer Science 23.2 (2013): 317-325. <http://eudml.org/doc/257112>.

@article{GuishengZhai2013,
abstract = {In this paper, we consider the design of interconnected $H_∞$ feedback control systems with quantized signals. We assume that a decentralized dynamic output feedback has been designed for an interconnected continuous-time LTI system so that the closed-loop system is stable and a desired $H_∞$ disturbance attenuation level is achieved, and that the subsystem measurement outputs are quantized before they are passed to the local controllers. We propose a local-output-dependent strategy for updating the parameters of the quantizers, so that the overall closed-loop system is asymptotically stable and achieves the same $H_∞$ disturbance attenuation level. Both the pre-designed controllers and the parameters of the quantizers are constructed in a decentralized manner, depending on local measurement outputs.},
author = {Guisheng Zhai, Ning Chen, Weihua Gui},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {interconnected systems; decentralized $H_∞$ control; dynamic output feedback; quantizer; quantization; matrix inequality; LMI; decentralized control},
language = {eng},
number = {2},
pages = {317-325},
title = {Decentralized design of interconnected $H_∞$ feedback control systems with quantized signals},
url = {http://eudml.org/doc/257112},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Guisheng Zhai
AU - Ning Chen
AU - Weihua Gui
TI - Decentralized design of interconnected $H_∞$ feedback control systems with quantized signals
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 2
SP - 317
EP - 325
AB - In this paper, we consider the design of interconnected $H_∞$ feedback control systems with quantized signals. We assume that a decentralized dynamic output feedback has been designed for an interconnected continuous-time LTI system so that the closed-loop system is stable and a desired $H_∞$ disturbance attenuation level is achieved, and that the subsystem measurement outputs are quantized before they are passed to the local controllers. We propose a local-output-dependent strategy for updating the parameters of the quantizers, so that the overall closed-loop system is asymptotically stable and achieves the same $H_∞$ disturbance attenuation level. Both the pre-designed controllers and the parameters of the quantizers are constructed in a decentralized manner, depending on local measurement outputs.
LA - eng
KW - interconnected systems; decentralized $H_∞$ control; dynamic output feedback; quantizer; quantization; matrix inequality; LMI; decentralized control
UR - http://eudml.org/doc/257112
ER -

References

top
  1. Brockett, R.W. and Liberzon, D. (2000). Quantized feedback stabilization of linear systems, IEEE Transactions on Automatic Control 45(7): 1279-1289. Zbl0988.93069
  2. Bushnell, L.G. (2001). Special section on networks & control, IEEE Control Systems Magazine 21(1): 22-99. 
  3. Chen, N., Shen, X. and Gui, W. (2011a). Decentralized quantized dynamic output feedback control for uncertain interconnected networked systems, Proceedings of the 8th Asian Control Conference, Kaohsiung, Taiwan, pp. 131-136. 
  4. Chen, W., Khan, A.Q., Abid, M. and Ding, S.X. (2011b). Integrated design of observer based fault detection for a class of uncertain nonlinear systems, International Journal of Applied Mathematics and Computer Science 21(3): 423-430, DOI: 10.2478/v10006-011-0031-0. Zbl1234.93036
  5. Delchamps, D.F. (1990). Stabilizing a linear system with quantized state feedback, IEEE Transactions on Automatic Control 35(8): 916-924. Zbl0719.93067
  6. Ikeda, M., Zhai, G. and Fujisaki, Y. (1996). Decentralized control for large-scale systems: A matrix inequality approach using a homotopy method, Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, pp. 1-6. 
  7. Ishii, H. and Francis, B. (2002). Limited Data Rate in Control Systems with Networks, Springer, Berlin. Zbl1001.93001
  8. Iwasaki, T., Skelton, R.E. and Grigoriadis, K.M. (1998). A Unified Algebraic Approach to Linear Control Design, Taylor & Francis, London. 
  9. Liberzon, D. (2000). Nonlinear stabilization by hybrid quantized feedback, Proceedings of the 3rd International Workshop on Hybrid Systems: Computation and Control, Pittsburgh, PA, USA, pp. 243-257. Zbl0952.93109
  10. Liberzon, D. (2003). Hybrid feedback stabilization of systems with quantized signals, Automatica 39(9): 1543-1554. Zbl1030.93042
  11. Ling, Q. and Lemmon, M.D. (2010). A necessary and sufficient feedback dropout condition to stabilize quantized linear control systems with bounded noise, IEEE Transactions on Automatic Control 55(11): 2590-2596. 
  12. Morawski, M. and Zajączkowski, A.M. (2010). Approach to the design of robust networked control systems, International Journal of Applied Mathematics and Computer Science 20(4): 689-698, DOI: 10.2478/v10006-010-0052-0. 
  13. Murao, S., Zhai, G., Ikeda, M. and Tamaoki, K. (2002). Decentralized controller design: An LMI approach, Proceedings of the 41st SICE Annual Conference, Osaka, Japan, pp. 2734-2739. 
  14. Tatikonda, S. and Mitter, S. (2004). Control under communication constraints, IEEE Transactions on Automatic Control 49(7): 1056-1068. 
  15. Zhai, G., Chen, N. and Gui, W. (2010). Quantizer design for interconnected feedback control systems, Journal of Control Theory and Applications 8(1): 93-98. 
  16. Zhai, G., Ikeda, M. and Fujisaki, Y. (2001). Decentralized controller design: A matrix inequality approach using a homotopy method, Automatica 37(4): 565-572. Zbl0982.93035
  17. Zhai, G., Matsumoto, Y., Chen, X. and Mi, Y. (2004). Hybrid stabilization of linear time-invariant systems with two quantizers, Proceedings of the 2004 IEEE International Symposium on Intelligent Control, Taipei, Taiwan, pp. 305-309. 
  18. Zhai, G., Mi, Y., Imae, J. and Kobayashi, T. (2005). Design of feedback control systems with quantized signals, Preprints of the 16th IFAC World Congress, Prague, Czech Republic, Fr-M17-TO/1. 

NotesEmbed ?

top

You must be logged in to post comments.