Decentralized robust tracking control of uncertain large scale systems with multiple delays in the interconnections

Hansheng Wu

Kybernetika (2009)

  • Volume: 45, Issue: 1, page 121-136
  • ISSN: 0023-5954

Abstract

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The problem of the decentralized robust tracking and model following is considered for a class of uncertain large scale systems including time-varying delays in the interconnections. On the basis of the Razumikhin-type theorem and the Lyapunov stability theory, a class of decentralized memoryless local state feedback controllers is proposed for robust tracking of dynamical signals. It is shown that by employing the proposed decentralized robust tracking controllers, one can guarantee that the tracking error between each time-delay subsystem and the corresponding local reference model without time-delay decreases uniformly asymptotically to zero. In this paper, it is assumed that the time-varying delays are any continuous and bounded nonnegative functions, and the proposed decentralized robust tracking controllers are independent of the delays. Therefore, the results obtained in the paper are applicable to large scale systems without exact knowledge of the delays, i. e. large systems with perturbed delays.

How to cite

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Wu, Hansheng. "Decentralized robust tracking control of uncertain large scale systems with multiple delays in the interconnections." Kybernetika 45.1 (2009): 121-136. <http://eudml.org/doc/37659>.

@article{Wu2009,
abstract = {The problem of the decentralized robust tracking and model following is considered for a class of uncertain large scale systems including time-varying delays in the interconnections. On the basis of the Razumikhin-type theorem and the Lyapunov stability theory, a class of decentralized memoryless local state feedback controllers is proposed for robust tracking of dynamical signals. It is shown that by employing the proposed decentralized robust tracking controllers, one can guarantee that the tracking error between each time-delay subsystem and the corresponding local reference model without time-delay decreases uniformly asymptotically to zero. In this paper, it is assumed that the time-varying delays are any continuous and bounded nonnegative functions, and the proposed decentralized robust tracking controllers are independent of the delays. Therefore, the results obtained in the paper are applicable to large scale systems without exact knowledge of the delays, i. e. large systems with perturbed delays.},
author = {Wu, Hansheng},
journal = {Kybernetika},
keywords = {large scale systems; time delay; decentralized control; robust tracking; large scale systems; time delay; decentralized control; robust tracking},
language = {eng},
number = {1},
pages = {121-136},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Decentralized robust tracking control of uncertain large scale systems with multiple delays in the interconnections},
url = {http://eudml.org/doc/37659},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Wu, Hansheng
TI - Decentralized robust tracking control of uncertain large scale systems with multiple delays in the interconnections
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 1
SP - 121
EP - 136
AB - The problem of the decentralized robust tracking and model following is considered for a class of uncertain large scale systems including time-varying delays in the interconnections. On the basis of the Razumikhin-type theorem and the Lyapunov stability theory, a class of decentralized memoryless local state feedback controllers is proposed for robust tracking of dynamical signals. It is shown that by employing the proposed decentralized robust tracking controllers, one can guarantee that the tracking error between each time-delay subsystem and the corresponding local reference model without time-delay decreases uniformly asymptotically to zero. In this paper, it is assumed that the time-varying delays are any continuous and bounded nonnegative functions, and the proposed decentralized robust tracking controllers are independent of the delays. Therefore, the results obtained in the paper are applicable to large scale systems without exact knowledge of the delays, i. e. large systems with perturbed delays.
LA - eng
KW - large scale systems; time delay; decentralized control; robust tracking; large scale systems; time delay; decentralized control; robust tracking
UR - http://eudml.org/doc/37659
ER -

References

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  1. Practical stabilization of a class of nonlinear systems with partially known uncertainties, Automatica 31 (1995), 145–150. MR1312210
  2. Adaptive regulation for a class of uncertain systems with partial knowledge of uncertainty bounds, IEEE Trans. Automat. Control 38 (1993), 1246–1250. MR1235256
  3. Uncertain dynamical systems – A Lyapunov min-max approach, IEEE Trans. Automat. Control 24 (1979), 437–443. Zbl0416.93076MR0533394
  4. Theory of Functional Differential Equations, Springer-Verlag, New York 1977. Zbl1092.34500MR0508721
  5. Introduction to Functional Differential Equations, Springer-Verlag, New York 1993. MR1243878
  6. Design of a linear controller for robust tracking and model following, ASME J. Dyn. Syst. Measurement Control 112 (1990), 552–558. 
  7. Stability of Functional Differential Equations, Academic Press, London 1986. MR0860947
  8. Robust tracking and model following of uncertain dynamic delay systems by memoryless linear controllers, IEEE Trans. Automat. Control 44 (1999), 1473–1577. Zbl0955.93026MR1697441
  9. Decentralized robust tracking and model following for uncertain large-scale interconnected systems, J. Optim. Theory Appl. 110 (2001), 35–52. MR1848040
  10. Robust tracking and model following for uncertain time-delay systems, Internat. J. Control 62 (1995), 589–600. MR1619686
  11. Robust model following control with prescribed accuracy for uncertain nonlinear systems, Internat. J. Control 58 (1993), 991–1009. MR1242436
  12. Eigenstructure assignment based robust stability conditions for uncertain systems with multiple time-varying delays, Automatica 33 (1997), 97–102. Zbl0886.93049MR1437901
  13. Continuous adaptive robust controllers guaranteeing uniform ultimate boundedness for uncertain nonlinear systems, Internat. J. Control 72 (1999), 115–122. Zbl0945.93019MR1670173
  14. Adaptive stabilizing state deedback controllers of uncertain dynamical systems with multiple time delays, IEEE Trans. Automat. Control 45 (2000), 1697–1701. MR1791700
  15. Robust tracking and model following control with zero-tracking error for uncertain dynamical systems, J. Optim. Theory Appl. 107 (2000), 169–182. Zbl0999.93062MR1800934
  16. Design of memoryless controllers for robust tracking and model following of uncertain systems with multiple time delays, IEEJ Trans. Electronics, Informat. Systems 121 (2001), 1268–1276. 
  17. Decentralized adaptive robust control for a class of large-scale systems including delayed state perturbations in the interconnections, IEEE Trans. Automat. Control 47 (2002), 1745–1751. MR1929953
  18. Adaptive robust tracking and model following of uncertain dynamical systems with multiple time delays, IEEE Trans. Automat. Control 49 (2004), 611–616. MR2049823
  19. Robust stability criteria for dynamical systems including delayed perturbations, IEEE Trans. Automat. Control 40 (1995), 487–490. MR1319250
  20. Linear and nonlinear stabilizing continuous controllers of uncertain dynamical systems including state delay, IEEE Trans. Automat. Control 41 (1996), 116–121. MR1372622

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