Geodesic
Decentralized robust tracking control of uncertain large scale systems with multiple delays in the interconnections
Kybernetika, Tome 45 (2009) no. 1, pp. 121-136 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 34K06, 93A14, 93A15, 93B52, 93C23, 93D21
Keywords: large scale systems; time delay; decentralized control; robust tracking 
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     title = {Decentralized robust tracking control of uncertain large scale systems with multiple delays in the interconnections},
     journal = {Kybernetika},
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     url = {http://geodesic.mathdoc.fr/item/KYB_2009_45_1_a8/}
}
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Wu, Hansheng. Decentralized robust tracking control of uncertain large scale systems with multiple delays in the interconnections. Kybernetika, Tome 45 (2009) no. 1, pp. 121-136. http://geodesic.mathdoc.fr/item/KYB_2009_45_1_a8/

[1] B. Brogliato and A. Trofino Neto: Practical stabilization of a class of nonlinear systems with partially known uncertainties. Automatica 31 (1995), 145–150. | MR

[2] C. H. Choi and H. S. Kim: Adaptive regulation for a class of uncertain systems with partial knowledge of uncertainty bounds. IEEE Trans. Automat. Control 38 (1993), 1246–1250. | MR

[3] S. Gutman: Uncertain dynamical systems – A Lyapunov min-max approach. IEEE Trans. Automat. Control 24 (1979), 437–443. | MR | Zbl

[4] J. K. Hale: Theory of Functional Differential Equations. Springer-Verlag, New York 1977. | MR | Zbl

[5] J. K. Hale and S. M. V. Lunel: Introduction to Functional Differential Equations. Springer-Verlag, New York 1993. | MR

[6] T. H. Hopp and W. E. Schmitendorf: Design of a linear controller for robust tracking and model following. ASME J. Dyn. Syst. Measurement Control 112 (1990), 552–558.

[7] V. B. Kolmanovskii and V. R. Nosov: Stability of Functional Differential Equations. Academic Press, London 1986. | MR

[8] S. Oucheriah: Robust tracking and model following of uncertain dynamic delay systems by memoryless linear controllers. IEEE Trans. Automat. Control 44 (1999), 1473–1577. | MR | Zbl

[9] S. Shigemaru and H. Wu: Decentralized robust tracking and model following for uncertain large-scale interconnected systems. J. Optim. Theory Appl. 110 (2001), 35–52. | MR

[10] K. K. Shyu and Y. C. Chen: Robust tracking and model following for uncertain time-delay systems. Internat. J. Control 62 (1995), 589–600. | MR

[11] T. Sugie and K. Osuka: Robust model following control with prescribed accuracy for uncertain nonlinear systems. Internat. J. Control 58 (1993), 991–1009. | MR

[12] H. Wu: Eigenstructure assignment based robust stability conditions for uncertain systems with multiple time-varying delays. Automatica 33 (1997), 97–102. | MR | Zbl

[13] H. Wu: Continuous adaptive robust controllers guaranteeing uniform ultimate boundedness for uncertain nonlinear systems. Internat. J. Control 72 (1999), 115–122. | MR | Zbl

[14] H. Wu: Adaptive stabilizing state deedback controllers of uncertain dynamical systems with multiple time delays. IEEE Trans. Automat. Control 45 (2000), 1697–1701. | MR

[15] H. Wu: Robust tracking and model following control with zero-tracking error for uncertain dynamical systems. J. Optim. Theory Appl. 107 (2000), 169–182. | MR | Zbl

[16] H. Wu: 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] H. Wu: 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. | MR

[18] H. Wu: Adaptive robust tracking and model following of uncertain dynamical systems with multiple time delays. IEEE Trans. Automat. Control 49 (2004), 611–616. | MR

[19] H. Wu and K. Mizukami: Robust stability criteria for dynamical systems including delayed perturbations. IEEE Trans. Automat. Control 40 (1995), 487–490. | MR

[20] H. Wu and K. Mizukami: Linear and nonlinear stabilizing continuous controllers of uncertain dynamical systems including state delay. IEEE Trans. Automat. Control 41 (1996), 116–121. | MR