Abstract
This chapter discusses adaptive control of continuous time systems with unknown time delay. In the controller design, the delay is taken into consideration by using rational approximation. For the implementation of controllers, no a priori knowledge, which is related to modeling errors due to the approximation of time delay, plant unmodeled dynamics and bounded external disturbances, is required. It is shown that, the resulting adaptive controller can ensure global boundedness of the overall closed loop system even in the presence of modeling errors. A small mean tracking error can also be ensured.
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References
G. C. Goodwin and K.S. Sin, Adaptive Filtering Prediction and Control, Prentice-Hall, New Jersey, 1984.
K.J. Astrom and B. Wittenmark, Adaptive Control, Addison-Wesley, 1989.
C.E. de Souza, G.C. Goodwin, D. Mayne and M. Palaniswami, An adaptive control algorithm for linear systems having unknown time delay, Automatica, 24, 327–341, 1988.
G. Kreisselmeier and B. D. O. Anderson, Robust model reference adaptive control, IEEE Trans. Automatic Control, 31, 127–133, 1986.
R.H. Middleton, G.C. Goodwin, D.J. Hill and D.Q. Mayne, Design issues in adaptive control, IEEE Trans. Automatic Control, 33, 50–58, 1988.
C. Wen, An indirect robust continuous-time adaptive controller with minimal modifications, Automatica, 31, 293–296, 1995.
C. Wen and D.J. Hill, Global boundedness of discrete-time adaptive control just using estimator projection, Automatica, 28, 1143–1157, 1992.
C. Wen and D.J. Hill, Robustness of adaptive control without deadzones, data normalization or persistence of excitation, Automatica, 25, No. 6, 943–947, 1989.
L. Praly, Robustness of model reference adaptive control, in Proc. III Yale Workshop on Adaptive Systems, 224–226, 1983.
P.A. Ioannou and K.S. Tsakalis, A robust direct adaptive controller, IEEE Trans. Automatic Control, 31, 1033–1043, 1986.
B.E. Ydstie, Stability of discrete MRAC — revisited, Syst. Control Lett., 13, 429–438, 1989.
S.M. Naik, P.R. Kumar and B.E. Ydstie, Robust continuous-time adaptive control by parameter projection, IEEE Trans. Automatic Control, 37, 182–197, 1992.
J.B. Pomet and L. Praly, Adaptive nonlinear regulation: estimation from the Lyapunov Equation, IEEE Trans. Automatic Control, 37, 729–740, 1992.
Goodwin, G.C. and D.Q. Mayne, A parameter estimation perspective of continuous model reference adaptive control, Automatica, 23, 57–70, 1987.
Middleton, R.H. and G.C. Goodwin, Digital Control and Estimation — A Unified Approach, Prentice Hall, New Jersey, 1990.
de Larminat, P. and H.F. Raynaud, A robust solution to the admissibility problem in indirect adaptive control without persistency of excitation, Int. J. of Adaptive Control and Signal Processing, 2, No.2, 95–110, 1988.
Giri, F., M. M’Saad, L. Dugard and J.-M. Dion, Robust adaptive regulation with minimal prior knowledge, IEEE Trans. Automatic Control, 37, 305–315, 1992.
Kreisselmeier, G. An approach to stable indirect adaptive control, Automatica, 21, No.4, 425–433, 1985.
Wen, C. Robust adaptive tracking using the internal model principle, Int. J. of Control, 64, 127–140, 1996.
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© 2001 Springer-Verlag London
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Wen, C., Soh, Y.C., Zhang, Y. (2001). Adaptive Control of Linear Systems with Unknown Time Delay. In: Tao, G., Lewis, F.L. (eds) Adaptive Control of Nonsmooth Dynamic Systems. Springer, London. https://doi.org/10.1007/978-1-4471-3687-3_16
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DOI: https://doi.org/10.1007/978-1-4471-3687-3_16
Publisher Name: Springer, London
Print ISBN: 978-1-84996-869-0
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