Abstract
We consider the problem of robust stochastic adaptive control of not necessarily minimum phase systems in the presence of unmodelled dynamics. Stochastic gradient algorithms with parameter projection and modified gain sequence are used for the estimation of the unknown controller parameters. Global stability of the adaptive system is achieved without requiring the strictly positive real condition and the persistency exciting condition to be satisfied.
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References
S. Boyd and J. Doyle, Comparison of peak and RMS gains for discrete-time systems,Systems Control Lett., No. 9, pp. 1–6, 1987.
H. F. Chen and L. Guo, A robust stochastic adaptive controller,IEEE Trans. Aut. Contr., Vol. 33, pp. 1035–1043.
B. Egardt,Stability of Adaptive Controllers, Springer-Verlag, Berlin and New York, 1979.
G. C. Goodwin and K. S. Sin,Adaptive Filtering, Prediction and Control, Prentice-Hall, Englewood Cliffs, NJ, 1984.
P. A. Ioannou and P. V. Kokotovic, Robust redesign of adaptive control,IEEE Trans. Aut. Contr., Vol. AC-29, No. 3, 1984.
P. A. Ioannou and K. S. Tsakalis, A robust direct adaptive controller,IEEE Trans. Aut. Contr., Vol. 31, pp. 1033–1043, 1986.
P. A. Ioannou and J. Sun, Theory and design of robust direct and indirect adaptive control schemes,Int. J. Control, Vol. 47, pp. 775–813, 1988.
G. Kreisselmeier and B. D. O. Anderson, Robust model reference adaptive control,IEEE Trans. Aut. Contr., Vol. 31, pp. 127–133, 1986.
P. R. Kumar and P. Varaiya,Stochastic Systems: Estimation, Identification and Adaptive Control, Prentice-Hall, Englewood Cliffs, NJ, 1986.
S. Naik, P. R. Kumar, and B. E. Ydstie, Robust continuous time adaptive control by parameter projection, submitted to theIEEE Trans. Aut. Cont. and the30th CDC.
R. Ortega and T. Yu, Theoretical results on robustness of direct adaptive controllers: A survey,Proc. 10th IFAC World Congress, pp. 26–31, Munich, Germany, 1987.
L. Praly, Robustness of model reference adaptive control, K. S. Narendra, ed.,Proc. III Yale Workshop on Adaptive Systems, pp. 224–226, 1983.
L. Praly, Robust model reference adaptive controllers, part I: Stability analysis,Proc. 23rd IEEE CDC, Dec. 1984.
L. Praly, Global stability of a direct adaptive control scheme which is robust w.r.t. a graph topology,Adaptive and Learning Systems: Theory and Applications, K.S. Narendra, ed., Plenum Press, New York, 1986.
L. Praly, S. F. Lin, and P. R. Kumar, A robust adaptive minimum variance controller,SIAM J. Control and Optim., Vol. 27, No. 2, pp. 235–266, 1989.
M. S. Radenkovic and A. N. Michel, Verification of the self-stabilization mechanism in robust stochastic adaptive control using Lyapunov function arguments,SIAM J. Control Optim., Vol. 30, No. 6, pp. 1270–1294, 1992.
M. S. Radenkovic and A. N. Michel, Robust adaptive systems and self-stabilization,IEEE Trans. Aut. Contr., AC-37, pp. 1355–1369, 1992.
W. F. Stout,Almost Sure Convergence, Academic Press, New York, 1974.
G. Tao and P. A. Ioannou, Robust stability and performance improvement of discrete-time multivariable adaptive control systems,Int. J. Control, Vol. 50, pp. 1835–1855, 1989.
B. E. Ydstie, Stability of discrete MRAC — Revisited,Systems and Control Lett., Vol. 13, pp. 429–438, 1989.
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This work was supported by NSF Grant ECS-88-02924.
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Radenkovic, M., Michel, A.N. Stochastic adaptive control of nonminimum phase systems in the presence of unmodelled dynamics. Circuits Systems and Signal Process 14, 317–349 (1995). https://doi.org/10.1007/BF01189016
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DOI: https://doi.org/10.1007/BF01189016