Abstract
Results presented in [1] can be considered as the fundamental one in the adaptive control theory. Essentially, it is shown that if the system is exactly modelled, a self-tuning controller provides the same performance as the minimum-variance controller. It turns out that similar results are valid even in the presence of a modelling error. In this paper it is proved that in the presence of unmodelled dynamics, adaptive controller guarantees in a certain sense the same performance as the best non-adaptive controller. Despite the fact that the estimation algorithm has a vanishing gain sequence, uniform boundedness of all signals is established.
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References
G.C. Goodwin, P.J. Ramadge and P.E. Caines, Discrete time stochastic adaptive control, SIAM J. Contr. and Optimization, 19 (1981) pp. 829–853.
R.L. Kosut and B. Friedlander, Robust adaptive control: conditions for global stability, IEEE Trans. Aut. Contr., AC-30 (1985) pp. 610–624.
B.E. Ydstie, Transient performance and robustness of direct adaptive control, IEEE Trans. Aut. Contr., AC-37 (1992) pp. 1092–1105.
E. Egardt, Stability of adaptive controllers (Springer-Verlag, New York, 1979).
C.E. Rohrs., L. Valavani, M. Athans and G. Stein, Analytical verification of undesirable properties of direct model reference adaptive control algorithm, Proc. 20th IEEE Conf. Decision and Contr., 2 (1981) pp. 1272–1284.
P.A. Ioannou and J. Sun, Theory and design of robust direct and indirect adaptive-control schemes, Int. J. Contr., 47 (1988) 775–813.
M.S. Radenkovic and B. Ydstie, Using persistent excitation with fixed energy to stabilize adaptive controllers and obtain hard bounds for the parameter estimation error, approved for publication in SIAM J. Contr. and Optimization, 1994.
M.S. Radenkovic and A.N. Michel, Robust adaptive systems and self stabilization, IEEE Trans. Aut. Contr., AC-37 (1992) pp. 1355–1369.
K. Glover, All optimal Hankel norm approximations of linear multivariable systems and their L∞-error bounds, Int. J. Contr., 39 (1984) pp. 1145–1193.
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© 1995 Springer Science+Business Media New York
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Radenkovic, M.S., Ydstie, B.E. (1995). Optimality of the Adaptive Controllers. In: Åström, K.J., Goodwin, G.C., Kumar, P.R. (eds) Adaptive Control, Filtering, and Signal Processing. The IMA Volumes in Mathematics and its Applications, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8568-2_14
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DOI: https://doi.org/10.1007/978-1-4419-8568-2_14
Publisher Name: Springer, New York, NY
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