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E. the center of interval Ck , as the parameter estimate at step k. In Fig. 7, we plot three curves b k , b k and θˆk . From this figure, we can see that, for this particular example, with the help of a priori knowledge, the upper estimates estimates bk consequently bk and lower given by the IC estimator converge to true parameter θ = 5 quickly, and θˆk also converges to true parameter. Fig. 7. This figure illustrates the parameter estimates obtained by the proposed informationconcentration estimator.
1. 1 (ii) indicates that in the special case of φt = yt , since the structure of parametric part is completely determined, the uncertainty in non- parametric part becomes the main difficulty in designing controller, and the parametric uncertainty has no influence on the capability of the feedback mechanism, that is to say, the feedback mechanism can still deal with the non-parametric uncertainty characterized by the set F(L) with L< 3 + 2. 1 is also consistent with classic results on adaptive control for linear systems.
The upper curve and lower curve represent the upper bounds and lower bounds θˆk = ( 1 bk + bk 2 bk bk for the parameter estimates. We use the center curve ) to yield the parameter estimates. We should also remark that the parameter estimates given by the IC estimator are not necessarily convergent as in this example. Whether the IC parameter estimates converge Adaptive Control 38 largely depend on the accuracy of a priori knowledge and the richness of the practical data. Note that the IC estimator generally does not require classical richness concepts (like persistent excitation) which are useful in the analysis of traditional recursive identification algorithms.