By Shankar Sastry
This quantity surveys the most important effects and strategies of research within the box of adaptive keep an eye on. concentrating on linear, non-stop time, single-input, single-output platforms, the authors supply a transparent, conceptual presentation of adaptive equipment, allowing a serious evaluate of those innovations and suggesting avenues of extra improvement. 1989 version
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Extra info for Adaptive control : stability, convergence, and robustness
One approach is to rely on the asymptotic behavior of the ML estimator $. That is, for large sample sizes n the sampling distribution f ($) approaches the Normal model with mean value 8 and variance MVBe. 2) as where the parameter 8 is evaluated at its ML estimate g,and zq is the standard Normal quantitle of order q. Also, the invariance property of ML estimators can be used to construct similar confidence intervals on a decision function g(8). For example, exact sampling distributions for estimators of Gamma parameters are not available.
The interval endpoints tl and t2 are the a/2- and the (1 - a/2)-quantiles of the sampling pdf f(t). 3 illustrates such an interval. For example, suppose one were to sample from a Normal process with known variance a:. 4). 3. An equal-sided (1 - a ) interval (tl,t2)from a sampling pdf f(t). 11), where q is the standard Normal q-quantile and z1-,/2 = -2+. 21 ) then reads The interval endpoints tl and t2 are expressions involving the unknown parameter Q. 22)is then no longer a probability statement.
The interpretation of this interval is that, since repeated samples would each produce slightly different calculated intervals, the proportion of intervals containing the unknown value Q CONFIDENCE INTERVALS approaches (1 - a ) , as the number of repetitions increases. Thus, (1 - a) is a measure of the statistical assurance that a specific interval estimate covers the unknown parameter 8. The value (1 - a) is specified by the decision maker. Clearly, the higher the required confidence level, the wider will be the corresponding interval (11, 12).