H " - Optimality of H 2 Predictors '
نویسنده
چکیده
Given past, observations of a process, { y j , j < i}, suppose we arc interested in constructing one-step-ahead predictors of y i , denoted by $ i l i l . We show that, irrespective of whether the process { y j } is stationary or non-stationary, or whether it is scalaror vector-valued, the H2-optimal one-step-ahead predictor is also H"optimal. Since the H2 and H" paradigms represent fundamentally different approaches to estimation and control, the estimators and controllers obtained from each forma:lism have often drastically different performances with respect to the other criterion. Our result, however, p:rovides a non-trivial example of when the two formalisms lead to the same optimal design.
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