H^∞-optimality of H^2 predictors

Hassibi, Babak
Kailath, Thomas

Publication date

December 1998

Publisher

Institute of Electrical and Electronics Engineers (IEEE)

Abstract

Given past observations of a process, {y_j,j<i}, suppose we are interested in constructing one-step-ahead predictors of y i, denoted by yˆ_(i|i-1). We show that, irrespective of whether the process {y_j} is stationary or non-stationary, or whether it is scalar- or vector-valued, the H^2 -optimal one-step-ahead predictor is also H^∞-optimal. Since the H^2 and H∞ paradigms represent fundamentally different approaches to estimation and control, the estimators and controllers obtained from each formalism have often drastically different performances with respect to the other criterion. Our result, however, provides a nontrivial example of when the two formalisms lead to the same optimal design

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H^∞-optimality of H^2 predictors

Abstract

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H^∞-optimality of H^2 predictors

Abstract

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