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Filtering and smoothing in an \(H^ \infty\) setting. (English) Zbl 0758.93074

A fairly complete theory of filtering and smoothing with an \(H^ \infty\) performance criterion is developed for a linear quadratic problem with finite or infinite horizon. Necessary and sufficient conditions for the existence of estimators achieving a prescribed performance bound are derived. For the smoothing problem a solution is presented that minimizes the performance measure. This smoother turns out to be the minimum smoother so that the optimal smoothers for the respectie \(H^ 2\)- and \(H^ \infty\)-problems are the same.

MSC:

93E11 Filtering in stochastic control theory
93E14 Data smoothing in stochastic control theory
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