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Basic optimal estimation and control problems in Hilbert space

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Abstract

The recently developed mathematical framework of Hilbert resolution space valued random processes is used to formulate and solve an abstract quadratic optimization problem. By particularizing the description of the operators appearing in the statement and solution formula of the problem, one rediscovers and generalizes most of the classical estimation and control theory problem statements and results. These include, among others, the Wiener smoothing prediction filter, the Kalman regulator, the Kalman-Bucy filter, the stochastic control separation principle and the more recent Youla-Jabr-Bongiorno optimal servo problem solution.

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Authors and Affiliations

  1. Ecole Polytechnique de Montreal, University of Montreal, Montreal, Quebec, Canada

    R. M. DeSantis

  2. Texas Tech University, 79409, Lubbock, Texas, USA

    R. Saeks

  3. University of Texas at El Paso, 79968, El Paso, Texas, USA

    L. J. Tung

Authors
  1. R. M. DeSantis
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  2. R. Saeks
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  3. L. J. Tung
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Additional information

This research has been supported in part by U.S. Air Force Office of Scientific Research Grant 74-2631 and Canadian Research Council Grant CNRC-8244.

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DeSantis, R.M., Saeks, R. & Tung, L.J. Basic optimal estimation and control problems in Hilbert space. Math. Systems Theory 12, 175–203 (1978). https://doi.org/10.1007/BF01776572

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  • DOI: https://doi.org/10.1007/BF01776572

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