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Optimal estimation and control of discrete multiplicative systems with unknown second order statistics

Yannis Phillis

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URIhttp://purl.tuc.gr/dl/dias/691BEFDE-95E8-42D9-B4E3-87E1C6EC29FB-
Identifierhttps://doi.org/10.1007/BF00940029-
Languageen-
Extent16 pagesen
Title Optimal estimation and control of discrete multiplicative systems with unknown second order statisticsen
CreatorYannis Phillisen
CreatorΦιλλης Ιωαννηςel
PublisherKluweren
Content SummaryThe problem of estimation and control for discrete-time systems with multiplicative noise is examined. Such systems occur naturally in the modeling of stochastic systems with random or unknown coefficients and appear to be robust in contrast to LQG regulators which are sensitive to errors in the coefficients. The statistics of the white sequences of the system are unknown. The problem of stochastic estimation and control of such a system is difficult not only because of the unknown statistics but also because the state is not Gaussian. The approach of this work is to convert the stochastic problem to a deterministic game-theoretic one. We find the estimator and controller so as to minimize a suitable performance measure assuming the worst behavior of nature. A set of necessary and sufficient conditions is developed for the existence of a saddle-point estimator. When both estimation and control are considered, two difficulties appear: the optimality conditions are only necessary and the separation principle collapses. As a result, the saddle-point conditions are only necessary. If the covariances belong to sets with maximal points, then the necessary conditions are satisfied at these points. If, on the other hand, they belong to convex and compact sets and the system has a steady state, then the estimation problem alone has always a saddle-point solution.en
Type of ItemPeer-Reviewed Journal Publicationen
Type of ItemΔημοσίευση σε Περιοδικό με Κριτέςel
Licensehttp://creativecommons.org/licenses/by/4.0/en
Date of Item2015-10-06-
Date of Publication1990-
Bibliographic CitationΥ. Α. Phillis, Optimal estimation and control of discrete multiplicative systems with unknown second order statistics", J. of Opt. Theory and Ap., vol. 64, no. 1, pp. 153-168, 1990.doi :10.1007/BF00940029el

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