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Mean and variance of the LQG cost function
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
2016 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 67, 216-223 p.Article in journal (Refereed) Published
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Abstract [en]

Linear Quadratic Gaussian (LQG) systems are well-understood and methods to minimize the expected cost are readily available. Less is known about the statistical properties of the resulting cost function. The contribution of this paper is a set of analytic expressions for the mean and variance of the LQG cost function. These expressions are derived using two different methods, one using solutions to Lyapunov equations and the other using only matrix exponentials. Both the discounted and the non-discounted cost function are considered, as well as the finite-time and the infinite-time cost function. The derived expressions are successfully applied to an example system to reduce the probability of the cost exceeding a given threshold.

Place, publisher, year, edition, pages
2016. Vol. 67, 216-223 p.
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:uu:diva-294647DOI: 10.1016/j.automatica.2016.01.030ISI: 000373540300025OAI: oai:DiVA.org:uu-294647DiVA: diva2:932560
Funder
Swedish Research Council, 621-2013-5524
Available from: 2016-02-04 Created: 2016-05-26 Last updated: 2017-11-30Bibliographically approved

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Schön, Thomas B.

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