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The separation principle in stochastic control, redux
University of Minnesota, United States.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0002-2681-8383
2013 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 58, no 10, 2481-2494 p.Article in journal (Refereed) Published
Abstract [en]

Over the last 50 years, a steady stream of accounts have been written on the separation principle of stochastic control. Even in the context of the linear-quadratic regulator in continuous time with Gaussian white noise, subtle difficulties arise, unexpected by many, that are often overlooked. In this paper we propose a new framework for establishing the separation principle. This approach takes the viewpoint that stochastic systems are well-defined maps between sample paths rather than stochastic processes per se and allows us to extend the separation principle to systems driven by martingales with possible jumps. While the approach is more in line with "real-life" engineering thinking where signals travel around the feedback loop, it is unconventional from a probabilistic point of view in that control laws for which the feedback equations are satisfied almost surely, and not deterministically for every sample path, are excluded.

Place, publisher, year, edition, pages
IEEE , 2013. Vol. 58, no 10, 2481-2494 p.
Keyword [en]
Certainty equivalence, separation principle, stochastic control
National Category
Mathematics Control Engineering
URN: urn:nbn:se:kth:diva-60768DOI: 10.1109/TAC.2013.2259207ISI: 000324931000004ScopusID: 2-s2.0-84884695200OAI: diva2:477904
Swedish Research Council

QC 20131025. Updated from accepted to published.

Available from: 2012-01-14 Created: 2012-01-14 Last updated: 2013-10-25Bibliographically approved

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Georgiou, TryphonLindquist, Anders
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Optimization and Systems TheoryCenter for Industrial and Applied Mathematics, CIAMACCESS Linnaeus Centre
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