Important moments in systems, control and optimizations
2009 (English)In: Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on, IEEE , 2009, 91-96 p.Conference paper (Refereed)
The moment problem matured from its various special forms in the late 19th and early 20th Centuries to a general class of problems that continues to exert profound influence on the development of analysis and its applications to a wide variety of fields. In particular, the theory of systems and control is no exception, where the applications have historically been to circuit theory, optimal control, robust control, signal processing, spectral estimation, stochastic realization theory and the use of the moments of a probability density. Many of these applications are also still works in progress. In this paper, we consider the generalized moment problem, expressed in terms of a basis of a finite-dimensional subspace β of the Banach space C[a, b] and a "positive" sequences c, but with a new wrinkle inspired by the applications to systems and control. We seek to parameterize solutions which are positive "rational" measures, in a suitably generalized sense. Our parameterization is given in terms of smooth objects. In particular, the desired solution space arises naturally as a manifold which can be shown to be diffeomorphic to a Euclidean space and which is the domain of some canonically defined functions. Moreover, on these spaces one can derive natural convex optimization criteria which characterize solutions to this new class of moment problems.
Place, publisher, year, edition, pages
IEEE , 2009. 91-96 p.
, IEEE Conference on Decision and Control. Proceedings, ISSN 0191-2216
IdentifiersURN: urn:nbn:se:kth:diva-60771DOI: 10.1109/CDC.2009.5400258ISI: 000336893600016ScopusID: 2-s2.0-77950845527ISBN: 978-142443871-6OAI: oai:DiVA.org:kth-60771DiVA: diva2:477907
48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009; Shanghai; 15 December 2009 through 18 December 2009
QC 201202212012-01-142012-01-142015-06-10Bibliographically approved