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Publications (10 of 52) Show all publications
Ringh, A., Karlsson, J. & Lindquist, A. (2018). Lower bounds on the maximum delay margin by analytic interpolation. In: 2018 IEEE 57th Annual Conference on Decision and Control (CDC): . Paper presented at IEEE 57th Annual Conference on Decision and Control (CDC),Miami Beach, FL, USA, December 17-19, 2018 (pp. 5463-5469). Institute of Electrical and Electronics Engineers (IEEE), Article ID 8618930.
Open this publication in new window or tab >>Lower bounds on the maximum delay margin by analytic interpolation
2018 (English)In: 2018 IEEE 57th Annual Conference on Decision and Control (CDC), Institute of Electrical and Electronics Engineers (IEEE), 2018, p. 5463-5469, article id 8618930Conference paper, Published paper (Refereed)
Abstract [en]

We study the delay margin problem in the context of recent works by T. Qi, J. Zhu, and J. Chen, where a sufficient condition for the maximal delay margin is formulated in terms of an interpolation problem obtained after introducing a rational approximation. Instead we omit the approximation step and solve the same problem directly using techniques from function theory and analytic interpolation. Furthermore, we introduce a constant shift in the domain of the interpolation problem. In this way we are able to improve on their lower bound for the maximum delay margin.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2018
Series
IEEE Conference on Decision and Control, ISSN 0743-1546
National Category
Control Engineering Other Mathematics
Identifiers
urn:nbn:se:kth:diva-239720 (URN)10.1109/CDC.2018.8618930 (DOI)000458114805008 ()2-s2.0-85062194089 (Scopus ID)9781538613955 (ISBN)
Conference
IEEE 57th Annual Conference on Decision and Control (CDC),Miami Beach, FL, USA, December 17-19, 2018
Funder
Swedish Research Council, 2014-5870
Note

QC 20181214

Available from: 2018-11-30 Created: 2018-11-30 Last updated: 2019-03-06Bibliographically approved
Ringh, A., Karlsson, J. & Lindquist, A. (2017). Further results on multidimensional rational covariance extension with application to texture generation. In: 2017 IEEE 56th Annual Conference on Decision and Control (CDC): . Paper presented at IEEE 56th Annual Conference on Decision and Control (CDC), DEC 12-15, 2017, Melbourne, AUSTRALIA. IEEE
Open this publication in new window or tab >>Further results on multidimensional rational covariance extension with application to texture generation
2017 (English)In: 2017 IEEE 56th Annual Conference on Decision and Control (CDC), IEEE , 2017Conference paper, Published paper (Refereed)
Abstract [en]

The rational covariance extension problem is a moment problem with several important applications in systems and control as, for example, in identification, estimation, and signal analysis. Here we consider the multidimensional counterpart and present new results for the well-posedness of the problem. We apply the theory to texture generation by modeling the texture as the output of a Wiener system. The static nonlinearity in the Wiener system is assumed to be a thresholding function and we identify both the linear dynamical system and the thresholding parameter.

Place, publisher, year, edition, pages
IEEE, 2017
Series
IEEE Conference on Decision and Control, ISSN 0743-1546
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-223868 (URN)10.1109/CDC.2017.8264252 (DOI)000424696903143 ()2-s2.0-85046261827 (Scopus ID)978-1-5090-2873-3 (ISBN)
Conference
IEEE 56th Annual Conference on Decision and Control (CDC), DEC 12-15, 2017, Melbourne, AUSTRALIA
Funder
Swedish Research CouncilSwedish Foundation for Strategic Research
Note

QC 20180306

Available from: 2018-03-06 Created: 2018-03-06 Last updated: 2018-12-04Bibliographically approved
Lindquist, A. (2017). Kalman's Influence on My Scientific Work: Some Recollections and Reflections. IEEE CONTROL SYSTEMS MAGAZINE, 37(2), 156-157
Open this publication in new window or tab >>Kalman's Influence on My Scientific Work: Some Recollections and Reflections
2017 (English)In: IEEE CONTROL SYSTEMS MAGAZINE, ISSN 1066-033X, Vol. 37, no 2, p. 156-157Article in journal (Refereed) Published
Abstract [en]

I first met Rudolf Kalman in Vienna, Austria, in the spring of 1972. I had recently finished my Ph.D. at the Royal Institute of Technology, Stockholm, Sweden, and I was invited to give a talk on my recent results in stochastic control theory at a small workshop that Kalman also attended. Apparently, Kalman was favorably impressed with my talk because he took me out for dinner the same evening and immediately invited me to come to Florida for the coming academic year. Kalman had just moved from Stanford to the University of Florida, and this is how I became his first postdoctoral associate at his new Center for Mathematical Systems Theory in the fall of 1972.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2017
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-208264 (URN)10.1109/MCS.2016.2643319 (DOI)000398902900011 ()2-s2.0-85016141113 (Scopus ID)
Note

QC 20170622

Available from: 2017-06-22 Created: 2017-06-22 Last updated: 2017-06-22Bibliographically approved
Georgiou, T. T. & Lindquist, A. (2017). Likelihood Analysis of Power Spectra and Generalized Moment Problems. IEEE Transactions on Automatic Control, 62(9), 4580-4592
Open this publication in new window or tab >>Likelihood Analysis of Power Spectra and Generalized Moment Problems
2017 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 9, p. 4580-4592Article in journal (Refereed) Published
Abstract [en]

We develop an approach to the spectral estimation that has been advocated by [ A. Ferrante et al., "Time and spectral domain relative entropy: A new approach to multivariate spectral estimation,"IEEE Trans. Autom. Control, vol. 57, no. 10, pp. 2561-2575, Oct. 2012.] and, in the context of the scalar-valued covariance extension problem, by [P. Enqvist and J. Karlsson, "Minimal itakurasaito distance and covariance interpolation," in Proc. 47th IEEE Conf. Decision Control, 2008, pp. 137-142]. The aim is to determine the power spectrum that is consistent with given moments and minimizes the relative entropy between the probability law of the underlying Gaussian stochastic process to that of a prior. The approach is analogous to the framework of earlier work by Byrnes, Georgiou, and Lindquist and can also be viewed as a generalization of the classical work by Burg and Jaynes on the maximum entropy method. In this paper, we present a new fast algorithm in the general case (i.e., for general Gaussian priors) and show that for priors with a specific structure the solution can be given in closed form.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2017
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-214494 (URN)10.1109/TAC.2017.2672862 (DOI)000408569300020 ()2-s2.0-85029838609 (Scopus ID)
Note

QC 20171009

Available from: 2017-10-09 Created: 2017-10-09 Last updated: 2017-10-09Bibliographically approved
Georgiou, T. T. & Lindquist, A. (2017). Optimal Estimation With Missing Observations via Balanced Time-Symmetric Stochastic Models. IEEE Transactions on Automatic Control, 62(11), 5590-5603
Open this publication in new window or tab >>Optimal Estimation With Missing Observations via Balanced Time-Symmetric Stochastic Models
2017 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 11, p. 5590-5603Article in journal (Refereed) Published
Abstract [en]

We consider data fusion for the purpose of smoothing and interpolation based on observation records with missing data. Stochastic processes are generated by linear stochastic models. The paper begins by drawing a connection between time reversal in stochastic systems and all-pass extensions. A particular normalization (choice of basis) between the two time-directions allows the two to share the same orthonormalized state process and simplifies the mathematics of data fusion. In this framework, we derive symmetric and balanced Mayne-Fraser-like formulas that apply simultaneously to continuous-time smoothing and interpolation, providing a definitive unification of these concepts. The absence of data over subintervals requires in general a hybrid filtering approach involving both continuous-time and discrete-time filtering steps.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2017
Keywords
Filtering theory, Kalman filters, missing observations
National Category
Robotics
Identifiers
urn:nbn:se:kth:diva-217419 (URN)10.1109/TAC.2017.2689685 (DOI)000413837700008 ()2-s2.0-85036458551 (Scopus ID)
Note

QC 20171117

Available from: 2017-11-17 Created: 2017-11-17 Last updated: 2017-12-15Bibliographically approved
Lindquist, A. (2017). Partial Realization Theory and System Identification Redux. In: 2017 11TH ASIAN CONTROL CONFERENCE (ASCC): . Paper presented at 2017 11th Asian Control Conference, ASCC 2017, Gold Coast Convention and Exhibition CentreGold Coast, Australia, 17 December 2017 through 20 December 2017 (pp. 1946-1950). IEEE
Open this publication in new window or tab >>Partial Realization Theory and System Identification Redux
2017 (English)In: 2017 11TH ASIAN CONTROL CONFERENCE (ASCC), IEEE , 2017, p. 1946-1950Conference paper, Published paper (Refereed)
Abstract [en]

Some twenty years ago we introduced a nonstandard matrix Riccati equation to solve the partial stochastic realization problem. In this paper we provide a new derivation of this equation in the context of system identification. This allows us to show that the nonstandard matrix Riccati equation is universal in the sense that it can be used to solve more general analytic interpolation problems by only changing certain parameters. Such interpolation problems are ubiquitous in systems and control. In this context we also discuss a question posed by R.E. Kalman in beginning of the 1970s.

Place, publisher, year, edition, pages
IEEE, 2017
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-225240 (URN)10.1109/ASCC.2017.8287472 (DOI)000426957300340 ()2-s2.0-85047464992 (Scopus ID)
Conference
2017 11th Asian Control Conference, ASCC 2017, Gold Coast Convention and Exhibition CentreGold Coast, Australia, 17 December 2017 through 20 December 2017
Note

QC 20180403

Available from: 2018-04-03 Created: 2018-04-03 Last updated: 2018-11-19Bibliographically approved
Ringh, A., Karlsson, J. & Lindquist, A. (2016). MULTIDIMENSIONAL RATIONAL COVARIANCE EXTENSION WITH APPLICATIONS TO SPECTRAL ESTIMATION AND IMAGE COMPRESSION. SIAM Journal of Control and Optimization, 54(4), 1950-1982
Open this publication in new window or tab >>MULTIDIMENSIONAL RATIONAL COVARIANCE EXTENSION WITH APPLICATIONS TO SPECTRAL ESTIMATION AND IMAGE COMPRESSION
2016 (English)In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 54, no 4, p. 1950-1982Article in journal (Refereed) Published
Abstract [en]

The rational covariance extension problem (RCEP) is an important problem in systems and control occurring in such diverse fields as control, estimation, system identification, and signal and image processing, leading to many fundamental theoretical questions. In fact, this inverse problem is a key component in many identification and signal processing techniques and plays a fundamental role in prediction, analysis, and modeling of systems and signals. It is well known that the RCEP can be reformulated as a (truncated) trigonometric moment problem subject to a rationality condition. In this paper we consider the more general multidimensional trigonometric moment problem with a similar rationality constraint. This generalization creates many interesting new mathematical questions and also provides new insights into the original one-dimensional problem. A key concept in this approach is the complete smooth parameterization of all solutions, allowing solutions to be tuned to satisfy additional design specifications without violating the complexity constraints. As an illustration of the potential of this approach we apply our results to multidimensional spectral estimation and image compression. This is just a first step in this direction, and we expect that more elaborate tuning strategies will enhance our procedures in the future.

Place, publisher, year, edition, pages
SIAM PUBLICATIONS, 2016
Keywords
covariance extension, trigonometric moment problem, convex optimization, generalized entropy, multidimensional spectral estimation, image compression
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-242737 (URN)10.1137/15M1043236 (DOI)000385011200006 ()2-s2.0-84984666883 (Scopus ID)
Note

QC 20190219

Available from: 2019-02-19 Created: 2019-02-19 Last updated: 2019-08-21Bibliographically approved
Karlsson, J., Lindquist, A. & Ringh, A. (2016). The Multidimensional Moment Problem with Complexity Constraint. Integral equations and operator theory, 84(3), 395-418
Open this publication in new window or tab >>The Multidimensional Moment Problem with Complexity Constraint
2016 (English)In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 84, no 3, p. 395-418Article in journal (Refereed) Published
Abstract [en]

A long series of previous papers have been devoted to the (one-dimensional) moment problem with nonnegative rational measure. The rationality assumption is a complexity constraint motivated by applications where a parameterization of the solution set in terms of a bounded finite number of parameters is required. In this paper we provide a complete solution of the multidimensional moment problem with a complexity constraint also allowing for solutions that require a singular measure added to the rational, absolutely continuous one. Such solutions occur on the boundary of a certain convex cone of solutions. In this paper we provide complete parameterizations of all such solutions. We also provide errata for a previous paper in this journal coauthored by one of the authors of the present paper.

Place, publisher, year, edition, pages
Springer, 2016
Keywords
complexity constraints, Moment problems, multidimensional moment problems, optimization, smooth parameterization
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-175025 (URN)10.1007/s00020-015-2248-z (DOI)000371077100004 ()2-s2.0-84959192629 (Scopus ID)
Note

QC 20160323

Available from: 2015-12-04 Created: 2015-10-09 Last updated: 2017-12-01Bibliographically approved
Lindquist, A. & Picci, G. (2014). Modeling of Periodic Time Series by Bilateral ARMA Representations. In: INTERNATIONAL WORK-CONFERENCE ON TIME SERIES (ITISE 2014): . Paper presented at 1st International Work-Conference on Time Series (ITISE), JUN 25-27, 2014, Granada, SPAIN (pp. 861-865).
Open this publication in new window or tab >>Modeling of Periodic Time Series by Bilateral ARMA Representations
2014 (English)In: INTERNATIONAL WORK-CONFERENCE ON TIME SERIES (ITISE 2014), 2014, p. 861-865Conference paper, Published paper (Refereed)
Abstract [en]

In this extended abstract for an oral presentation we describe a moment-based approach to modeling of stationary, periodic time series from a finite sequence of covariance lags. We present a complete parameterization of a family of solutions and a convex optimization procedure to determine each solution, which is seen to be represented as a bilateral ARMA model.

Keywords
periodic stationary time series, bilateral ARMA models, moment problems, convex optimization
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-173302 (URN)000359136600097 ()978-84-15814-97-9 (ISBN)
Conference
1st International Work-Conference on Time Series (ITISE), JUN 25-27, 2014, Granada, SPAIN
Note

QC 20150909

Available from: 2015-09-09 Created: 2015-09-09 Last updated: 2015-09-09Bibliographically approved
Hanebeck, U. D. & Lindquist, A. (2014). Moment-based dirac mixture approximation of circular densities. In: IFAC Proceedings Volumes (IFAC-PapersOnline): . Paper presented at 19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014, 24 August 2014 through 29 August 2014 (pp. 5040-5048).
Open this publication in new window or tab >>Moment-based dirac mixture approximation of circular densities
2014 (English)In: IFAC Proceedings Volumes (IFAC-PapersOnline), 2014, p. 5040-5048Conference paper, Published paper (Refereed)
Abstract [en]

Given a circular probability density function, called the true probability density function, the goal is to find a Dirac mixture approximation based on some circular moments of the true density. When keeping the locations of the Dirac points fixed, but almost arbitrarily located, we are applying recent results on the circulant rational covariance extension problem to the problem of calculating the weights. For the case of simultaneously calculating optimal locations, additional constraints have to be deduced from the given density. For that purpose, a distance measure for the deviation of the Dirac mixture approximation from the true density is derived, which then is minimized while considering the moment conditions as constraints. The method is based on progressive numerical minimization, converges quickly and gives well-distributed Dirac mixtures that fulfill the constraints, i.e., have the desired circular moments.

Keywords
Circular densities, Dirac mixture approximation, Moment problem
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-175343 (URN)2-s2.0-84929773553 (Scopus ID)9783902823625 (ISBN)
Conference
19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014, 24 August 2014 through 29 August 2014
Note

QC 20151012

Available from: 2015-10-12 Created: 2015-10-12 Last updated: 2015-10-12Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-2681-8383

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