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  • 1.
    Byrnes, Christopher
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM. KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Georgiou, T. T.
    Lindquist, Anders
    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.
    Megretski, A.
    Generalized interpolation in H-infinity with a complexity constraint2006In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 358, no 3, p. 965-987Article in journal (Refereed)
    Abstract [en]

    In a seminal paper, Sarason generalized some classical interpolation problems for H-infinity functions on the unit disc to problems concerning lifting onto H-2 of an operator T that is defined on K=H-2 circle minus phi H-2 (phi is an inner function) and commutes with the (compressed) shift S. In particular, he showed that interpolants (i.e., f is an element of H-infinity such that f(S)=T) having norm equal to parallel to T parallel to exist, and that in certain cases such an f is unique and can be expressed as a fraction f=b/a with a, b is an element of K. In this paper, we study interpolants that are such fractions of K functions and are bounded in norm by 1 (assuming that parallel to T parallel to<1, in which case they always exist). We parameterize the collection of all such pairs (a, b)is an element of K x K and show that each interpolant of this type can be determined as the unique minimum of a convex functional. Our motivation stems from the relevance of classical interpolation to circuit theory, systems theory, and signal processing, where phi is typically a finite Blaschke product, and where the quotient representation is a physically meaningful complexity constraint.

  • 2. Byrnes, Christopher I.
    et al.
    Lindquist, Anders
    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.
    The moment problem for rational measures: convexity in the spirit of Krein2009In: MODERN ANALYSIS AND APPLICATIONS: MARK KREIN CENTENARY CONFERENCE / [ed] Adamyan, V; Berezansky, Y; Gohberg, I; Gorbachuk, M; Gorbachuk, V; Kochubei, A; Langer, H; Popov, G, Birkhäuser Verlag, 2009, Vol. 190, p. 157-169Conference paper (Refereed)
    Abstract [en]

    The moment problem as formulated by Krein and Nudel'man is a beautiful generalization of several important classical moment problems, including the power moment problem, the trigonometric moment problem and the moment problem arising in Nevanlinna-Pick interpolation. Motivated by classical applications and examples, in both finite and infinite dimensions, we recently formulated a new version of this problem that we call the moment problem for positive rational measures. The formulation reflects the importance of rational functions in signals, systems and control. While this version of the problem is decidedly nonlinear, the basic tools still rely on convexity. In particular, we present a solution to this problem in terms of a nonlinear convex optimization problem that generalizes the maximum entropy approach used in several classical special cases.

  • 3.
    Byrnes, Christopher
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM.
    Lindquist, Anders
    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.
    Important moments in systems, control and optimizations2009In: 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, p. 91-96Conference paper (Refereed)
    Abstract [en]

    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.

  • 4.
    Byrnes, Christopher
    et al.
    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.
    Lindquist, Anders
    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.
    On the Stability and Instability of Padé Approximants2010In: Lecture notes in control and information sciences, ISSN 0170-8643, E-ISSN 1610-7411, Vol. 398, p. 165-175Article in journal (Refereed)
    Abstract [en]

    Over the past three decades there has been interest in using Pade approximants K with n = deg(K) < deg(G) = N as "reduced-order models" for the transfer function G of a linear system The attractive feature of this approach is that by matching the moments of G we can reproduce the steady-state behavior of G by the steady-state behavior of K. for certain classes of Inputs Indeed, we illustrate this by finding a first-order model matching a fixed set of moments for G. the causal inverse of a heat equation A key feature of this example is that the heat equation is a minimum phase system, so that its inverse system has a stable transfer function G and that K can also be chosen to be stable On the other hand, elementary examples show that both stability and instability can occur in reduced order models of a stable system obtained by matching moments using Pade approximants and, in the absence of stability, it does not make much sense to talk about steady-state responses nor does it make sense to match moments In this paper, we review Pack approximains. and their intimate relationship to continued fractions and Riccati equations, in a historical context that underscores why Pade approximation, as useful as it is, is not an approximation in any sense that reflects stability. Our main results on stability and instability states that if N >= 2 and l, r >= 0 with 0<l+r=n<N there is a non-empty open set U-lr of stable transfer functions G, having infinite Lebesque measure, such that each degree n proper rational function K matching the moments of G has e poles lying in C- and r poles lying in C+ The proof is constructive.

  • 5.
    Elvander, Filip
    et al.
    Lund Univ, Div Math Stat, Lund, Sweden..
    Jakobsson, Andreas
    Lund Univ, Div Math Stat, Lund, Sweden..
    Karlsson, Johan
    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 Royal Inst Technol, Dept Math, Stockholm, Sweden..
    USING OPTIMAL MASS TRANSPORT FOR TRACKING AND INTERPOLATION OF TOEPLITZ COVARIANCE MATRICES2018In: 2018 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), IEEE , 2018, p. 4469-4473Conference paper (Refereed)
    Abstract [en]

    In this work, we propose a novel method for interpolation and extrapolation of Toeplitz structured covariance matrices. By considering a spectral representation of Toeplitz matrices, we use an optimal mass transport problem in the spectral domain in order to define a notion of distance between such matrices. The obtained optimal transport plan naturally induces a way of interpolating, as well as extrapolating, Toeplitz matrices. The constructed covariance matrix interpolants and extrapolants preserve the Toeplitz structure, as well as the positive semi-definiteness and the zeroth covariance of the original matrices. We demonstrate the proposed method's ability to model locally linear shifts of spectral power for slowly varying stochastic processes, illustrating the achievable performance using a simple tracking problem.

  • 6.
    Fanizza, Giovanna
    et al.
    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.
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Nagamune, Ryozo
    A global analysis approach to passivity preserving model reduction2006In: Proceedings Of The 45th IEEE Conference On Decision And Control, Vols 1-14, 2006, p. 3399-3404Conference paper (Refereed)
    Abstract [en]

    Passivity-preserving model reduction for linear time-invariant systems amounts to approximating a positive-real rational transfer function with one of lower degree. Recently Antoulas and Sorensen have proposed such a model-reduction method based on Krylov projections. The method is based on an observation by Antoulas (in the single-input/single-output case) that if the approximant is preserving a subset of the spectral zeros and takes the same values as the original transfer function in the mirror points of the preserved spectral zeros, then the approximant is also positive real. However, this turns out to be a special solution in the theory of analytic interpolation with degree constraint developed by Byrnes, Georgiou and Lindquist, namely the maximum-entropy (central) solution. By tuning the interpolation points and the spectral zeros, as prescribed by this theory, one is able to obtain considerably better reduced-order models.

  • 7. Georgiou, T. T.
    et al.
    Lindquist, Anders
    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.
    On time-reversibility of linear stochastic models2014In: IFAC Proceedings Volumes (IFAC-PapersOnline), IFAC Papers Online, 2014, p. 10403-10408Conference paper (Refereed)
    Abstract [en]

    Reversal of the time direction in stochastic systems driven by white noise has been of central importance throughout the development of stochastic realization theory, filtering and smoothing. Similarly, in connection with certain problems in the theory of moments, the duality induced by time reversal was the key to deriving a compact parametrization and an interpretation of solutions. By combining ideas from these two lines of development we present herein a general view and a simplified account of time-reversal in stochastic models.

  • 8.
    Georgiou, Tryphon
    et al.
    University of Minnesota, United States.
    Lindquist, Anders
    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.
    The separation principle in stochastic control, redux2013In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 58, no 10, p. 2481-2494Article in journal (Refereed)
    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.

  • 9.
    Georgiou, Tryphon
    et al.
    University of Minnesota.
    Lindquist, Anders
    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.
    Two alternative views on control design with degree constraint2005In: Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, IEEE , 2005, p. 3645-3650Conference paper (Refereed)
    Abstract [en]

    The purpose of this note is to highlight similarities and differences between two alternative methodologies for feedback control design under constraints on the McMillan degree of the feedback system. Both sets of techniques focus on uniformly optimal designs. The first is based on the work of Gahinet and Apkarian, and Skelton, Iwasaki, Grigoriades and their co-workers, while the other is based on earlier joint work of the authors with C. I. Byrnes.

  • 10. Georgiou, Tryphon T.
    et al.
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Shanghai Jiao Tong Univ, Peoples R China.
    Optimal Estimation With Missing Observations via Balanced Time-Symmetric Stochastic Models2017In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 11, p. 5590-5603Article in journal (Refereed)
    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.

  • 11. Gopinath, A.
    et al.
    Xu, G.
    Ress, D.
    Öktem, Ozan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM.
    Subramaniam, S.
    Bajaj, C.
    Shape-based regularization of electron tomographic reconstruction2012In: IEEE Transactions on Medical Imaging, ISSN 0278-0062, E-ISSN 1558-254X, Vol. 31, no 12, p. 2241-2252Article in journal (Refereed)
    Abstract [en]

    We introduce a tomographic reconstruction method implemented using a shape-based regularization technique. Spatial models of known features in the structure being reconstructed are integrated into the reconstruction process as regularizers. Our regularization scheme is driven locally through shape information obtained from segmentation and compared with a known spatial model. We demonstrated our method on tomography data from digital phantoms, simulated data, and experimental electron tomography (ET) data of virus complexes. Our reconstruction showed reduced blurring and an improvement in the resolution of the reconstructed volume was also measured. This method also produced improved demarcation of spike boundaries in viral membranes when compared with popular techniques like weighted back projection and the algebraic reconstruction technique. Improved ET reconstructions will provide better structure elucidation and improved feature visualization, which can aid in solving key biological issues. Our method can also be generalized to other tomographic modalities.

  • 12. Hanebeck, U. D.
    et al.
    Lindquist, Anders
    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.
    Moment-based dirac mixture approximation of circular densities2014In: IFAC Proceedings Volumes (IFAC-PapersOnline), 2014, p. 5040-5048Conference 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.

  • 13.
    Karlsson, Johan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM.
    Georgiou, Tryphon
    Lindquist, Anders
    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.
    The inverse problem of analytic interpolation with degree constraint2006In: Proceedings Of The 45th IEEE Conference On Decision And Control, Vols 1-14, 2006, p. 559-564Conference paper (Refereed)
    Abstract [en]

    In [7], (6] a theory for degree-constrained analytic interpolation was developed in terms of the minimizers of certain convex entropy functionals. In the present paper, we introduce and study relevant inverse problems. More specifically, we answer the following two questions. First, given a function f which satisfies specified interpolation conditions, when is it that f can be obtained as the minimizer of a suitably chosen entropy functional? Second, given a function g, when does there exist a suitably entropy functional so that the unique minitnizer f which is subject to interpolation constraints also satisfies vertical bar f vertical bar = vertical bar g vertical bar on the unit circle. The theory and answers to these questions suggest an approach to identifying interpolants of a given degree and of a given approximate shape.

  • 14.
    Karlsson, Johan
    et al.
    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.
    Georgiou, Tryphon T.
    Department of Electrical Engineering, University of Minnesota.
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    The Inverse Problem of Analytic Interpolation With Degree Constraint and Weight Selection for Control Synthesis2010In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 55, no 2, p. 405-418Article in journal (Refereed)
    Abstract [en]

    The minimizers of certain weighted entropy functionals are the solutions to an analytic interpolation problem with a degree constraint, and all solutions to this interpolation problem arise in this way by a suitable choice of weights. Selecting appropriate weights is pertinent to feedback control synthesis, where interpolants represent closed-loop transfer functions. In this paper we consider the correspondence between weights and interpolants in order to systematize feedback control synthesis with a constraint on the degree. There are two basic issues that we address: we first characterize admissible shapes of minimizers by studying the corresponding inverse problem, and then we develop effective ways of shaping minimizers via suitable choices of weights. This leads to a new procedure for feedback control synthesis.

  • 15.
    Karlsson, Johan
    et al.
    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.
    Lindquist, Anders
    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.
    On Degree-Constrained Analytic Interpolation With Interpolation Points Close to the Boundary2009In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 54, no 6, p. 1412-1418Article in journal (Refereed)
    Abstract [en]

    In the recent article [4], a theory for complexity-constrained interpolation of contractive functions is developed. In particular, it is shown that any such interpolant may be obtained as the unique minimizer of a (convex) weighted entropy gain. In this technical note we study this optimization problem in detail and describe how the minimizer depends on weight selection and on interpolation conditions. We first show that, if, for a sequence of interpolants, the values of the entropy gain of the interpolants converge to the optimum, then the interpolants converge in H-2, but not in H-infinity This result is then used to describe the asymptotic behavior of the interpolant as an interpolation point approaches the boundary of the domain of analyticity. For loop shaping to specifications in control design, it might at first seem natural to place strategically additional interpolation points close to the boundary. However, our results indicate that such a strategy will have little effect on the shape. Another consequence of our results relates to model reduction based on minimum-entropy principles, where one should avoid placing interpolation points too close to the boundary.

  • 16.
    Karlsson, Johan
    et al.
    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.
    Lindquist, Anders
    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.
    Stability-preserving rational approximation subject to interpolation constraints2008In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 53, no 7, p. 1724-1730Article in journal (Refereed)
    Abstract [en]

    A quite comprehensive theory of analytic interpolation with degree constraint, dealing with rational analytic interpolants with an a priori bound, has been developed in recent years. In this paper, we consider the limit case when this bound is removed, and only stable interpolants with a prescribed maximum degree are sought. This leads to weighted H-2 minimization, where the interpolants are parameterized by the weights. The inverse problem of determining the weight given a desired interpolant profile is considered, and a rational approximation procedure based on the theory is proposed. This provides a tool for tuning the solution to specifications. The basic idea could also be applied to the case with bounded analytic interpolants.

  • 17.
    Karlsson, Johan
    et al.
    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.
    Lindquist, Anders
    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.
    Stable rational approximation in the context of interpolation and convex optimization2007In: Proceedings Of The 46th IEEE Conference On Decision And Control, Vols 1-14, 2007, p. 2214-2221Conference paper (Refereed)
    Abstract [en]

    A quite comprehensive theory of analytic interpolation with degree constraint, dealing with rational interpolants with an a priori bound, has been developed in recent years. In this paper we consider the limit case when this bound is removed, and only stable interpolants with a prescribed maximum degree are sought. This leads to weighted H-2 minimization, where the interpolants are parameterized by the weights. The inverse problem of determining the weight and the interpolation points given a desired interpolant profile is considered, and a rational approximation procedure based on the theory is proposed. This provides a tool for tuning the solution to specifications. The basic idea could also be applied to the case with bounded interpolants.

  • 18.
    Kuroiwa, Yohei
    et al.
    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.
    Lindquist, Anders
    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.
    A benchmark problem in robust control with degree constraint: two-sided Nudelman interpolation with complexity constraint approachManuscript (preprint) (Other academic)
  • 19.
    Lindquist, Anders
    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.
    New Directions and Applications in Control Theory2005Collection (editor) (Refereed)
  • 20.
    Lindquist, Anders
    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.
    Prediction-error approximation by convex optimization2007In: Modeling, Estimation and Control:Festschrift in honor of Giorgio Picci on the occation of his sixty-fifth birthday, BERLIN: SPRINGER-VERLAG BERLIN , 2007, Vol. 364, p. 239-249Chapter in book (Refereed)
    Abstract [en]

    This paper is dedicated to Giorgio Picci on the occasion of his 65th birthday. I have come to appreciate Giorgio not only as a great friend but also as a great scholar. When we first met at Brown University in 1973, he introduced me to his seminal paper [29] on splitting subspaces, which became the impetus for our joint work on the geometric theory of linear stochastic systems [23,24,25,26]. This led to a life-long friendship and a book project that never seemed to converge, but now is close to being finished [27]. I have learned a lot from Giorgio. The present paper grew out of a discussion in our book project, when Giorgio taught me about the connections between prediction-error identification and the Kullback-Leibler criterion. These concepts led directly into the recent theory of analytic interpolation with complexity constraint, with which I have been deeply involved in recent times. I shall try to explain these connections in the following paper.

  • 21.
    Lindquist, Anders
    et al.
    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.
    Avventi, Enrico
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Graphical Models of Autoregressive Moving-Average ProcessesIn: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523Article in journal (Other academic)
  • 22.
    Lindquist, Anders G.
    et al.
    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.
    Picci, Giorgio
    The Circulant Rational Covariance Extension Problem: The Complete Solution2013In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 58, no 11, p. 2848-2861Article in journal (Refereed)
    Abstract [en]

    The rational covariance extension problem to determine a rational spectral density given a finite number of covariance lags can be seen as a matrix completion problem to construct an infinite-dimensional positive-definite Toeplitz matrix the northwest corner of which is given. The circulant rational covariance extension problem considered in this paper is a modification of this problem to partial stochastic realization of periodic stationary process, which are better represented on the discrete unit circle Z(2N) rather than on the discrete real line Z. The corresponding matrix completion problem then amounts to completing a finite-dimensional Toeplitz matrix that is circulant. Another important motivation for this problem is that it provides a natural approximation, involving only computations based on the fast Fourier transform, for the ordinary rational covariance extension problem, potentially leading to an efficient numerical procedure for the latter. The circulant rational covariance extension problem is an inverse problem with infinitely many solutions in general, each corresponding to a bilateral ARMA representation of the underlying periodic process. In this paper, we present a complete smooth parameterization of all solutions and convex optimization procedures for determining them. A procedure to determine which solution that best matches additional data in the form of logarithmic moments is also presented.

  • 23.
    Lindquist, Anders
    et al.
    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.
    Karlsson, Johan
    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.
    Georgiou, Tryphon
    Weight selection for gap robustness with degree-constrained controllers2008In: Proc. 47th IEEE Conference on Decision and Control, 2008, p. 4127-4134Conference paper (Refereed)
    Abstract [en]

    In modern robust control, control synthesis may be cast as an interpolation problem where the interpolant relates to robustness and performance criteria. In particular,robustness in the gap fits into this framework and the magnitude of the corresponding interpolant dictate the robustness to perturbations of the plant as a function of frequency. In this paper we consider the correspondence between weighted entropy functionals and minimizing interpolants in order to find appropriate interpolants for e.g. control synthesis. There are two basic issues that we address: we first characterize admissible shapes of minimizers by studying the corresponding inverse problem, and then we develop effective ways of shaping minimizers via suitable choices of weights. These results are used in order to systematize feedback control synthesis to obtain frequency dependentrobustness bounds with a constraint on the controller degree. 

  • 24.
    Lindquist, Anders
    et al.
    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. Shanghai Jiao Tong University, Shanghai, China .
    Masiero, C.
    Picci, G.
    On the multivariate circulant rational covariance extension problem2013In: 2013 IEEE 52nd Annual Conference on Decision and Control (CDC), IEEE conference proceedings, 2013, p. 7155-7161Conference paper (Refereed)
    Abstract [en]

    Partial stochastic realization of periodic processes from finite covariance data leads to the circulant rational covariance extension problem and bilateral ARMA models. In this paper we present a convex optimization-based theory for this problem that extends and modifies previous results by Carli, Ferrante, Pavon and Picci on the AR solution, which have been successfully applied to image processing of textures. We expect that our present results will provide an enhancement of these procedures.

  • 25.
    Möller, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Input-Output Analysis of Power Control in Wireless Networks2013In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 58, no 4, p. 834-846Article in journal (Refereed)
    Abstract [en]

    In a wireless communication network, different users share a common resource. An objective of radio resource management is to assign the resources in an effective way among the users. Power control is an important component in this setting that has been extensively studied over the last two decades. In many real networks, there are inherent time delays due to filtering of signals and control signalling. Time delays can affect stability and convergence properties of the power control algorithms. We therefore consider power control laws of higher order to include models with delays and delay compensation. The main contribution of this paper is to exploit more structure of the interference feedback to prove less conservative conditions for system stability. Our primary tool to reduce conservativeness is to use scalings in an input-output framework for stability analysis.

  • 26.
    Möller, Anders
    et al.
    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.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Blomgren, Mats
    Gunnarsson, Fredrik
    Stability of Rate and Power Control Algorithms in Wireless Cellular Networks2011In: 2011 50th IEEE Conference On Decision And Control And European Control Conference (CDC-ECC), IEEE , 2011, p. 4535-4541Conference paper (Refereed)
    Abstract [en]

    In radio resource management for cellular networks a trade-off has to be made between the congestion level, related to cell coverage and intercell interference, and the Quality of Service (QoS) or data rates of the users. This is implemented by using a fast inner power control loop and an outer rate control algorithm, working on a slower time scale. Due to the distributed nature of the network, both information and control is distributed. Measurements of congestion and QoS are used in the control loops and this introduces a nonlinear feedback. Another complicating factor is that filtering, computations and information exchange in the network introduce time delays. In this paper we propose a general high order model as a cascade system with an outer and inner control loop. The control algorithms use distributed information available in the network. The full system model includes the nonlinear feedback from congestion and QoS measurements, time delays and time scale modelling. We provide sufficient conditions for stability and convergence of the system. Our primary analysis tool is input output theory.

  • 27. Norlén, L.
    et al.
    Öktem, Ozan
    KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM. KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Skoglund, U.
    Molecular cryo-electron tomography of vitreous tissue sections: current challenges2009In: Journal of Microscopy, ISSN 0022-2720, E-ISSN 1365-2818, Vol. 235, no 3, p. 293-307Article in journal (Refereed)
    Abstract [en]

    Electron tomography of vitreous tissue sections (tissue TOVIS) allows the study of the three-dimensional structure of molecular complexes in a near-native cellular context. Its usage is, however, limited by an unfortunate combination of noisy and incomplete data, by a technically demanding sample preparation procedure, and by a disposition for specimen degradation during data collection. Here we outline some major challenges as experienced from the application of TOVIS to human skin. We further consider a number of practical measures as well as theoretical approaches for its future development.

  • 28.
    Ringh, Axel
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Karlsson, Johan
    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.
    Lindquist, Anders
    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, Superseded Departments (pre-2005), Mathematics. Shanghai Jiao Tong Univ, Dept Automat, Shanghai, Peoples R China; Shanghai Jiao Tong Univ, Sch Math, Shanghai, Peoples R China.
    Lower bounds on the maximum delay margin by analytic interpolation2018In: 2018 IEEE 57th Annual Conference on Decision and Control (CDC), 2018Conference 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.

  • 29.
    Ringh, Axel
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Karlsson, Johan
    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.
    Lindquist, Anders
    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, Superseded Departments (pre-2005), Mathematics. Department of Automation, Shanghai Jiao Tong University, Shanghai, China.
    Multidimensional rational covariance extensionManuscript (preprint) (Other academic)
    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 parametrization 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, Wiener system identification, and image compression.

  • 30. Rullgard, H.
    et al.
    Ofverstedt, L. -G
    Masich, S.
    Daneholt, B.
    Öktem, Ozan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM.
    Simulation of transmission electron microscope images of biological specimens2011In: Journal of Microscopy, ISSN 0022-2720, E-ISSN 1365-2818, Vol. 243, no 3, p. 234-256Article in journal (Refereed)
    Abstract [en]

    We present a new approach to simulate electron cryo-microscope images of biological specimens. The framework for simulation consists of two parts; the first is a phantom generator that generates a model of a specimen suitable for simulation, the second is a transmission electron microscope simulator. The phantom generator calculates the scattering potential of an atomic structure in aqueous buffer and allows the user to define the distribution of molecules in the simulated image. The simulator includes a well defined electron-specimen interaction model based on the scalar Schrodinger equation, the contrast transfer function for optics, and a noise model that includes shot noise as well as detector noise including detector blurring. To enable optimal performance, the simulation framework also includes a calibration protocol for setting simulation parameters. To test the accuracy of the new framework for simulation, we compare simulated images to experimental images recorded of the Tobacco Mosaic Virus (TMV) in vitreous ice. The simulated and experimental images show good agreement with respect to contrast variations depending on dose and defocus. Furthermore, random fluctuations present in experimental and simulated images exhibit similar statistical properties. The simulator has been designed to provide a platform for development of new instrumentation and image processing procedures in single particle electron microscopy, two-dimensional crystallography and electron tomography with well documented protocols and an open source code into which new improvements and extensions are easily incorporated.

  • 31.
    Tavabi, Amir H.
    et al.
    Forschungszentrum Julich, Ernst Ruska Ctr Microscopy & Spect Electrons, D-52428 Julich, Germany.;Forschungszentrum Julich, Peter Grunberg Inst, D-52428 Julich, Germany..
    Beleggia, Marco
    Tech Univ Denmark, Ctr Elect Nanoscopy, DK-2800 Lyngby, Denmark..
    Migunov, Vadim
    Forschungszentrum Julich, Ernst Ruska Ctr Microscopy & Spect Electrons, D-52428 Julich, Germany.;Forschungszentrum Julich, Peter Grunberg Inst, D-52428 Julich, Germany..
    Savenko, Alexey
    FEI Co, Achtseweg Noord 5, NL-5600 KA Eindhoven, Netherlands..
    Öktem, Ozan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM.
    Dunin-Borkowski, Rafal E.
    Forschungszentrum Julich, Ernst Ruska Ctr Microscopy & Spect Electrons, D-52428 Julich, Germany.;Forschungszentrum Julich, Peter Grunberg Inst, D-52428 Julich, Germany..
    Pozzi, Giulio
    Forschungszentrum Julich, Ernst Ruska Ctr Microscopy & Spect Electrons, D-52428 Julich, Germany.;Forschungszentrum Julich, Peter Grunberg Inst, D-52428 Julich, Germany.;Univ Bologna, Dept Phys & Astron, Viale B Pichat 6-2, I-40127 Bologna, Italy..
    Tunable Ampere phase plate for low dose imaging of biomolecular complexes2018In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 8, article id 5592Article in journal (Refereed)
    Abstract [en]

    A novel device that can be used as a tunable support-free phase plate for transmission electron microscopy of weakly scattering specimens is described. The device relies on the generation of a controlled phase shift by the magnetic field of a segment of current-carrying wire that is oriented parallel or antiparallel to the electron beam. The validity of the concept is established using both experimental electron holographic measurements and a theoretical model based on Ampere's law. Computer simulations are used to illustrate the resulting contrast enhancement for studies of biological cells and macromolecules.

  • 32. Vulovic, Milos
    et al.
    Ravelli, Raimond B. G.
    van Vliet, Lucas J.
    Koster, Abraham J.
    Lazic, Ivan
    Lucken, Uwe
    Rullgård, Hans
    Öktem, Ozan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM.
    Rieger, Bernd
    Image formation modeling in cryo-electron microscopy2013In: Journal of Structural Biology, ISSN 1047-8477, E-ISSN 1095-8657, Vol. 183, no 1, p. 19-32Article in journal (Refereed)
    Abstract [en]

    Accurate modeling of image formation in cryo-electron microscopy is an important requirement for quantitative image interpretation and optimization of the data acquisition strategy. Here we present a forward model that accounts for the specimen's scattering properties, microscope optics, and detector response. The specimen interaction potential is calculated with the isolated atom superposition approximation (IASA) and extended with the influences of solvent's dielectric and ionic properties as well as the molecular electrostatic distribution. We account for an effective charge redistribution via the Poisson-Boltzmann approach and find that the IASA-based potential forms the dominant part of the interaction potential, as the contribution of the redistribution is less than 10%. The electron wave is propagated through the specimen by a multislice approach and the influence of the optics is included via the contrast transfer function. We incorporate the detective quantum efficiency of the camera due to the difference between signal and noise transfer characteristics, instead of using only the modulation transfer function. The full model was validated against experimental images of 20S proteasome, hemoglobin, and GroEL. The simulations adequately predict the effects of phase contrast, changes due to the integrated electron flux, thickness, inelastic scattering, detective quantum efficiency and acceleration voltage. We suggest that beam-induced specimen movements are relevant in the experiments whereas the influence of the solvent amorphousness can be neglected. All simulation parameters are based on physical principles and, when necessary, experimentally determined.

  • 33.
    Öktem, Ozan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM.
    Quinto, Eric Todd
    Tufts University.
    Skoglund, Ulf
    Okinawa Institute of Science and Technology.
    Electron Lambda-tomography2009In: Proceedings of the National Academy of Sciences of the United States of America, ISSN 0027-8424, E-ISSN 1091-6490, Vol. 106, no 51, p. 21842-21847Article in journal (Refereed)
    Abstract [en]

    Filtered back-projection and weighted back-projection have long been the methods of choice within the electron microscopy com- munity for reconstructing the structure of macromolecular assem- blies from electron tomography data. Here, we describe electron lambda-tomography, a reconstruction method that enjoys the ben- efits of the above mentioned methods, namely speed and ease of implementation, but also addresses some of their shortcomings. In particular, compared to these standard methods, electron lambda- tomography is less sensitive to artifacts that come from structures outside the region that is being reconstructed, and it can sharpen boundaries.

1 - 33 of 33
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