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  • 1.
    Dai, Liang
    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.
    Identification using Convexification and Recursion2016Doctoral thesis, monograph (Other academic)
    Abstract [en]

    System identification studies how to construct mathematical models for dynamical systems from the input and output data, which finds applications in many scenarios, such as predicting future output of the system or building model based controllers for regulating the output the system.

    Among many other methods, convex optimization is becoming an increasingly useful tool for solving system identification problems. The reason is that many identification problems can be formulated as, or transformed into convex optimization problems. This transformation is commonly referred to as the convexification technique. The first theme of the thesis is to understand the efficacy of the convexification idea by examining two specific examples. We first establish that a l1 norm based approach can indeed help in exploiting the sparsity information of the underlying parameter vector under certain persistent excitation assumptions. After that, we analyze how the nuclear norm minimization heuristic performs on a low-rank Hankel matrix completion problem. The underlying key is to construct the dual certificate based on the structure information that is available in the problem setting.        

    Recursive algorithms are ubiquitous in system identification. The second theme of the thesis is the study of some existing recursive algorithms, by establishing new connections, giving new insights or interpretations to them. We first establish a connection between a basic property of the convolution operator and the score function estimation. Based on this relationship, we show how certain recursive Bayesian algorithms can be exploited to estimate the score function for systems with intractable transition densities. We also provide a new derivation and interpretation of the recursive direct weight optimization method, by exploiting certain structural information that is present in the algorithm. Finally, we study how an improved randomization strategy can be found for the randomized Kaczmarz algorithm, and how the convergence rate of the classical Kaczmarz algorithm can be studied by the stability analysis of a related time varying linear dynamical system.

  • 2.
    Dai, Liang
    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.
    On some sparsity related problems and the randomized Kaczmarz algorithm2014Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis studies several problems related to recovery and estimation. Specifically, these problems are about sparsity and low-rankness, and the randomized Kaczmarz algorithm. This thesis includes four papers referred to as Paper A, Paper B, Paper C, and Paper D.

    Paper A considers how to make use of the fact that the solution to an overdetermined system is sparse. This paper presents a three-stage approach to accomplish the task. We show that this strategy, under the assumptions as made in the paper, achieves the oracle property.

    In Paper B, a Hankel-matrix completion problem arising in system theory is studied. The use of the nuclear norm heuristic for this basic problem is considered. Theoretical justification for the case of a single real pole is given. Results show that for the case of a single real pole, the nuclear norm heuristic succeeds in the matrix completion task. Numerical simulations indicate that this result does not always carry over to the case of two real poles.

    Paper C discusses a screening approach for improving the computational performance of the Basis Pursuit De-Noising problem. The key ingredient for this work is to make use of an efficient ellipsoid update algorithm. The results of the experiments show that the proposed scheme can improve the overall time complexity for solving the problem.

    Paper D studies the choice of the probability distribution for implementing the row-projections in the randomized Kaczmarz algorithm. This relates to an open question in the recent literature. The result proves that a probability distribution resulting in a faster convergence of the algorithm can be found by solving a related Semi-Definite Programming optimization problem.

    List of papers
    1. Sparse estimation from noisy observations of an overdetermined linear system
    Open this publication in new window or tab >>Sparse estimation from noisy observations of an overdetermined linear system
    2014 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 50, no 11, p. 2845-2851Article in journal (Refereed) Published
    National Category
    Signal Processing
    Identifiers
    urn:nbn:se:uu:diva-226192 (URN)10.1016/j.automatica.2014.08.018 (DOI)000345727700010 ()
    Available from: 2014-10-07 Created: 2014-06-12 Last updated: 2017-12-05Bibliographically approved
    2. On the nuclear norm heuristic for a Hankel matrix completion problem
    Open this publication in new window or tab >>On the nuclear norm heuristic for a Hankel matrix completion problem
    2015 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 51, p. 268-272Article in journal (Refereed) Published
    Abstract [en]

    This note addresses the question if and why the nuclear norm heuristic can recover an impulse response generated by a stable single-real-pole system, if elements of the upper-triangle of the associated Hankel matrix are given. Since the setting is deterministic, theories based on stochastic assumptions for low-rank matrix recovery do not apply in the considered situation. A 'certificate' which guarantees the success of the matrix completion task is constructed by exploring the structural information of the hidden matrix. Experimental results and discussions regarding the nuclear norm heuristic applied to a more general setting are also given.

    National Category
    Control Engineering
    Identifiers
    urn:nbn:se:uu:diva-226193 (URN)10.1016/j.automatica.2014.10.045 (DOI)000348015500032 ()
    Available from: 2014-10-29 Created: 2014-06-12 Last updated: 2017-12-05Bibliographically approved
    3. An ellipsoid based, two-stage screening test for BPDN
    Open this publication in new window or tab >>An ellipsoid based, two-stage screening test for BPDN
    2012 (English)In: Proc. 20th European Signal Processing Conference, IEEE , 2012, p. 654-658Conference paper, Published paper (Refereed)
    Place, publisher, year, edition, pages
    IEEE, 2012
    National Category
    Signal Processing
    Identifiers
    urn:nbn:se:uu:diva-183856 (URN)978-1-4673-1068-0 (ISBN)
    Conference
    EUSIPCO 2012, August 27-31, Bucharest, Romania
    Available from: 2012-08-31 Created: 2012-11-05 Last updated: 2014-06-12Bibliographically approved
    4. On the randomized Kaczmarz algorithm
    Open this publication in new window or tab >>On the randomized Kaczmarz algorithm
    2014 (English)In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 21, no 3, p. 330-333Article in journal (Refereed) Published
    National Category
    Signal Processing
    Identifiers
    urn:nbn:se:uu:diva-211501 (URN)10.1109/LSP.2013.2294376 (DOI)000331299200004 ()
    Available from: 2014-01-31 Created: 2013-11-25 Last updated: 2017-12-06Bibliographically approved
  • 3.
    Dai, Liang
    et al.
    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.
    Pelckmans, Kristiaan
    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.
    An ellipsoid based, two-stage screening test for BPDN2012In: Proc. 20th European Signal Processing Conference, IEEE , 2012, p. 654-658Conference paper (Refereed)
  • 4.
    Dai, Liang
    et al.
    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.
    Pelckmans, Kristiaan
    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.
    An online algorithm for controlling a monotone Wiener system2012In: Proceedings of the 2012 24th Chinese Control and Decision Conference (CCDC), Piscataway, NJ: IEEE , 2012, p. 1585-1590Conference paper (Refereed)
    Abstract [en]

    This paper proposes and studies an online algorithm ('NORTKNAR') for controlling a monotone Wiener system to a given level. Such systems consist of a FIR model, followed by a monotonically in-or decreasing nonlinear static function. We consider phenomena which obey such system up to stochastic perturbations. We study almost sure convergence under weak regularity assumptions. Theoretical results are complemented by empirical results on the control of a PharmacoKinetics-PharmacoDynamic (PK-PD) system regulating concentrations of levuodopa in the bloodstream. Finally, we indicate how those ideas find application to regulating the rate of events in pulsatile systems.

  • 5.
    Dai, Liang
    et al.
    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.
    Pelckmans, Kristiaan
    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.
    On the nuclear norm heuristic for a Hankel matrix completion problem2015In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 51, p. 268-272Article in journal (Refereed)
    Abstract [en]

    This note addresses the question if and why the nuclear norm heuristic can recover an impulse response generated by a stable single-real-pole system, if elements of the upper-triangle of the associated Hankel matrix are given. Since the setting is deterministic, theories based on stochastic assumptions for low-rank matrix recovery do not apply in the considered situation. A 'certificate' which guarantees the success of the matrix completion task is constructed by exploring the structural information of the hidden matrix. Experimental results and discussions regarding the nuclear norm heuristic applied to a more general setting are also given.

  • 6.
    Dai, Liang
    et al.
    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.
    Pelckmans, Kristiaan
    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.
    Sparse estimation from noisy observations of an overdetermined linear system2014In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 50, no 11, p. 2845-2851Article in journal (Refereed)
  • 7.
    Dai, Liang
    et al.
    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.
    Pelckmans, Kristiaan
    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.
    Bai, Er-Wei
    Identifiability and convergence analysis of the MINLIP estimator2015In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 51, p. 104-110Article in journal (Refereed)
  • 8.
    Dai, Liang
    et al.
    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.
    Schön, Thomas B.
    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.
    A new structure exploiting derivation of recursive direct weight optimization2015In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 60, no 6, p. 1683-1685Article in journal (Refereed)
    Abstract [en]

    The recursive direct weight optimization method is used to solve challenging nonlinear system identification problems. This note provides a new derivation and a new interpretation of the method. The key underlying the note is to acknowledge and exploit a certain structure inherent in the problem.

  • 9.
    Dai, Liang
    et al.
    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.
    Schön, Thomas B.
    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.
    On the exponential convergence of the Kaczmarz algorithm2015In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 22, no 10, p. 1571-1574Article in journal (Refereed)
    Abstract [en]

    The Kaczmarz algorithm (KA) is a popular method for solving a system of linear equations. In this note we derive a new exponential convergence result for the KA. The key allowing us to establish the new result is to rewrite the KA in such a way that its solution path can be interpreted as the output from a particular dynamical system. The asymptotic stability results of the corresponding dynamical system can then be leveraged to prove exponential convergence of the KA. The new bound is also compared to existing bounds.

  • 10.
    Dai, Liang
    et al.
    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.
    Schön, Thomas B.
    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.
    Using convolution to estimate the score function for intractable state-transition models2016In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 23, no 4, p. 498-501Article in journal (Refereed)
  • 11.
    Dai, Liang
    et al.
    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.
    Soltanalian, Mojtaba
    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.
    Pelckmans, Kristiaan
    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.
    On the randomized Kaczmarz algorithm2014In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 21, no 3, p. 330-333Article in journal (Refereed)
  • 12.
    Pelckmans, Kristiaan
    et al.
    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.
    Dai, Liang
    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.
    A simple recursive algorithm for learning a monotone Wiener system2011In: Proc. 50th Conference on Decision and Control, Piscataway, NJ: IEEE , 2011, p. 3622-3627Conference paper (Refereed)
  • 13.
    Pelckmans, Kristiaan
    et al.
    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.
    Dai, Liang
    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.
    Bai, Er-Wei
    On the Convergence Analysis of the MINLIP Estimator2012In: Proceedings of the 16th IFAC Symposium on System Identification / [ed] Michel Kinnaert, 2012, p. 482-487Conference paper (Refereed)
1 - 13 of 13
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