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  • 1.
    Engström, Christian
    et al.
    Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
    Grubisic, Luka
    University of Zagreb.
    A Subspace Iteration Algorithm for Fredholm Valued Functions2015In: Mathematical problems in engineering (Print), ISSN 1024-123X, E-ISSN 1563-5147, Vol. 2015, article id 459895Article in journal (Refereed)
    Abstract [en]

    We present an algorithm for approximating an eigensubspace of a spectral component of an analytic Fredholm valued function. Our approach is based on numerical contour integration and the analytic Fredholm theorem. The presented method can be seen as a variant of the FEAST algorithm for infinite dimensional nonlinear eigenvalue problems. Numerical experiments illustrate the performance of the algorithm for polynomial and rational eigenvalue problems.

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  • 2. Huang, Xiao-Yu
    et al.
    Xiang, Xian-Hong
    Li, Wubin
    Umeå University, Faculty of Science and Technology, Department of Computing Science.
    Chen, Kang
    Cai, Wen-Xue
    Li, Lei
    Matrix Factorization for Evolution Data2014In: Mathematical problems in engineering (Print), ISSN 1024-123X, E-ISSN 1563-5147, p. 525398-Article in journal (Refereed)
    Abstract [en]

    We study a matrix factorization problem, that is, to find two factor matrices U and V such that R approximate to U-T x V, where R is a matrix composed of the values of the objects O-1, O-2, ... , O-n at consecutive time points T-1, T-2, ... , T-t. We first present MAFED, a constrained optimization model for this problem, which straightforwardly performs factorization on R. Then based on the interplay of the data in U,V, and R, a probabilistic graphical model using the same optimization objects is constructed, in which structural dependencies of the data in these matrices are revealed. Finally, we present a fitting algorithm to solve the proposed MAFED model, which produces the desired factorization. Empirical studies on real-world datasets demonstrate that our approach outperforms the state-of-the-art comparison algorithms.

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  • 3. Ortega-Montiel, T.
    et al.
    Villafuerte-Segura, R.
    Vázquez-Aguilera, C.
    Freidovich, Leonid
    Umeå University, Faculty of Science and Technology, Department of Applied Physics and Electronics.
    Proportional Retarded Controller to Stabilize Underactuated Systems with Measurement Delays: Furuta Pendulum Case Study2017In: Mathematical problems in engineering (Print), ISSN 1024-123X, E-ISSN 1563-5147, article id 2505086Article in journal (Refereed)
    Abstract [en]

    The design and tuning of a simple feedback strategy with delay to stabilize a class of underactuated mechanical systems with dead time are presented. A linear time-invariant (LTI) model with time delay of fourth order and a Proportional Retarded (PR) controller are considered. The PR controller is shown as an appealing alternative to the application of observer-based controllers. This paper gives a step forward to obtain a better understanding of the effect of output delays and related phenomena in mechatronic systems, making it possible to design resilient control laws under the presence of uncertain time delays in measurements and obtain an acceptable performance without using a derivative action. The Furuta pendulum is a standard two-degrees-of-freedom benchmark example from the class of underactuated mechanical systems. The configuration under study includes an inherent output delay due to wireless communication used to transmit measurements of the pendulum's angular position. Our approach offers a constructive design and a procedure based on a combination of root loci and Mikhailov methods for the analysis of stability. Experiments over a laboratory platform are reported and a comparison with a standard linear state feedback control law shows the advantages of the proposed scheme.

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