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Numerical Solution of mean-square Approximation Problem of Real Nonnegative Function by the Modulus of Double Fourier Integral

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Applied Mathematics 2011年第9期2卷 1076-1090页

作者： Petro Savenko Myroslava Tkach 不详

A nonlinear problem of mean-square approximation of a real nonnegative continuous function with respect to two variables by the modulus of double Fourier integral dependent on two real parameters with use of the smoothing functional is studied. Finding the optimal solutions of this problem is reduced to solution of the Hammerstein type two-dimensional nonlinear integral equation. The numerical algorithms to find the branching lines and branching-off solutions of this equation are constructed and justified. Numerical examples are presented.

关键词： mean-square Approximation Discrete Fourier Transform Two-Dimensional Nonlinear Integral Equation Nonuniqueness and Branching of Solutions Two-Dimensional Nonlinear Spectral Problem

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Stochastic Iterative Learning Control With Faded Signals

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IEEE/CAA Journal of Automatica Sinica 2019年第5期6卷 1196-1208页

作者： Ganggui Qu Dong Shen the College of Information Science and Technology Beijing University of Chemical TechnologyBeijing 100029China

Stochastic iterative learning control(ILC) is designed for solving the tracking problem of stochastic linear systems through fading channels. Consequently, the signals used in learning control algorithms are faded in the sense that a random variable is multiplied by the original signal. To achieve the tracking objective, a two-dimensional Kalman filtering method is used in this study to derive a learning gain matrix varying along both time and iteration axes. The learning gain matrix minimizes the trace of input error covariance. The asymptotic convergence of the generated input sequence to the desired input value is strictly proved in the mean-square sense. Both output and input fading are accounted for separately in turn, followed by a general formulation that both input and output fading coexists.Illustrative examples are provided to verify the effectiveness of the proposed schemes.

关键词： Fading channels iterative learning control (ILC) Kalman filtering, mean-square convergence stochastic systems

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Numerical Approximation of Real Finite Nonnegative Function by the Modulus of Discrete Fourier Transform

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Applied Mathematics 2010年第1期1卷 65-75页

作者： Petro Savenko Myroslava Tkach Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine Lviv Ukraine

The numerical algorithms for finding the lines of branching and branching-off solutions of nonlinear problem on mean-square approximation of a real finite nonnegative function with respect to two variables by the modu... 详细信息

关键词： mean-square Approximation Discrete Fourier Transform Two-Dimensional Nonlinear Integral Equation Nonuniqueness And Branching of Solutions

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