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A New Varying-Parameter Design Formula for Solving Time-Varying Problems

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Abstract

A novel finite-time convergent zeroing neural network (ZNN) based on varying gain parameter for solving time-varying (TV) problems is presented. The model is based on the improvement and generalization of the finite-time ZNN (FTZNN) dynamics by means of the varying-parameter ZNN (VPZNN) dynamics, and termed as VPFTZNN. More precisely, the proposed model replaces fixed and large values of the scaling parameter by an appropriate time-dependent gain parameter, which leads to a faster and bounded convergence of the error function in comparison to previous ZNN methods. The convergence properties of the proposed VPFTZNN dynamical evolution in its generic form is verified. Particularly, VPFTZNN for solving linear matrix equations and for computing generalized inverses are investigated theoretically and numerically. Moreover, the proposed design is applicable in solving the TV matrix inversion problem, solving the Lyapunov and Sylvester equation as well as in approximating the matrix square root. Theoretical analysis as well as simulation results validate the effectiveness of the introduced dynamical evolution. The main advantages of the proposed VPFTZNN dynamics are their generality and faster finite-time convergence with respect to FTZNN models.

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Authors and Affiliations

  1. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, Niš, 18000, Serbia

    Predrag S. Stanimirović

  2. Department of Economics, Division of Mathematics and Informatics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559, Athens, Greece

    Vasilios N. Katsikis

  3. School of Informatics, Aristotle University of Thessaloniki, Thessaloníki, Greece

    Dimitrios Gerontitis

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  1. Predrag S. Stanimirović
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  2. Vasilios N. Katsikis
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  3. Dimitrios Gerontitis
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Correspondence to Predrag S. Stanimirović.

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This author gratefully acknowledges support from the Ministry of Education, Science and Technological Development, Republic of Serbia, Grant No. 174013.

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Stanimirović, P.S., Katsikis, V.N. & Gerontitis, D. A New Varying-Parameter Design Formula for Solving Time-Varying Problems. Neural Process Lett 53, 107–129 (2021). https://doi.org/10.1007/s11063-020-10386-6

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