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Towards Higher-Order Zeroing Neural Network Dynamics for Solving Time-Varying Algebraic Riccati Equations

Author

Listed:
  • Houssem Jerbi

    (Department of Industrial Engineering, College of Engineering, University of Háil, Hail 1234, Saudi Arabia)

  • Hadeel Alharbi

    (Department of Computer Engineering, College of Computer Science and Engineering, University of Háil, Hail 1234, Saudi Arabia)

  • Mohamed Omri

    (Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Lotfi Ladhar

    (Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdul Aziz University, Jeddah 21589, Saudi Arabia)

  • Theodore E. Simos

    (Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia
    Data Recovery Key Laboratory of Sichun Province, Neijing Normal University, Neijiang 641100, China
    Section of Mathematics, Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, Greece)

  • Spyridon D. Mourtas

    (Department of Economics, Mathematics-Informatics and Statistics-Econometrics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece
    Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, 660041 Krasnoyarsk, Russia)

  • Vasilios N. Katsikis

    (Department of Economics, Mathematics-Informatics and Statistics-Econometrics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece)

Abstract

One of the most often used approaches for approximating various matrix equation problems is the hyperpower family of iterative methods with arbitrary convergence order, whereas the zeroing neural network (ZNN) is a type of neural dynamics intended for handling time-varying problems. A family of ZNN models that correlate with the hyperpower iterative methods is defined on the basis of the analogy that was discovered. These models, known as higher-order ZNN models (HOZNN), can be used to find real symmetric solutions of time-varying algebraic Riccati equations. Furthermore, a noise-handling HOZNN (NHOZNN) class of dynamical systems is introduced. The traditional ZNN and HOZNN dynamic flows are compared theoretically and numerically.

Suggested Citation

  • Houssem Jerbi & Hadeel Alharbi & Mohamed Omri & Lotfi Ladhar & Theodore E. Simos & Spyridon D. Mourtas & Vasilios N. Katsikis, 2022. "Towards Higher-Order Zeroing Neural Network Dynamics for Solving Time-Varying Algebraic Riccati Equations," Mathematics, MDPI, vol. 10(23), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4490-:d:986833
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    References listed on IDEAS

    as
    1. Simos, Theodore E. & Katsikis, Vasilios N. & Mourtas, Spyridon D. & Stanimirović, Predrag S., 2022. "Unique non-negative definite solution of the time-varying algebraic Riccati equations with applications to stabilization of LTV systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 164-180.
    2. Spyridon D. Mourtas & Chrysostomos Kasimis, 2022. "Exploiting Mean-Variance Portfolio Optimization Problems through Zeroing Neural Networks," Mathematics, MDPI, vol. 10(17), pages 1-20, August.
    3. Mariya Kornilova & Vladislav Kovalnogov & Ruslan Fedorov & Mansur Zamaleev & Vasilios N. Katsikis & Spyridon D. Mourtas & Theodore E. Simos, 2022. "Zeroing Neural Network for Pseudoinversion of an Arbitrary Time-Varying Matrix Based on Singular Value Decomposition," Mathematics, MDPI, vol. 10(8), pages 1-12, April.
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    Cited by:

    1. Jianrong Chen & Xiangui Kang & Yunong Zhang, 2023. "Continuous and Discrete ZND Models with Aid of Eleven Instants for Complex QR Decomposition of Time-Varying Matrices," Mathematics, MDPI, vol. 11(15), pages 1-18, July.
    2. Stanimirović, Predrag S. & Mourtas, Spyridon D. & Mosić, Dijana & Katsikis, Vasilios N. & Cao, Xinwei & Li, Shuai, 2024. "Zeroing neural network approaches for computing time-varying minimal rank outer inverse," Applied Mathematics and Computation, Elsevier, vol. 465(C).

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