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Research Articles

Prescribed time convergence and robust zeroing neural network for solving time-varying linear matrix equation

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Pages 1094-1109 | Received 12 May 2022, Accepted 15 Jan 2023, Published online: 23 Jan 2023

References

  • J. Dai, L. Jia, and L. Xiao, Design and analysis of two prescribed-time and robust ZNN models with application to time-variant stein matrix equation. IEEE Trans. Neural Netw. Learn. Syst. 32(4) (2021), pp. 1668–1677. doi:10.1109/TNNLS.2020.2986275.
  • J. Dai, Y. Li, L. Xiao, and L. Jia, Zeroing neural network for time-varying linear equations with application to dynamic positioning. IEEE Trans. Ind. Inf. 18(3) (2022), pp. 1552–1561. doi:10.1109/TII.2021.3087202.
  • J. Dai, Y. Li, L. Xiao, L. Jia, Q. Liao, and J. Li, Comprehensive study on complex-valued ZNN models activated by novel nonlinear functions for dynamic complex linear equations. Inf. Sci. 561 (2021), pp. 101–114. doi:10.1016/j.ins.2020.12.078.
  • J. Dai, P. Tan, X. Yang, L. Xiao, L. Jia, and Y. He, A fuzzy adaptive zeroing neural network with superior finite-time convergence for solving time-variant linear matrix equations. Knowledge-Based Syst. 242 (2022), p. 108405. doi:10.1016/j.knosys.2022.108405.
  • J. Dai, X. Yang, L. Xiao, L. Jia, X. Liu, and Y. Wang, Design and analysis of a self-adaptive zeroing neural network for solving time-varying quadratic programming. IEEE Trans. Neural Netw. Learn. Syst. (2022), pp. 1–10. doi:10.1109/TNNLS.2021.3138900.
  • Y. He, B. Liao, L. Xiao, L. Han, and X. Xiao, Double accelerated convergence ZNN with noise-suppression for handling dynamic matrix inversion. Mathematics 10 (2022), p. 50. doi:10.3390/math10010050.
  • Z. Hu, L. Xiao, J. Dai, Y. Xu, Q. Zuo, and C. Liu, A unified predefined-time convergent and robust ZNN model for constrained quadratic programming. IEEE Trans. Ind. Inf. 17(3) (2021), pp. 1998–2010. doi:10.1109/TII.2020.2996215.
  • J. Jin and J. Gong, A noise-tolerant fast convergence ZNN for dynamic matrix inversion. Int. J. Comput. Math. 98(11) (2021), pp. 2202–2219. doi:10.1080/00207160.2021.1881498.
  • J. Jin, L. Xiao, M. Lu, and J. Li, Design and analysis of two FTRNN models with application to time-varying Sylvester equation. IEEE. Access. 7 (2019), pp. 58945–58950. doi:10.1109/ACCESS.2019.2911130.
  • J. Jin, J. Zhu, J. Gong, and W. Chen, Novel activation functions-based ZNN models for fixed-time solving dynamirc Sylvester equation. Neural Comput. Appl. 34(17) (2022), pp. 14297–14315. doi:10.1007/s00521-022-06905-2.
  • L. Jin, S. Li, B. Hu, M. Liu, and J. Yu, A noise-suppressing neural algorithm for solving the time-varying system of linear equations: A control-based approach. IEEE Trans. Ind. Inf. 15(1) (2019), pp. 236–246. doi:10.1109/TII.2018.2798642.
  • L. Jin, S. Li, H. Wang, and Z. Zhang, Nonconvex projection activated zeroing neurodynamic models for time-varying matrix pseudoinversion with accelerated finite-time convergence. Appl. Soft Comput. 62 (2018), pp. 840–850. doi:10.1016/j.asoc.2017.09.016.
  • W. Li, A recurrent neural network with explicitly definable convergence time for solving time-variant linear matrix equations. IEEE Trans. Ind. Inf. 14(12) (2018), pp. 5289–5298. doi:10.1109/TII.2018.2817203.
  • J. Li, Y. Shi, and H. Xuan, Unified model solving nine types of time-varying problems in the frame of zeroing neural network. IEEE Trans. Neural Netw. Learn. Syst. 32(5) (2021), pp. 1896–1905. doi:10.1109/TNNLS.2020.2995396.
  • W. Li, L. Xiao, and B. Liao, A finite-time convergent and noise-rejection recurrent neural network and its discretization for dynamic nonlinear equations solving. IEEE Trans. Cybern. 50(7) (2020), pp. 3195–3207. doi:10.1109/TCYB.2019.2906263.
  • X. Li, J. Yu, S. Li, and L. Ni, A nonlinear and noise-tolerant ZNN model solving for time-varying linear matrix equation. Neurocomputing 317 (2018), pp. 70–78. doi:10.1016/j.neucom.2018.07.067.
  • Z. Li, Y. Zhang, L. Ming, J. Guo, and V.N. Katsikis, Real-domain QR decomposition models employing zeroing neural network and time-discretization formulas for time-varying matrices. Neurocomputing 448 (2021), pp. 217–227. doi:10.1016/j.neucom.2021.03.014.
  • Y. Sun, J. Cao, and C. Li, A universal noise-suppressing neural algorithm framework aided with nonconvex activation function for time-varying quadratic programming problems. J. Oper. Res. Soc. (2022), pp. 1–19. doi:10.1080/01605682.2022.2096501.
  • L. Xiao, A finite-time convergent Zhang neural network and its application to real-time matrix square root finding. Neural Comput. Appl. 31(2) (2019), pp. 793–800. doi:10.1007/s00521-017-3010-z.
  • L. Xiao, J. Dai, L. Jin, W. Li, S. Li, and J. Hou, A noise-enduring and finite-time zeroing neural network for equality-constrained time-varying nonlinear optimization. IEEE Trans. Syst. Man Cybern. Syst. 51(8) (2021), pp. 4729–4740. doi:10.1109/TSMC.2019.2944152.
  • L. Xiao, Y. He, and B. Liao, A parameter-changing zeroing neural network for solving linear equations with superior fixed-time convergence. Expert Syst. Appl. 208 (2022), p. 118086. doi:10.1016/j.eswa.2022.118086.
  • L. Xiao, B. Liao, S. Li, and K. Chen, Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations. Neural Netw. 98 (2018), pp. 102–113. doi:10.1016/j.neunet.2017.11.011.
  • L. Xiao, P. Liu, Y. He, L. Jia, and J. Tao, A novel ZNN model for fast synchronisation of chaos systems with external disturbances. Neurocomputing 491 (2022), pp. 197–205. doi:10.1016/j.neucom.2022.03.053.
  • L. Xiao, H. Tan, L. Jia, J. Dai, and Y. Zhang, New error function designs for finite-time ZNN models with application to dynamic matrix inversion. Neurocomputing 402 (2020), pp. 395–408. doi:10.1016/j.neucom.2020.02.121.
  • L. Xiao and Y. Zhang, Different Zhang functions resulting in different ZNN models demonstrated via time-varying linear matrix–vector inequalities solving. Neurocomputing 121 (2013), pp. 140–149. doi:10.1016/j.neucom.2013.04.041.
  • L. Xiao, Y. Zhang, J. Dai, J. Li, and W. Li, New noise-tolerant ZNN models with predefined-time convergence for time-variant sylvester equation solving. IEEE Trans. Syst. Man Cybern. Syst. 51(6) (2021), pp. 3629–3640. doi:10.1109/TSMC.2019.2930646.
  • L. Xiao, Y. Zhang, K. Li, B. Liao, and Z. Tan, A novel recurrent neural network and its finite-time solution to time-varying complex matrix inversion. Neurocomputing 331 (2019), pp. 483–492. doi:10.1016/j.neucom.2018.11.071.
  • Z. Yunong, J. Danchi, and W. Jun, A recurrent neural network for solving Sylvester equation with time-varying coefficients. IEEE Trans. Neural Netw. 13(5) (2002), pp. 1053–1063. doi:10.1109/TNN.2002.1031938.
  • L. Zhao, J. Jin, and J. Gong, A novel robust fixed-time convergent zeroing neural network for solving time-varying noise-polluted nonlinear equations. Int. J. Comput. Math. 98(12) (2021), pp. 2514–2532. doi:10.1080/00207160.2021.1902512.

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