A novel robust fixed-time convergent zeroing neural network for solving time-varying noise-polluted nonlinear equations

References

• S. Abbasbandy, Improving Newton–Raphson method for nonlinear equations by modified Adomian decomposition method. Appl. Math. Comput. 145(2–3) (2003), pp. 887–893.
   Web of Science ®Google Scholar
• A. Amiri, A. Cordero, M.T. Darvishi, et al., A fast algorithm to solve systems of nonlinear equations. J. Comput. Appl. Math. 354 (2019), pp. 242–258.
   Web of Science ®Google Scholar
• E.G. Birgin, and J.M. Martínez, A Newton-like method with mixed factorizations and cubic regularization for unconstrained minimization. Comput. Optim. Appl. 73(3) (2019), pp. 707–753.
   Web of Science ®Google Scholar
• L. Chen, Q. Guo, Z. Liu, et al., Enhanced synchronization-inspired clustering for high-dimensional data. Complex Intell. Syst. 7 (2021), pp. 203–223.
   Web of Science ®Google Scholar
• L. Chen, J. Zhang, L. Cai, et al., Fast community detection based on distance dynamics nonlinear recurrent neural networks . Tsinghua. Sci. Technol. 22(6) (2017), pp. 564–585.
   Web of Science ®Google Scholar
• C. Chun, Construction of newton-like iteration methods for solving nonlinear equations. Numer. Math. 104(3) (2006), pp. 297–315.
   Web of Science ®Google Scholar
• P. Dai, Q. Wu, Y. Wu, and W. Liu, Modified Newton-PSS method to solve nonlinear equations. Appl. Math. Lett. 86 (2018), pp. 305–312.
   Web of Science ®Google Scholar
• F. Ding, and H. Zhang, Brief paper–- gradient-based iterative algorithm for a class of the coupled matrix equations related to control systems. IET Control Theory Appl. 8(15) (2014), pp. 1588–1595.
   Web of Science ®Google Scholar
• J. Gong, and J. Jin, A better robustness and fast convergence zeroing neural network for solving dynamic nonlinear equations. Neural Comput. Appl. (2021). doi:https://doi.org/10.1007/s00521-020-05617-9.
   Web of Science ®Google Scholar
• D. Guo, and Y. Zhang, ZNN for solving online time-varying linear matrix–vector inequality via equality conversion. Appl. Math. Comput. 259 (2015), pp. 327–338.
   Web of Science ®Google Scholar
• J. Jin, A robust zeroing neural network for solving dynamic nonlinear equations and its application to kinematic control of mobile manipulator. Complex Intell. Syst. (2020). doi:https://doi.org/10.1007/s40747-020-00178-9.
   Web of Science ®Google Scholar
• J. Jin, An improved finite time convergence recurrent neural network with application to time-varying linear complex matrix equation solution. Neural Process. Lett. (2021). doi:https://doi.org/10.1007/s11063-021-10426-9.
   Web of Science ®Google Scholar
• J. Jin, and J. Gong, An interference-tolerant fast convergence zeroing neural network for dynamic matrix inversion and its application to mobile manipulator path tracking. Alexandria Eng. J. 60 (2020), pp. 659–669.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• J. Jin, L. Zhao, M. Li, F. Yu, and Z. Xi, Improved zeroing neural networks for finite time solving nonlinear equations. Neural Comput. Appl. 32(2) (2020), pp. 4151–4160.
   Google Scholar
• L. Jin, S. Li, B. Hu, et al., Noise-suppressing neural algorithm for solving time-varying system of linear equations: A control-based approach. IEEE Trans. Ind. Inf. 15(1) (2019), pp. 236–246.
   Web of Science ®Google Scholar
• L. Jin, Z. Xie, M. Liu, K. Chen, C. Li, and C. Yang, Novel joint-drift-free scheme at acceleration level for robotic redundancy resolution with tracking error theoretically eliminated. IEEE/ASME Trans. Mechatron. 26(1) (2021), pp. 90–101.
   Web of Science ®Google Scholar
• L. Jin, J. Yan, X. Du, X. Xiao, and D. Fu, RNN for solving time-variant generalized Sylvester equation with applications to robots and acoustic source localization. IEEE Trans. Ind. Inf. (In Press). doi:https://doi.org/10.1109/TII.2020.2964817.
   Google Scholar
• S. Li, S. Chen, and B. Liu, Accelerating a recurrent neural network to finite-time convergence for solving time-varying Sylvester equation by using a sign-bi-power activation function. Neural Process. Lett. 37(2) (2013), pp. 189–205.
   Web of Science ®Google Scholar
• S. Li, Y. Zhang, and L. Jin, Kinematic control of redundant manipulators using neural networks[J]. IEEE Trans. Neural Networks Learn. Syst. 28(10) (2017), pp. 2243–2254.
   PubMed Web of Science ®Google Scholar
• W. Li, B. Liao, L. Xiao, and R. Lu, A recurrent neural network with predefined-time convergence and improved noise tolerance for dynamic matrix square root finding. Neurocomputing 337 (2019), pp. 262–273.
   Web of Science ®Google Scholar
• K. Madhu, and J. Jayaraman, Some higher order Newton-like Methods for solving system of nonlinear equations and its applications. Int. J. Appl. Comput. Math. 2016 (2016), pp. 1–18.
   Google Scholar
• P. Miao, Y. Shen, Y. Huang, and Y.W. Wang, Solving time-varying quadratic programs based on finite-time Zhang neural networks and their application to robot tracking. Neural Comput. Appl. 26(3) (2015), pp. 693–703.
   Web of Science ®Google Scholar
• P.H.A. Ngoc, and T.T. Anh, Stability of nonlinear Volterra equations and applications. Appl. Math. Comput. 341 (2019), pp. 1–14.
   Web of Science ®Google Scholar
• B. Saheya, G.Q. Chen, Y.K. Sui, et al., A new Newton-like method for solving nonlinear equations. Springerplus. 5(1) (2016), pp. 1269.
   PubMedGoogle Scholar
• J.R. Sharma, A composite third order Newton–Steffensen method for solving nonlinear equations. Appl. Math. Comput. 169(1) (2005), pp. 242–246.
   Web of Science ®Google Scholar
• J.R. Sharma, and H. Arora, Improved Newton-like methods for solving systems of nonlinear equations. Sema J. 74(2) (2016), pp. 1–17.
   Google Scholar
• Y. Shen, P. Miao, Y. Huang, and Y. Shen, Finite-time stability and its application for solving time-varying Sylvester equation by recurrent neural network. Neural Process. Lett. 42(3) (2015), pp. 763–784.
   Web of Science ®Google Scholar
• Z. Sun, H. Li, J. Wang, and Y. Tian, Two modified spectral conjugate gradient methods with a new conjugacy condition for unconstrained optimization. Int. J. Comput. Math. 95(10) (2018), pp. 2082–2099.
   Web of Science ®Google Scholar
• Z. Sun, T. Shi, L. Wei, Y. Sun, K. Liu, and L. Jin, Noise-suppressing zeroing neural network for online time-varying nonlinear optimization problems: A control-based approach. Neural Comput. Appl. 32 (2020), pp. 11505–11520.
   Web of Science ®Google Scholar
• Z. Sun, Y. Sun, Y. Li, and K. Liu, A new trust region-sequential quadratic programming approach for nonlinear systems based on nonlinear model predictive control. Eng. Optim. 51(6) (2019), pp. 1071–1096.
   Web of Science ®Google Scholar
• Z. Sun, Y. Tian, H. Li, and J. Wang, A superlinear convergence feasible sequential quadratic programming algorithm for Bipedal dynamic walking robot via discrete mechanics and Optimal control. Optimal Control Appl. Methods 37(6) (2016), pp. 1139–1161.
   Web of Science ®Google Scholar
• Z. Sun, Y. Tian, and J. Wang, A novel projected fletcher-reeves Conjugate Gradient Approach for finite-time optimal robust controller of linear constraints optimization problem: Application to Bipedal Walking robots. Optimal Control Appl. Methods 39(1) (2018), pp. 130–159.
   Web of Science ®Google Scholar
• N. Ujevic, A method for solving nonlinear equations. Appl. Math. Comput. 174(2) (2006), pp. 1416–1426.
   Web of Science ®Google Scholar
• J. Wang, L. Chen, and Q. Guo, Iterative solution of the dynamic responses of locally nonlinear structures with drift. Nonlinear Dyn. 88(3) (2017), pp. 1551–1564.
   Web of Science ®Google Scholar
• 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.
   Google Scholar
• L. Xiao, K. Li, Z. Tan, et al., Nonlinear gradient neural network for solving system of linear equations. Inf. Process. Lett. 142 (2019), pp. 35–40.
   Web of Science ®Google Scholar
• L. Xiao, and B. Liao, A convergence-accelerated Zhang neural network and its solution application to Lyapunov equation. Neurocomputing 193 (2016), pp. 213–218.
   Web of Science ®Google Scholar
• 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.
   PubMed Web of Science ®Google Scholar
• L. Xiao, B. Liao, S. Li, et al., Design and analysis of FTZNN applied to the real-time solution of a nonstationary Lyapunov equation and tracking control of a wheeled mobile manipulator. IEEE Trans. Ind. Inf. 14(5) (2018), pp. 98–105.
   Google Scholar
• L. Xiao, and Y. Zhang, Solving time-varying inverse kinematics problem of wheeled mobile manipulators using Zhang neural network with exponential convergence. Nonlinear Dyn. 76(2) (2014), pp. 1543–1559.
   Web of Science ®Google Scholar
• Z. Xie, L. Jin, X. Luo, Z. Sun, and M. Liu, RNN for repetitive motion generation of redundant robot manipulators: An orthogonal projection-based scheme. IEEE Trans. Neural Networks Learn. Syst., (In Press). doi:https://doi.org/10.1109/TNNLS.2020.3028304.
   Google Scholar
• C. Yi, Y. Chen, and X. Lan, Comparison on neural solvers for the Lyapunov matrix equation with stationary nonstationary coefficients. Appl. Math. Model. 37(4) (2013), pp. 2495–2502.
   Web of Science ®Google Scholar
• C. Yi, Y. Chen, and Z. Lu, Improved gradient-based neural networks for online solution of Lyapunov matrix equation. Inf. Process. Lett. 111(16) (2011), pp. 780–786.
   Web of Science ®Google Scholar
• Y. Zhang, K. Chen, X. Li, C. Yi, and H. Zhu. Simulink modeling and comparison of Zhang neural networks and gradient neural networks for time-varying Lyapunov equation solving, in: Proceedings of IEEE International Conference on Natural Computation, vol. 3, pp. 521–525, 2008.
   Google Scholar
• Y. Zhang, and C. Yi, Zhang Neural Networks and Neural-Dynamic Method, Nova Science Publishers, New York, 2011.
   Google Scholar
• Z. Zhang, Z. Li, Y. Zhang, et al., Neural-dynamic-method-based dual-arm CMG scheme with time-varying constraints applied to humanoid robots. IEEE Transactions on Neural Networks and Learning Systems 26(12) (2015), pp. 3251–3262.
   PubMed Web of Science ®Google Scholar
• L. Zhao, J. Jin, J. Gong, Robust zeroing neural network for fixed-time kinematic control of wheeled mobile robot in noise-polluted environment. Math. Comput. Simul. 185 (2021), pp. 289–307. doi:https://doi.org/10.1016/j.matcom.2020.12.030.
   Web of Science ®Google Scholar
• Z. Zuo, and L. Tie, Distributed robust finite-time nonlinear consensus protocols for multi-agent systems. Int. J. Syst. Sci. 47(6) (2016), pp. 1366–1375.
   Web of Science ®Google Scholar