Robust zeroing neural networks with two novel power-versatile activation functions for solving dynamic Sylvester equation

• Autorzy: Zhou Peng , Tan Mingtao

Identyfikatory

DOI

10.24425/bpasts.2022.141307

• Języki publikacji: EN

Abstrakty

EN

In this work, two robust zeroing neural network (RZNN) models are presented for online fast solving of the dynamic Sylvester equation (DSE), by introducing two novel power-versatile activation functions (PVAF), respectively. Differing from most of the zeroing neural network (ZNN) models activated by recently reported activation functions (AF), both of the presented PVAF-based RZNN models can achieve predefined time convergence in noise and disturbance polluted environment. Compared with the exponential and finite-time convergent ZNN models, the most important improvement of the proposed RZNN models is their fixed-time convergence. Their effectiveness and stability are analyzed in theory and demonstrated through numerical and experimental examples.

Słowa kluczowe

EN

recurrent neural network; RNN; zeroing neural network; ZNN; robust zeroing neural network; RZNN; fixed-time convergence

PL

rekurencyjna sieć neuronowa; zerowanie sieci neuronowej; konwergencja w ustalonym czasie

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2022
• Tom: Vol. 70, nr 3
• Strony: art. no. e141307
• Opis fizyczny: Bibliogr. 47 poz., rys., tab.

Twórcy

autor

Zhou Peng

• College of Electronic Information and Automation, Guilin University of Aerospace Technology, Guilin 541004, China

autor

Tan Mingtao

• School of Computer and Electrical Engineering, Hunan University of Arts and Science, Changde 415000, China

• https://orcid.org/0000-0001-9319-6417

Bibliografia

• [1] A. Benzaouia, M. Ait Rami, and S. El Faiz, “Stabilization of linear systems with saturation: a Sylvester equation approach”, IMA J. Math. Control Inf., vol. 21, no. 3, pp. 247–259, Sept. 2004.
• [2] Q. Wei, N. Dobigeon, and J. Tourneret, “Fast Fusion of Multi-Band Images Based on Solving a Sylvester Equation,” IEEE Trans. Image Process., vol. 24, no. 11, pp. 4109–4121, Nov. 2015.
• [3] Q. Wei, N. Dobigeon, J. Tourneret, J. Bioucas-Dias, and S. Godsill, “R-FUSE: Robust Fast Fusion of Multiband Images Based on Solving a Sylvester Equation,” IEEE Signal Process. Lett., vol. 23, no. 11, pp. 1632–1636, Nov. 2016.
• [4] V.L. Syrmos, “Disturbance decoupling using constrained Sylvester equations,” IEEE Trans. Autom. Control, vol. 39, no. 4, pp. 797–803, April 1994.
• [5] W. Zhang and D. Zhou, “Coupled iterative algorithms based on optimisation for solving Sylvester matrix equations,” IET Contr. Theory Appl., vol. 13, no. 4, pp. 584–593, 2019.
• [6] A. Wu and G. Duan, “Solution to the generalised sylvester matrix equation AV + BW = AVF,” IET Contr. Theory Appl., vol. 1, no. 1, pp. 402–408, January 2007.
• [7] G.R. Duan, “On the solution to the Sylvester matrix equation AV+BW=EVF,” IEEE Trans. Autom. Control, vol. 41, no. 4, pp. 612–614, April 1996.
• [8] M. Dehghan, and M. Hajarian, “Efficient iterative method for solving the second-order Sylvester matrix equation EVF2-AVFCV=BW,” IET Contr. Theory Appl., vol. 3, no. 10, pp. 1401–1408, October 2009.
• [9] G.R. Duan and B, Zhou, “Solution to the second-order Sylvester matrix equation MVF/sup 2/+DVF+KV=BW,” IEEE Trans. Autom. Control, vol. 51, no. 5, pp. 805–809, 2006.
• [10] A. Wu, G. Duan, and Y. Xue, “Kronecker Maps and Sylvester-Polynomial Matrix Equations,” IEEE Trans. Autom. Control, vol. 52, no. 5, pp. 905–910, May 2007.
• [11] Y. Lin, L. Bao, and Y. Wei, “Matrix Sign Function Methods for Solving Projected Generalized Continuous-Time Sylvester Equations,” IEEE Trans. Autom. Control, vol. 55, no. 11, pp. 2629–2634, Nov. 2010.
• [12] F. Ding and T. Chen, “Gradient based iterative algorithms for solving a class of matrix equations,” IEEE Trans. Autom. Control, vol. 50, no. 8, pp. 1216–1221, Aug. 2005.
• [13] Z. Huamin, “Gradient-based iterative algorithm for the extended coupled Sylvester matrix equations,” 2017 29th Chinese Control and Decision Conference (CCDC), Chongqing, 2017, pp. 1562–1567.
• [14] J. Zhu, J. Jin, W. Chen, and J, Gong, “A combined power activation function based convergent factor-variable ZNN model for solving dynamic matrix inversion,” Math. Comput. Simul., vol. 197, pp. 291–307, 2022.
• [15] J. Jin, “An Improved Finite Time Convergence Recurrent Neural Network with Application to Time-Varying Linear Complex Matrix Equation Solution,” Neural Process. Lett., vol. 53, pp. 777–786, 2021.
• [16] 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, vol. 7, pp. 58945–58950, 2019.
• [17] F. Yu, L. Liu, L. Xiao, K. Li, and S. Cai, “A robust and fixed-time zeroing neural dynamics for computing time-variant nonlinear equation using a novel nonlinear activation function,” Neurocomputing, vol. 350, pp. 108–116, 2019.
• [18] J.H. Mathews and K.D. Fink, Numerical methods using MATLAB. Englewood Cliffs, NJ, USA: Prentice-Hall, 2004.
• [19] Y. Zhang and H.F. Peng, “Zhang Neural Network for Linear Time-Varying Equation Solving and its Robotic Application,” 2007 International Conference on Machine Learning and Cybernetics, pp. 3543–3548 2007.
• [20] 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,” Proceedings of IEEE International Conference on Natural Computation, vol. 3, pp. 521–525, 2008.
• [21] 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., vol. 50, no. 7, pp. 3195–3207, 2020.
• [22] Z. Zhang, Z. Li, and S. Yang, “A Barrier Varying-Parameter Dynamic Learning Network for Solving Time-Varying Quadratic Programming Problems with Multiple Constraints,” IEEE Trans. Cybern., doi: 10.1109/TCYB.2021.3051261.
• [23] 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., vol. 37, no. 2, pp. 189–205, 2013.
• [24] L. Xiao, J. Dai, R. Lu, S. Li, J. Li, and S. Wang, “Design and Comprehensive Analysis of a Noise-Tolerant ZNN Model With Limited-Time Convergence for Time-Dependent Nonlinear Minimization,” IEEE Trans. Neural Networks, Learn. Syst., vol. 31, no. 12, pp. 5339–5348, 2020.
• [25] L. Xiao, Y. Zhang, Q. Zuo, J. Dai, J. Li, and W. Tang, “A Noise-Tolerant Zeroing Neural Network for Time-Dependent Complex Matrix Inversion Under Various Kinds of Noises,” IEEE Trans. Ind. Inf., vol. 16, no. 6, pp. 3757–3766, 2020. doi: 10.1109/TII.2019.2936877.
• [26] J. Jin, and J. Gong, “A noise-tolerant fast convergence ZNN for Dynamic Matrix Inversion,” Int. J. Comput. Math., vol. 98, no. 11, pp. 2202–2219, 2021.
• [27] L. Xiao, Z. Zhang, and S. Li, “Solving Time-Varying System of Nonlinear Equations by Finite-Time Recurrent Neural Networks, With Application to Motion Tracking of Robot Manipulators,” IEEE Trans. Syst. Man Cybern.: Syst., vol. 49, no. 11, pp. 2210–2220, 2019.
• [28] J. Jin, L. Zhao, M. Li, F. Yu, and Z. Xi, “Improved zeroing Neural Networks, for finite time solving nonlinear equations,” Neural Comput. Appl., vol. 32, pp. 4151–4160, 2020.
• [29] L. Jin, Y. Zhang, and S. Li, “Integration-enhanced Zhang neural network for real-time-varying matrix inversion in the presence of various kinds of noises,” IEEE Trans. Neural Networks, Learn. Syst., vol. 27, no. 12, pp. 2615–2627, 2016.
• [30] L. Jin, Y. Zhang, S. Li, and Y. Zhang, “Noise-tolerant ZNN models for solving time-varying zero-finding problems: A controltheoretic approach,” IEEE Trans. Autom. Control, vol. 62, no. 2, pp. 992–997, Feb. 2017.
• [31] L. Xiao et al., “A new noise-tolerant and predefined-time ZNN model for time-dependent matrix inversion,” Neural Networks, vol. 117, pp. 124–134, 2019.
• [32] C. Hu, J. Yu, Z. Chen, H. Jiang, and T. Huang, “Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous Neural Networks,” Neural Networks, vol. 89, pp. 74–83, 2017.
• [33] C. Aouiti and F. Miaadi, “A new fixed-time stabilization approach for Neural Networks, with time-varying delays,” Neural Comput. Appl., vol. 32, pp. 3295–3309, 2020.
• [34] A. Polyakov, “Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems,” IEEE Trans. Autom. Control, vol. 57, no. 8, pp. 2106–2110, 2012.
• [35] J. Jin, J. Zhu, J. Gong, and W. Chen, “Novel activation functionsbased ZNN models for fixed-time solving dynamic Sylvester equation,” Neural Comput. Appl., 2022, doi: 10.1007/s00521-022-06905-2.
• [36] J. Jin and L. Qiu, “A robust fast convergence zeroing neural network and its applications to dynamic Sylvester equation solving and robot trajectory tracking,” J. Franklin Inst., vol. 359, pp. 3183–3209, 2022.
• [37] J. Gong and J. Jin, “A better robustness and fast convergence zeroing neural network for solving dynamic nonlinear equations,” Neural Comput. Appl., 2021, doi: 10.1007/s00521-020-05617-9.
• [38] F. Yu, H. Shen, Z. Zhang, Y. Huang, S. Cai, and S. Du, “A new multi-scroll Chua’s circuit with composite hyperbolic tangentcubic nonlinearity: Complex dynamics, Hardware implementation and Image encryption application,” Integration, vol. 81, pp. 71–83, 2021.
• [39] F. Yu et al., “A 6D Fractional-Order Memristive Hopfield Neural Network and its Application in Image Encryption,” Front. Phys., vol. 10, p. 847385, 2022.
• [40] D. Pazderski, “Application of transverse functions to control differentially driven wheeled robots using velocity fields,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 64, no. 4, pp. 831–851, 2016. doi: 10.1515/bpasts-2016-0092.
• [41] Z. Hendzel, “Collision free path planning and control of wheeled mobile robot using Kohonen self-organising map,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 53, no. 1, pp. 39–47, 2005.
• [42] W. Kowalczyk and K. Kozłowski, “Trajectory tracking and collision avoidance for the formation of two-wheeled mobile robots,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 67, no. 5, pp. 915–924, 2019. doi: 10.24425/bpas.2019.128652.
• [43] X. Ji, Q. Zhu, J. Wang, C. Cai, and J. Ma, “Mobile robot visual homing by vector pre-assigned mechanism,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 67, no. 2, pp. 213–227, 2019.
• [44] J. Jin, “A robust zeroing neural network for solving dynamic nonlinear equations and its application to kinematic control of mobile manipulator,” Complex Intell. Syst., vol. 7, pp. 87–99, 2021.
• [45] 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., vol. 60, pp. 659–669, 2021.
• [46] L. Xiao and Y. Zhang, “A New Performance Index for the Repetitive Motion of Mobile Manipulators,” IEEE Trans. Cybern., vol. 44, no. 2, pp. 280–292, 2014.
• [47] D. Chen, S. Li, F.J. Lin, and Q. Wu, “New Super-Twisting Zeroing Neural-Dynamics Model for Tracking Control of Parallel Robots: A Finite-Time and Robust Solution,” IEEE Trans. Cybern., vol. 50, no. 6, pp. 2651–2660, 2020.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).