Document Type : Technical Paper

Author

Department of Electrical Engineering, Faculty of Electrical and Computer Engineering, Urmia University, Urmia, Iran.

Abstract

This paper explores fixed-time synchronization for discontinuous fuzzy delay recurrent neural networks (DFRNNs) with time-varying delays. Based on a generalized variable transformation, the error system has been developed to effectively manage discontinuities in neural systems. This research addresses the fixed-time stability problem using a novel discontinuous state-feedback control input and a simple switching adaptive control scheme. The proposed method ensures robust synchronization of the drive and response neural systems within a fixed time. Practical applications of this work include improvements in protocols for secure communications, robotic control systems, and intelligent control frameworks over dynamic systems. A numerical example substantiates the theoretical claims, demonstrating the strengths of the proposed approach. The results show fixed-time convergence of error margins to zero, ensuring unbiased performance within a predefined timeframe, independent of initial conditions.

Keywords

Main Subjects

[1]  A. Polyakov, “Nonlinear feedback design for fixed-time stabilization of linear control systems," IEEE Transactions on Automatic Control, vol. 57, no. 8, pp. 2106-2110, 2011, 10.1109/TAC.2011.2179869.
 
[2]  J. Yu, S. Yu, J. Li, and Y. Yan, “Fixed-time stability theorem of stochastic nonlinear systems," International Journal of Control, vol. 92, no. 9, pp. 2194-2200, 2019, 10.1080/00207179.2018.1430900.
 
[3]  Y. Zhang and F. Wang, “Observer-based fixed-time neural control for a class of nonlinear systems," IEEE Transactions on Neural Networks and Learning Systems, 2021, 10.1109/TNNLS.2020.3046865.
 
[4]  J. Liu, Y. Zhang, Y. Yu, and C. Sun, “Fixed-time leader-follower consensus of networked nonlinear systems via event/self-triggered control," IEEE Transactions on Neural Networks and Learning Systems, vol. 31, no. 11, pp. 5029-5037, 2020, 10.1109/TNNLS.2019.2957069.
 
[5]  J. Liu, Y. Yu, H. He, and C. Sun, “Team-triggered practical fixed-time consensus of double-integrator agents with uncertain disturbance," IEEE Transactions on Cybernetics, vol. 51, no. 6, pp. 3263-3272, 2020, 10.1109/TCYB.2020.2999199.
 
[6]  K. Garg, E. Arabi, and D. Panagou, “Prescribed-time convergence with input constraints: A control Lyapunov function based approach," in 2020 American Control Conference (ACC), IEEE, 2020, pp. 962-967, 10.23919/ACC45564.2020.9147641.
 
[7]  H. Min, S. Xu, B. Zhang, Q. Ma, and D. Yuan, “Fixed-time Lyapunov criteria and state-feedback controller design for stochastic nonlinear systems," IEEE/CAA Journal of Automatica Sinica, vol. 9, no. 6, pp. 1005 - 1014, 2022, 10.1109/JAS.2022.105539.
 
[8]  H. Ren, Z. Peng, and Y. Gu, “Fixed-time synchronization of stochastic memristor-based neural networks with adaptive control," Neural Networks, vol. 130, pp. 165-175, 2020, 10.1016/j.neunet.2020.07.002.
 
[9]  C. Guo , J. Hu,  “Fixed-Time Stabilization of High-Order Uncertain Nonlinear Systems: Output Feedback Control Design and Settling Time Analysis," Journal of Systems Science and Complexity, 10.1007/s11424-023-2370-y, 2023.
 
[10]  M. V. Basin, P. Yu, and Y. B. Shtessel, “Hypersonic missile adaptive sliding mode control using finite- and fixed-time observers," IEEE Transactions on Industrial Electronics, vol. 65, no. 1, pp. 930-941, 2017, 10.1109/TIE.2017.2701776.
 
[11]  F. Gao, H. Chen, J. Huang, and Y. Wu, “A general fixed-time observer for lower-triangular nonlinear systems," IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 68, no. 6, pp. 1992-1996, 2020, 10.1109/TCSII.2020.3039572.
 
[12]  J. Zhang, D. Xu, X. Li, and Y. Wang, “Singular system full-order and reduced-order fixed-time observer design," IEEE Access, vol. 7, pp. 112113-112119, 2019, 10.1109/ACCESS.2019.2935238.
 
[13]  P. Zhang and J. Yu, “Stabilization of USVs under mismatched condition based on fixed-time observer," IEEE Access, vol. 8, pp. 195305-195316, 2020, 10.1109/ACCESS.2020.3034237.
 
[14]  X. Yu, P. Li, and Y. Zhang, “The design of fixed-time observer and finite-time fault-tolerant control for hypersonic gliding vehicles," IEEE Transactions on Industrial Electronics, vol. 65, no. 5, pp. 4135-4144, 2017, 10.1109/TIE.2017.2772192.
 
[15]  M. Noack, J. G. Rueda-Escobedo, J. Reger, and J. A. Moreno, “Fixed-time parameter estimation in polynomial systems through modulating functions," in 2016 IEEE 55th Conference on Decision and Control (CDC), IEEE, 2016, pp. 2067-2072, 10.1109/CDC.2016.7798568.
 
[16]  C. Zhu, Y. Jiang, and C. Yang, “Online parameter estimation for uncertain robot manipulators with fixed-time convergence," in 2020 15th IEEE Conference on Industrial Electronics and Applications (ICIEA), IEEE, 2020, pp. 1808-1813, 10.1109/ICIEA48937.2020.9248176.
 
[17]  J. Wang, D. Efimov, S. Aranovskiy, and A. A. Bobtsov, “Fixed-time estimation of parameters for non-persistent excitation," European Journal of Control, vol. 55, pp. 24-32, 2020, 10.1016/j.ejcon.2019.07.005.
 
[19]  D. Efimov, S. Aranovskiy, A. A. Bobtsov, and T. Raïssi, “On fixed-time parameter estimation under interval excitation," in 2020 European Control Conference (ECC), IEEE, 2020, pp. 246-251, 10.23919/ECC51009.2020.9143735.
 
[19]  H. Ríos, D. Efimov, J. A. Moreno, W. Perruquetti, and J. G. Rueda-Escobedo, “Time-varying parameter identification algorithms: Finite and fixed-time convergence," IEEE Transactions on Automatic Control, vol. 62, no. 7, pp. 3671-3678, 2017, 10.1109/TAC.2017.2673413.
 
[20]  G. Ji, C.  Hu, J. Yu, H. Jiang,“Finite-time and fixed-time synchronization of discontinuous complex networks: A unified control framework design,”  Journal of the Franklin Institute,, vol. 355, no. 11, pp. 4665-4685, doi:j.jfranklin.2018.04.026, 2018.
 
[21]  F. Kong, Q. Zhu, R. Sakthivel,“Finite-time and fixed-time synchronization control of fuzzy Cohen-Grossberg neural networks,”  Fuzzy Sets and Systems,, vol. 394, no. 11, pp. 87-109, doi:10.1016/j.fss.2019.12.002, 2020.
 
[22]  W. Yang, W. Yu, J. Cao, F.E. Alsaadi, T. Hayat,“Global exponential stability and lag synchronization for delayed memristive fuzzy CohenGrossberg BAM neural networks with impulses,”  Neural Network,, vol. 98, no. , pp. 122–153, doi:10.1016/j.neunet.2017.11.001, 2018.
 
[23]  C. Hu, J. Yu, Z.H. Chen, H.J. Jiang, T.W. Huang,“Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks,”  Neural Network,, vol. 89, no. , pp. 74–83, doi: , 2017, 10.1016/j.neunet.2017.02.001.
 
[24]  T. H. Gronwall, "Note on the derivatives with respect to a parameter of the solutions of a system of differential equations." Annals of Mathematics, vol. 20, no. 4,  pp. 292-296, 1919, doi.org/10.2307/1967124.
 
[25] F. Sabahi, M. R. Akbarzadeh-T, “A framework for analysis of extended fuzzy logic.” J. Zhejiang Univ. - Sci. C 15, 584–591 (2014). https://doi.org/10.1631/jzus.C
1300217
 
[26] F. Sabahi, “Fuzzy Adaptive Granulation Multi-Objective Multi-microgrid Energy Management. Journal of AI and Data Mining8(4), 481-489. 2020. doi: 10.22044/jadm.2019.6985.1828
 
[27] A. Polyakov, “Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems," in IEEE Transactions on Automatic Control, vol. 57, no. 8, pp. 2106-2110, Aug. 2012, doi: 10.1109/TAC.2011.2179869.
 
[28] J. Zhou, T. Chen, L. Xiang, “Adaptive Synchronization of Delayed Neural Networks Based on Parameters Identification”. In: Wang, J., Liao, X., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427391_48