Abstract
In order to improve the reliability of mobile network, a mathematical model of mobile network reliability control based on nonlinear PDE is proposed. Fuzzy Smith neural network structure is used to construct the controlled object model of mobile network reliability control, and the time-varying delay function of mobile network control is constructed by non-linear proportional differential equation under the condition of bounded delay. The convergence constraint function of mobile network control is combined with Lyapunov function, and the fuzzy adaptive learning is carried out according to the weight of network output. A time-delay hyperbolic proportional differential control feedback unit for hidden layer weight learning of mobile network is constructed. Robustness training of reliability output of mobile network is carried out in the boundary value control node. The singular eigenvalues of the control output of mobile network are extracted, and the convergence is judged in the solution space of the singular value distribution. The optimal solution of the network output is obtained according to the learning method of LM-Smith neural network. A non-linear Jacobian matrix is constructed to analyze the stability of the mathematical model of the reliability control of mobile network. The simulation results show that this method has good reliability and fine steady-state convergence for mobile network output control, which reduces the output error of the mobile network.
Similar content being viewed by others
References
Chi Y, Liu XM (2013) Research on power control method of mobile communication network based on swarm intelligence method[J]. J Hebei Univer Sci Techno 34(4):334–339
Dang XY, Liu ZT, Li BL et al (2016) Noncoherent multiple symbol detection for continuous phase modulation in physical-layer network coding [J]. J Electron Inf Technol 38(4):877–884
Du L, Zhang Y, Hu GG, Youming L (2017) Research on chaos control of a duopoly Cournot-Puu model[J]. Appl Math Mech 38(2):224–232
Duan JB (2017) Load balance improvement technology for fiber cloud platform terminal interface[J]. Laser J 38(1):140–143
Jiang BL, Zhang XP (2016) Design and improvement of equilibrium scheduling platform for big data network[J]. Mod Electron Tech 39(6):62–65
Li YG, Zhang ZZ, Li LJ (2017) A load balancing algorithm between WLAN and eHRPD systems[J]. Microelectron Computer 34(1):44–47
Nobahari H, Nasrollahi S. A Nonlinear Robust Model Predictive Differential Game Guidance Algorithm Based on the Particle Swarm Optimization[J]. Journal of the Franklin Institute, 2020, 357(15).
Qiu XL, Jia WS (2018) Berge maximum inverse theorem and Nash equilibrium theorem[J]. Acta Math Appl Sin 41(2):280–288
Razavian AS, Sullivan J, Carlsson S (2016) Visual instance retrieval with deep convolutional networks[J]. ITE Trans Media Technol Appl 4(3):251–258
Tang YX, Li YL, Yang C, Wang B (2018) Time-frequency synchronization algorithm based on OFDM/OQAM system in ground-air channel[J]. J Computer Appl 38(3):741–745
Wei XS, Luo JH, Wu J (2017) Selective convolutional descriptor aggregation for fine-grained image retrieval[J]. IEEE Trans Image Process 26(6):2868–2881
Wu LG, Wang CH, Gao HJ et al (2007) Stability conditions for time-delay uncertain stochastic systems based on parameter-dependent Lyapunov function[J]. Control Theory Appl 24(4):607–612
Xu JH, Rong MT, Liu Y (2004) A call access control scheme in wireless mobile networks[J]. J Shanghai Jiaotong Univ (chin Ed) 38(2):181–184
Xue Y, Chen LQ, Liu YZ (2004) The relative constant special solution of Kirchhoff equation and its Lyapunov stability[J]. Acta Physica Sinica 53(12):4029–4036
Zhang Y, Fu P, Liu W et al (2014) Imbalanced data classification based on scaling kernel-based support vector machine[J]. Neural Comput Appl 25(3/4):927–935
Funding
There was no funding or grants received that assisted in this study.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Shao, L., Zhang, Y. Mathematical model of mobile network reliability control based on nonlinear proportional differential. Int J Syst Assur Eng Manag 14, 128–134 (2023). https://doi.org/10.1007/s13198-021-01210-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13198-021-01210-y