Autors: Stamov, T. G.
Title: Practical stability criteria for discrete fractional neural networks in product form design analysis
Keywords: Controllers, Discrete models, Forms analysis, Fractional derivative, Neural networks, Stability

Abstract: Namely, fractional-order neural network models are proposed as more flexible mechanism to study product form design. Since control and stability methods are fundamental in the construction and practical significance of a neural network model, appropriate controllers are designed and practical stability criteria are proposed for the fractional-order model under consideration. The stability and control analysis are based on the Lyapunov function method. Examples are elaborated to demonstrate the established results. The proposed modeling approach and the stability results are also applicable to numerous industrial design tasks.

References

  1. Haykin, S., Neural networks: A comprehensive foundation. 1st ed., 1999, Prentice-Hall, New Jersey.
  2. Kathamuthu, N.D., Subramaniam, S., Le, Q.H., Muthusamy, S., Panchal, H., Sundararajan, S.C.M., et al. A deep transfer learning-based convolution neural network model for COVID-19 detection using computed tomography scan images for medical applications. Adv Eng Softw, 175, 2023, 103317, 10.1016/j.advengsoft.2022.103317.
  3. Moon, S., Hou, L., Han, S., Empirical study of an artificial neural network for a manufacturing production operation. Oper Manag Res 16 (2023), 311–323, 10.1007/s12063-022-00309-0.
  4. Sharma, M., Pant, S., Yadav, P., Sharma, D.K., Gupta, N., Srivastava, G., Advancing security in the industrial internet of things using deep progressive neural networks. Mob Netw Appl 28 (2023), 782–794, 10.1007/s11036-023-02104-y.
  5. Xiang, L., Gai, J., Bao, Y., Yu, J., Schnable, P.S., Tang, L., Field-based robotic leaf angle detection and characterization of maize plants using stereo vision and deep convolutional neural networks. J Field Robot 40 (2023), 1034–1053, 10.1002/rob.22166.
  6. Aivaliotis, P., Zampetis, A., Michalos, G., Makris, S., A machine learning approach for visual recognition of complex parts in robotic manipulation. Procedia Manuf 11 (2017), 423–430, 10.1016/j.promfg.2017.07.130.
  7. Cakar, T., Cil, I., Artificial neural networks for design of manufacturing systems and selection of priority rules. Int J Comput Integr Manuf 17 (2004), 195–211, 10.1080/09511920310001607078.
  8. Han, J.X., Ma, M.Y., Wang, K., Product modeling design based on genetic algorithm and BP neural network. Neural Comput Appl 33 (2021), 4111–4117, 10.1007/s00521-020-05604-0.
  9. Krache, C., Bräunche, A., Jacob, A., Stricker, N., Lanza, G., Deep learning for automated product design. Procedia CIRP 91 (2020), 3–8, 10.1016/j.procir.2020.01.135.
  10. Pandremenos, J., Chryssolouris, G., A neural network approach for the development of modular product architectures. Int J Comput Integr Manuf 24 (2011), 879–887, 10.1080/0951192X.2011.602361.
  11. Artificial neural networks for engineering applications. 2019, Academic Press, St. Louis.
  12. Hyndman, R.J., Athanasopoulos, G., Forecasting: Principles and practice. 2nd ed., 2018, OTexts, Online https://OTexs.com/fpp2/.
  13. Stamov, T., On the applications of neural networks in industrial design: a survey of the state of the art. J Eng Appl Sci 15 (2020), 1797–1804, 10.36478/jeasci.2020.1797.1804.
  14. Wu, D., Wang, G.G., Causal artificial neural network and its applications in engineering design. Eng Appl Artif Intell, 97, 2021, 104089, 10.1016/j.engappai.2020.104089.
  15. Stamov, T., Shapes applicable in design of contemporary vehicles: differences in emotional impact and applications. Int J Emerg Sci Eng 3 (2015), 38–42 https://www.ijese.org/portfolio-item/H1001063815/.
  16. Itten, J., Design and form. The basic course at the Bauhaus and later. 1st ed., 1964, Reinhold, New York.
  17. Williams, R., The geometrical foundation of natural structure: A source book of design. 1st ed., 1979, Dover Publications, New York.
  18. Zitzmann, L., Schulz, B., Dokumente zur visuellgestalterischen grundlagenausbildung. 1st ed., 1990, Giebichenstein, Halle Burg.
  19. Papia, E.M., Kondi, A., Constantoudis, V., Entropy and complexity analysis of AI-generated and human-made paintings. Chaos Solitons Fractals, 170, 2023, 113385, 10.1016/j.chaos.2023.113385.
  20. Chen, C.F., Yeh, C.H., Lin, Y.C., A neural network approach to eco-product form design. Proceedings of the 5th IEEE conference on industrial electronics and applications, 2010, 1445–1450, 10.1109/ICIEA.2010.5514832.
  21. Hsiao, S.W., Huang, H.C., A neural network based approach for product form design. Des Stud 1 (2002), 67–84, 10.1016/S0142-694X(01)00015-1.
  22. Hsiao, S.W., Tsai, H.C., Applying a hybrid approach based on fuzzy neural network and genetic algorithm to product form design. Int J Ind Ergon 35 (2005), 411–428, 10.1016/j.ergon.2004.10.007.
  23. Wei, C.C., Yeh, C.H., Wang, I., Walsh, B., Lin, Y.C., Deep neural networks for new product form design. Proceedings of the 16th international conference on informatics in control, automation and robotics (ICINCO 2019), 2019, 653–657, 10.5220/0007933506530657.
  24. Wu, Y., Product form evolutionary design system construction based on neural network model and multi-objective optimization. J Intell Fuzzy Syst 39 (2020), 7977–7991, 10.3233/JIFS-201439.
  25. Zheng, H., Form finding and evaluating through machine learning: the prediction of personal design preference in polyhedral structures. Yuan, P.F., Xie, M., Leach, N., Yao, J., Wang, X., (eds.) Architectural intelligence, 2020, Springer, Singapore, 207–217.
  26. Berlyand, L., Jabin, P.E., Safsten, C.A., Stability for the training of deep neural networks and other classifiers. Math Models Methods Appl Sci 31 (2021), 2345–2390, 10.1142/S0218202521500500.
  27. Zheng, S., Song, Y., Leung, T., Goodfellow, I., Improving the robustness of deep neural networks via stability training. Proceedings of the 2016 IEEE conference on computer vision and pattern recognition (CVPR), 2016, 4480–4488, 10.1109/CVPR.2016.485.
  28. Colbrook, M.J., Antun, V., Hansen, A.C., The difficulty of computing stable and accurate neural networks: on the barriers of deep learning and Smale's 18th problem. Proc Natl Acad Sci USA, 119, 2022, e2107151119, 10.1073/pnas.21071511191of10.
  29. Lin, X., Liu, W., The application of fractal art in ceramic product design. IOP Conf Ser, 573, 2019, 012003, 10.1088/1757-899X/573/1/012003.
  30. Sala, N., Complex and fractal components in industrial design. Int J Des Nat 1 (2017), 161–173, 10.2495/DN-V1-N2-161-173.
  31. Kilbas, A., Srivastava, H.M., Trujillo, J.J., Theory and applications of fractional differential equations. 1st ed., 2006, Elsevier, New York.
  32. Singh, H., Srivastava, H.M., Nieto, J.J., (eds.) Handbook of fractional calculus for engineering and science, 1st ed., 2022, CRC Press, Boca Raton.
  33. Sun, H.G., Zhang, Y., Baleanu, D., Chen, W., Chen, Y.Q., A new collection of real world applications of fractional calculus in science and engineering. Commun Nonlinear Sci Numer Simul 64 (2018), 213–231, 10.1016/j.cnsns.2018.04.019.
  34. Yang, Y., Zhang, H.H., Fractional calculus with its applications in engineering and technology. 1st ed., 2019, Springer, Cham.
  35. Joshi, M., Bhosale, S., Vyawahare, V.A., A survey of fractional calculus applications in artificial neural networks. Artif Intell Rev 56 (2023), 13897–13950, 10.1007/s10462-023-10474-8.
  36. Maiti, M., Sunder, M., Abishek, R., Bingi, K., Shaik, N.B., Benjapolakul, W., Recent advances and applications of fractional-order neural networks. Eng J 26 (2022), 49–67, 10.4186/ej.2022.26.7.49.
  37. Viera-Martin, E., Gómez-Aguilar, J.F., Solís-Pérez, J.E., Hernández-Pérez, J.A., Escobar-Jiménez, R.F., Artificial neural networks: a practical review of applications involving fractional calculus. Eur Phys J Spec Top 231 (2022), 2059–2095, 10.1140/epjs/s11734-022-00455-3.
  38. Gupta, K., Kaakai, F., Pesquet-Popescu, B., Pesquet, J.C., Safe design of stable neural networks for fault detection in small UAVs. Trapp, M., Schoitsch, E., Guiochet, J., Bitsch, F., (eds.) Computer safety, reliability, and security, 2022, Springer, Cham, 263–275.
  39. Korkobi, T., Djemel, M., Chtourou, M., Stability analysis of neural networks-based system identification. Model Simul Eng, 2008, 2008, 343940, 10.1155/2008/343940.
  40. Panda, S.K., Nagy, A.M., Vijayakumar, V., Hazarika, B., Stability analysis for complex-valued neural networks with fractional order. Chaos Solitons Fractals, 175, 2023, 114045, 10.1016/j.chaos.2023.114045.
  41. Song, H., Hu, C., Yu, J., Stability and synchronization of fractional-order complex-valued inertial neural networks: a direct approach. Math, 10, 2022, 4823, 10.3390/math10244823.
  42. Thanh, N.T., Niamsup, P., Phat, V.N., New results on finite-time stability of fractional-order neural networks with time-varying delay. Neural Comput Appl 33 (2021), 17489–17496, 10.1007/s00521-021-06339-2.
  43. Yang, Y., He, Y., Wang, Y., Wu, M., Stability analysis of fractional-order neural networks: An LMI approach. Neurocomputing 285 (2018), 82–93, 10.1016/j.neucom.2018.01.036.
  44. Gao, P., Zhang, H., Ye, R., Stamova, I., Cao, J., Quasi-uniform synchronization of fractional fuzzy discrete-time delayed neural networks via delayed feedback control design. Commun Nonlinear Sci Numer Simul, 126, 2023, 107507, 10.1016/j.cnsns.2023.107507.
  45. Heilat, A.S., Karoun, R.C., Al-Husban, A., Abbes, A., Al Horani, M., Grassi, G., Ouannas, A., The new fractional discrete neural network model under electromagnetic radiation: chaos, control and synchronization. Alex Eng J 76 (2023), 391–409, 10.1016/j.aej.2023.06.017.
  46. Hioual, A., Ouannas, A., Oussaeif, T.E., Grassi, G., Batiha, I.M., Momani, S., On variable-order fractional discrete neural networks: solvability and stability. Fractal Fract, 6, 2022, 119, 10.3390/fractalfract6020119.
  47. Li, H.L., Cao, J., Hu, C., Jiang, H., Asaedi, A., Synchronization analysis of nabla fractional-order fuzzy neural networks with time delays via nonlinear feedback control. Fuzzy Sets Syst, 475, 2024, 108750, 10.1016/j.fss.2023.108750.
  48. Li, H.L., Cao, J., Hu, C., Zhang, L., Jiang, H., Adaptive control-based synchronization of discrete-time fractional-order fuzzy neural networks with time-varying delays. Neural Netw 168 (2023), 59–73, 10.1016/j.neunet.2023.09.019.
  49. Ouannas, A., Khennaoui, A., Odibat, Z., Pham, V., Grassi, G., On the dynamics, control and synchronization of fractional-order Ikeda map. Chaos Solitons Fractals 123 (2019), 108–115, 10.1016/j.chaos.2019.04.002.
  50. Perumal, R., Hymavathi, M., Ali, M.S., Mahmoud, B.A.A., Osman, W.M., Ibrahim, T.F., Synchronization of discrete-time fractional-order complex-valued neural networks with distributed delays. Fractal Fract, 7, 2023, 452, 10.3390/fractalfract7060452.
  51. Pratap, A., Raja, R., Cao, J., Huang, C., Niezabitowski, M., Bagdasar, O., Stability of discrete-time fractional-order time-delayed neural networks in complex field. Math Methods Appl Sci 44 (2021), 419–440, 10.1002/mma.6745.
  52. You, X., Song, Q., Zhao, Z., Global Mittag–Leffler stability and synchronization of discrete-time fractional-order complex-valued neural networks with time delay. Neural Netw 122 (2020), 382–394, 10.1016/j.neunet.2019.11.004.
  53. Zhang, H., Chen, X., Ye, R., Stamova, I., Cao, J., Quasi-projective synchronization analysis of discrete-time FOCVNNs via delay-feedback control. Chaos Solitons Fractals, 173, 2023, 113629, 10.1016/j.chaos.2023.113629.
  54. Zhang, X.L., Li, H.L., Kao, Y., Zhang, L., Jiang, H., Global Mittag-Leffler synchronization of discrete-time fractional-order neural networks with time delays. Appl Math Comput, 433, 2022, 127417, 10.1016/j.amc.2022.127417.
  55. Allehiany, F.M., Mahmoud, E.E., Jahanzaib, L.S., Trikha, P., Alotaibi, H., Chaos control and analysis of fractional order neural network under electromagnetic radiation. Results Phys, 21, 2021, 103786, 10.1016/j.rinp.2020.103786.
  56. Yang, X., Li, C., Huang, T., Song, Q., Huang, J., Global Mittag-Leffler synchronization of fractional-order neural networks via impulsive control. Neural Process Lett 48 (2018), 459–479, 10.1007/s11063-017-9744-x.
  57. Zhang, H., Chen, J., Zhang, H., Zhang, W., Cao, J., Quasi-uniform synchronization of Caputo type fractional neural networks with leakage and discrete delays. Chaos Solitons Fractals, 152, 2021, 111431, 10.1016/j.chaos.2021.111432.
  58. Zouari, F., Ibeas, A., Boulkroune, A., Cao, J., Arefi, M.M., Neural network controller design for fractional-order systems with input nonlinearities and asymmetric time-varying pseudo-state constraints. Chaos Solitons Fractals, 144, 2021, 110742, 10.1016/j.chaos.2021.110742.
  59. Chen, F.C., Chang, C.H., Practical stability issues in CMAC neural network control systems. IEEE Trans Control Syst Technol 4 (1996), 86–91.
  60. Jiao, T., Zong, G., Ahn, C.K., Noise-to-state practical stability and stabilization of random neural networks. Nonlinear Dynam 100 (2020), 2469–2481, 10.1007/s11071-020-05628-0.
  61. Stamov, T., Neural networks in engineering design: robust practical stability analysis. Cybern Inf Technol 21 (2021), 3–14, 10.2478/cait-2021-0039.
  62. Stamov, T., Discrete bidirectional associative memory neural networks of the Cohen–Grossberg type for engineering design symmetry related problems: practical stability of sets analysis. Symmetry, 14, 2022, 216, 10.3390/sym14020216.
  63. Sun, L., Liu, C., Li, X., Practical stability of impulsive discrete systems with time delays. Abstr Appl Anal, 2014, 2014, 954121, 10.1155/2014/954121.
  64. Tian, Y., Sun, Y., Practical stability and stabilisation of switched delay systems with non-vanishing perturbations. IET Control Theory Appl 13 (2019), 1329–1335, 10.1049/iet-cta.2018.5332.
  65. Wangrat, S., Niamsup, P., Exponentially practical stability of impulsive discrete time system with delay. Adv Differ Equ, 2016, 2016, 277, 10.1186/s13662-016-1005-1.
  66. Tinh, C.T., Thuan, D.D., Son, N.K., Hieu, L.T., Practical exponential stability of nonlinear nonautonomous differential equations under perturbations. Mediterr J Math, 20, 2023, 103, 10.1007/s00009-023-02311-7.
  67. Lakshmikantham, V., Leela, S., Martynyuk, A.A., Practical stability of nonlinear systems. 1st ed., 1990, World Scientific, Teaneck.
  68. Buslowicz, M., Kaaczorek, T., Simple conditions for practical stability of positive fractional discrete-time linear systems. Int J Appl Math Comput Sci 19 (2009), 263–269, 10.2478/v10006-009-0022-6.
  69. Oprzedkiewicz, K., Gawin, W., The practical stability of the discrete, fractional order, state space model of the heat transfer process. Arch Control Sci 28 (2018), 463–482, 10.24425/acs.2018.124712.
  70. Ruszewski, A., Practical and asymptotic stability of fractional discrete-time scalar systems described by a new model. Arch Control Sci 26 (2016), 441–452, 10.1515/acsc-2016-0024.
  71. Lai, H.H., Lin, Y.C., Yeh, C.H., Form design of product image using grey relational analysis and neural network models. Comput Oper Res 32 (2005), 2689–2711, 10.1016/j.cor.2004.03.021.
  72. Stamov, T., Stability analysis of neural network models in engineering design. Int J Eng Adv Technol 9 (2020), 1862–1866, 10.35940/ijeat.C5562.029320.
  73. Baleanu, D., Wu, G.C., Bai, Y.R., Chen, F.L., Stability analysis of Caputo–like discrete fractional systems. Commun Nonlinear Sci Numer Simul 48 (2017), 520–530, 10.1016/j.cnsns.2017.01.002.
  74. Abdeljawad, T., On Riemann and Caputo fractional differences. Comput Math Appl 62 (2011), 1602–1611, 10.1016/j.camwa.2011.03.036.
  75. Lin, H., Wang, C., Sun, J., Zhang, X., Sun, Y., Iu, H.H.C., Memristor-coupled asymmetric neural networks: Bionic modeling, chaotic dynamics analysis and encryption application. Chaos Solitons Fractals, 166, 2023, 112905, 10.1016/j.chaos.2022.112905.
  76. Lin, H., Wang, C., Yu, F., Sun, J., Du, S., Deng, Z., Deng, Q., A review of chaotic systems based on memristive Hopfield neural networks. Math, 11, 2023, 1369, 10.3390/math11061369.
  77. Torvik, P.J., Bagley, R.L., Appearance of the fractional derivative in the behavior of real materials. J Appl Mech 51 (1984), 294–298, 10.1115/1.3167615.

Issue

Chaos, Solitons and Fractals, vol. 179, 2024, , https://doi.org/10.1016/j.chaos.2024.114465

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