{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T12:40:29Z","timestamp":1773060029108,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,2]],"date-time":"2024-06-02T00:00:00Z","timestamp":1717286400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62062036"],"award-info":[{"award-number":["62062036"]}]},{"name":"National Natural Science Foundation of China","award":["62066015"],"award-info":[{"award-number":["62066015"]}]},{"name":"National Natural Science Foundation of China","award":["62006095"],"award-info":[{"award-number":["62006095"]}]},{"name":"National Natural Science Foundation of China","award":["JDCX20231012"],"award-info":[{"award-number":["JDCX20231012"]}]},{"name":"College Students\u2019 Innovation Training Center Project at Jishou University","award":["62062036"],"award-info":[{"award-number":["62062036"]}]},{"name":"College Students\u2019 Innovation Training Center Project at Jishou University","award":["62066015"],"award-info":[{"award-number":["62066015"]}]},{"name":"College Students\u2019 Innovation Training Center Project at Jishou University","award":["62006095"],"award-info":[{"award-number":["62006095"]}]},{"name":"College Students\u2019 Innovation Training Center Project at Jishou University","award":["JDCX20231012"],"award-info":[{"award-number":["JDCX20231012"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The problem of inverting dynamic complex matrices remains a central and intricate challenge that has garnered significant attention in scientific and mathematical research. The zeroing neural network (ZNN) has been a notable approach, utilizing time derivatives for real-time solutions in noiseless settings. However, real-world disturbances pose a significant challenge to a ZNN\u2019s convergence. We design an accelerated dual-integral structure zeroing neural network (ADISZNN), which can enhance convergence and restrict linear noise, particularly in complex domains. Based on the Lyapunov principle, theoretical analysis proves the convergence and robustness of ADISZNN. We have selectively integrated the SBPAF activation function, and through theoretical dissection and comparative experimental validation we have affirmed the efficacy and accuracy of our activation function selection strategy. After conducting numerous experiments, we discovered oscillations and improved the model accordingly, resulting in the ADISZNN-Stable model. This advanced model surpasses current models in both linear noisy and noise-free environments, delivering a more rapid and stable convergence, marking a significant leap forward in the field.<\/jats:p>","DOI":"10.3390\/axioms13060374","type":"journal-article","created":{"date-parts":[[2024,6,3]],"date-time":"2024-06-03T05:58:00Z","timestamp":1717394280000},"page":"374","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Accelerated Dual-Integral Structure Zeroing Neural Network Resistant to Linear Noise for Dynamic Complex Matrix Inversion"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-6064-3932","authenticated-orcid":false,"given":"Feixiang","family":"Yang","sequence":"first","affiliation":[{"name":"College of Computer Science and Engineering, Jishou University, Jishou 416000, China"}]},{"given":"Tinglei","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Engineering, Jishou University, Jishou 416000, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-8173-0147","authenticated-orcid":false,"given":"Yun","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Engineering, Jishou University, Jishou 416000, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1109\/TETCI.2023.3301793","article-title":"A time-varying fuzzy parameter zeroing neural network for the synchronization of chaotic systems","volume":"8","author":"Jin","year":"2023","journal-title":"IEEE Trans. Emerg. Top. Comput. Intell."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zhang, R., Xi, X., Tian, H., and Wang, Z. (2022). Dynamical analysis and finite-time synchronization for a chaotic system with hidden attractor and surface equilibrium. Axioms, 11.","DOI":"10.3390\/axioms11110579"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Rasouli, M., Zare, A., Hallaji, M., and Alizadehsani, R. (2022). The synchronization of a class of time-delayed chaotic systems using sliding mode control based on a fractional-order nonlinear PID sliding surface and its application in secure communication. Axioms, 11.","DOI":"10.3390\/axioms11120738"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"6199","DOI":"10.1007\/s12652-020-01815-4","article-title":"Inverse kinematics solution of Robotics based on neural network algorithms","volume":"11","author":"Gao","year":"2020","journal-title":"J. Ambient Intell. Humaniz. Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"106735","DOI":"10.1016\/j.asoc.2020.106735","article-title":"Performance analysis of nonlinear activated zeroing neural networks for time-varying matrix pseudoinversion with application","volume":"98","author":"Hu","year":"2021","journal-title":"Appl. Soft Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.cam.2016.12.019","article-title":"A new approach based on the Newton\u2019s method to solve systems of nonlinear equations","volume":"318","author":"Ramos","year":"2017","journal-title":"J. Comput. Appl. Math."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1902","DOI":"10.1093\/imanum\/drx011","article-title":"A second-order sequential optimality condition associated to the convergence of optimization algorithms","volume":"37","author":"Andreani","year":"2017","journal-title":"IMA J. Numer. Anal."},{"key":"ref_8","unstructured":"Zhang, Y. (2005, January 27\u201329). Revisit the analog computer and gradient-based neural system for matrix inversion. Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, Limassol, Cyprus."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1940","DOI":"10.1109\/TAC.2009.2023779","article-title":"Performance analysis of gradient neural network exploited for online time-varying matrix inversion","volume":"54","author":"Zhang","year":"2009","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_10","first-page":"1301","article-title":"Global exponential convergence and stability of gradient-based neural network for online matrix inversion","volume":"215","author":"Zhang","year":"2009","journal-title":"Appl. Math. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/j.ipl.2018.10.004","article-title":"Nonlinear gradient neural network for solving system of linear equations","volume":"142","author":"Xiao","year":"2019","journal-title":"Inf. Process. Lett."},{"key":"ref_12","first-page":"6169","article-title":"A general recurrent neural network model for time-varying matrix inversion","volume":"Volume 6","author":"Zhang","year":"2003","journal-title":"Proceedings of the 42nd IEEE International Conference on Decision and Control (IEEE Cat. No. 03CH37475)"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Johnson, M.A., and Moradi, M.H. (2005). PID Control, Springer.","DOI":"10.1007\/1-84628-148-2"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2615","DOI":"10.1109\/TNNLS.2015.2497715","article-title":"Integration-enhanced Zhang neural network for real-time-varying matrix inversion in the presence of various kinds of noises","volume":"27","author":"Jin","year":"2015","journal-title":"IEEE Trans. Neural Networks Learn. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Golub, G.H., and Van Loan, C.F. (2013). Matrix Computations, JHU Press.","DOI":"10.56021\/9781421407944"},{"key":"ref_16","unstructured":"Ogata, K. (2010). Control systems analysis in state space. Modern Control Engineering, Pearson Education, Inc."},{"key":"ref_17","unstructured":"Smith, S. (2003). Digital Signal Processing: A Practical Guide for Engineers and Scientists, Newnes."},{"key":"ref_18","unstructured":"Saleh, B.E., and Teich, M.C. (2019). Fundamentals of Photonics, John Wiley & Sons."},{"key":"ref_19","unstructured":"Trefethen, L.N., and Bau, D. (2022). Numerical Linear Algebra, Siam."},{"key":"ref_20","first-page":"10066","article-title":"Complex-valued Zhang neural network for online complex-valued time-varying matrix inversion","volume":"217","author":"Zhang","year":"2011","journal-title":"Appl. Math. Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3757","DOI":"10.1109\/TII.2019.2936877","article-title":"A noise-tolerant zeroing neural network for time-dependent complex matrix inversion under various kinds of noises","volume":"16","author":"Xiao","year":"2019","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"65991","DOI":"10.1109\/ACCESS.2023.3290046","article-title":"Dynamic Neural Network Models for Time-Varying Problem Solving: A Survey on Model Structures","volume":"11","author":"Hua","year":"2023","journal-title":"IEEE Access"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1668","DOI":"10.1109\/TNNLS.2020.2986275","article-title":"Design and analysis of two prescribed-time and robust ZNN models with application to time-variant Stein matrix equation","volume":"32","author":"Dai","year":"2020","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/s11063-012-9241-1","article-title":"Accelerating a recurrent neural network to finite-time convergence for solving time-varying Sylvester equation by using a sign-bi-power activation function","volume":"37","author":"Li","year":"2013","journal-title":"Neural Process. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1159212","DOI":"10.3389\/fphy.2023.1159212","article-title":"Towards non-linearly activated ZNN model for constrained manipulator trajectory tracking","volume":"11","author":"Lan","year":"2023","journal-title":"Front. Phys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1016\/j.neucom.2013.12.001","article-title":"From different ZFs to different ZNN models accelerated via Li activation functions to finite-time convergence for time-varying matrix pseudoinversion","volume":"133","author":"Liao","year":"2014","journal-title":"Neurocomputing"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1983","DOI":"10.1016\/j.neucom.2015.08.031","article-title":"A nonlinearly activated neural dynamics and its finite-time solution to time-varying nonlinear equation","volume":"173","author":"Xiao","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/s00521-011-0692-5","article-title":"Superior robustness of power-sum activation functions in Zhang neural networks for time-varying quadratic programs perturbed with large implementation errors","volume":"22","author":"Yang","year":"2013","journal-title":"Neural Comput. Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1621","DOI":"10.1109\/TNNLS.2013.2271779","article-title":"Different complex ZFs leading to different complex ZNN models for time-varying complex generalized inverse matrices","volume":"25","author":"Liao","year":"2013","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/j.neucom.2020.02.121","article-title":"New error function designs for finite-time ZNN models with application to dynamic matrix inversion","volume":"402","author":"Xiao","year":"2020","journal-title":"Neurocomputing"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1016\/j.neucom.2018.06.057","article-title":"Wsbp function activated Zhang dynamic with finite-time convergence applied to Lyapunov equation","volume":"314","author":"Lv","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5244","DOI":"10.1109\/TSMC.2018.2870523","article-title":"A New Repetitive Motion Planning Scheme With Noise Suppression Capability for Redundant Robot Manipulators","volume":"50","author":"Li","year":"2020","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1049\/cit2.12161","article-title":"Double integral-enhanced Zeroing neural network with linear noise rejection for time-varying matrix inverse","volume":"9","author":"Liao","year":"2023","journal-title":"CAAI Trans. Intell. Technol."},{"key":"ref_34","unstructured":"Zhang, M. (2023). A varying-gain ZNN model with fixed-time convergence and noise-tolerant performance for time-varying linear equation and inequality systems. Authorea Prepr., Available online: https:\/\/www.techrxiv.org\/doi\/full\/10.36227\/techrxiv.16988404.v1."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"77940","DOI":"10.1109\/ACCESS.2018.2884497","article-title":"A varying-gain recurrent neural network and its application to solving online time-varying matrix equation","volume":"6","author":"Zhang","year":"2018","journal-title":"IEEE Access"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Han, L., Liao, B., He, Y., and Xiao, X. (2021, January 3\u20137). Dual noise-suppressed ZNN with predefined-time convergence and its application in matrix inversion. Proceedings of the 2021 11th International Conference on Intelligent Control and Information Processing (ICICIP), Dali, China.","DOI":"10.1109\/ICICIP53388.2021.9642164"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/6\/374\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:52:34Z","timestamp":1760107954000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/6\/374"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,2]]},"references-count":36,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["axioms13060374"],"URL":"https:\/\/doi.org\/10.3390\/axioms13060374","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,2]]}}}