{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:03:59Z","timestamp":1760144639235,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,5,8]],"date-time":"2024-05-08T00:00:00Z","timestamp":1715126400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundations of China","doi-asserted-by":"publisher","award":["62173126","61821001","62127802","242102210212","242102311217","ZHJT202403","234200510027"],"award-info":[{"award-number":["62173126","61821001","62127802","242102210212","242102311217","ZHJT202403","234200510027"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Henan Provincial Science and Technology Tackling Projects","award":["62173126","61821001","62127802","242102210212","242102311217","ZHJT202403","234200510027"],"award-info":[{"award-number":["62173126","61821001","62127802","242102210212","242102311217","ZHJT202403","234200510027"]}]},{"name":"Open Subjects of Key Cultivation Laboratory of Intelligent Transportation Policing in Henan Police Academy","award":["62173126","61821001","62127802","242102210212","242102311217","ZHJT202403","234200510027"],"award-info":[{"award-number":["62173126","61821001","62127802","242102210212","242102311217","ZHJT202403","234200510027"]}]},{"name":"Central Plains Science and Technology Innovation Leader Support Program","award":["62173126","61821001","62127802","242102210212","242102311217","ZHJT202403","234200510027"],"award-info":[{"award-number":["62173126","61821001","62127802","242102210212","242102311217","ZHJT202403","234200510027"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>With the continuous development and progress of wireless self-organizing network communication technology, how to carry out long-distance cooperative control of multiple intelligences under the framework of an air\u2013ground integrated wireless high-mobility self-organizing network has become a hot and difficult topic that needs to be solved urgently. This paper takes the air\u2013ground integrated wireless high-mobility self-organizing network system as the basic framework and focuses on solving the long-distance cooperative fault-tolerant control of multi-intelligent bodies and the topological stability of a wireless mobile self-organizing network. To solve the above problems, a direct neural network with a robust adaptive fault-tolerant controller is designed in this paper. By constructing a symmetric population neural network model and combining it with the Lyapunov stabilization criterion, the system feedback matrix K has the ability of autonomous adaptive learning, and symmetrically distorts, rotates, or scales the training data to instantly adjust the system\u2019s fault-tolerant corrections and adaptive adjusting factors to resist the unknown disturbances and faults, to achieve the goals of multi-intelligent body stable control and the stable operation of a wireless high-mobility self-organizing network topology. Simulation results show that with the feedback adjustment of the multi-system under the designed controller, the multi-system as a whole has good fault-tolerant performance and autonomous learning approximation performance, and the tracking error asymptotically converges to zero. The experimental results show that the multi-flight subsystems fly stably, the air\u2013ground integrated wireless high-mobility self-organizing network topology has good stability performance, and the maximum relative improvement of the topology stability performance is 50%.<\/jats:p>","DOI":"10.3390\/sym16050582","type":"journal-article","created":{"date-parts":[[2024,5,8]],"date-time":"2024-05-08T12:27:11Z","timestamp":1715171231000},"page":"582","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Symmetric Collaborative Fault-Tolerant Control of Multi-Intelligence under Long-Range Transmission in Air\u2013Ground Integrated Wireless High-Mobility Self-Organizing Networks"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9104-9031","authenticated-orcid":false,"given":"Zhifang","family":"Wang","sequence":"first","affiliation":[{"name":"Intelligent Investigation Research Center, Henan Police College, Zhengzhou 450046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mingzhe","family":"Shao","sequence":"additional","affiliation":[{"name":"Key Cultivation Laboratory of Intelligent Transportation Policing, Henan Police College, Zhengzhou 450046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenke","family":"Xu","sequence":"additional","affiliation":[{"name":"Criminal Science and Technology Research Center, Henan Police College, Zhengzhou 450046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuewei","family":"Huang","sequence":"additional","affiliation":[{"name":"Criminal Science and Technology Research Center, Henan Police College, Zhengzhou 450046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Bai","sequence":"additional","affiliation":[{"name":"Criminal Science and Technology Research Center, Henan Police College, Zhengzhou 450046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Quanzhen","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Electrical and Information Engineering, Henan University of Engineering, Zhengzhou 451191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianguo","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3545","DOI":"10.1109\/TAES.2020.2975446","article-title":"Robust Fault-Tolerant Control for Underactuated Takeoff and Landing UAVs","volume":"56","author":"Zou","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1109\/TII.2019.2914478","article-title":"Robust Fault-Tolerant Formation Control for Tail-Sitters in Aggressive Flight Mode Transitions","volume":"16","author":"Liu","year":"2020","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_3","first-page":"5044","article-title":"Robust Backstepping Sliding-Mode Control and Observer-Based Fault Estimation for a Quadrotor UAV","volume":"63","author":"Chen","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_4","first-page":"537","article-title":"Neural network-based direct robust adaptive non-fragile fault-tolerant control of amorphous flattened air-ground wireless self-assembly system","volume":"43","author":"Wang","year":"2023","journal-title":"Robot. Intell. Autom."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1016\/j.isatra.2022.05.043","article-title":"Bidirectional Robust and Fault-tolerant H\u221e Non-sensitive Compensation Filter Controller based on Amorphous Flattened Air-to-ground Wireless Self-assembly System","volume":"132","author":"Wang","year":"2023","journal-title":"ISA Trans."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"7541","DOI":"10.1109\/TII.2022.3211878","article-title":"Intelligent Containment Control with Double Constraints for Cloud-Based Collaborative Manufacturing","volume":"19","author":"Zhou","year":"2023","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1109\/TNNLS.2019.2923241","article-title":"Disturbance Observer-Based Neural Network Control of Cooperative Multiple Manipulators with Input Saturation","volume":"31","author":"He","year":"2020","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Liu, L., Song, S., and Wang, Z. (2022, January 19\u201321). A Novel Interleaving Scheme for Concatenated Codes on Burst-Error Channel. Proceedings of the 2022 27th Asia Pacific Conference on Communications (APCC), Jeju Island, Republic of Korea.","DOI":"10.1109\/APCC55198.2022.9943640"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1109\/TETC.2019.2953139","article-title":"Protecting Memories against Soft Errors: The Case for Customizable Error Correction Codes","volume":"9","author":"Li","year":"2021","journal-title":"IEEE Trans. Emerg. Top. Comput."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1109\/TDMR.2021.3132045","article-title":"Correction Masking: A Technique to Implement Efficient SET Tolerant Error Correction Decoders","volume":"22","author":"Liu","year":"2022","journal-title":"IEEE Trans. Device Mater. Reliab."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zhang, J., Jiang, Y., Liu, X., Lee, M., Gao, H., and Yu, G. (2022, January 19\u201321). Design of Retransmission Mechanism for Decentralized Inference with Graph Neural Networks. Proceedings of the 2022 27th Asia Pacific Conference on Communications (APCC), Jeju Island, Republic of Korea.","DOI":"10.1109\/APCC55198.2022.9943706"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Hourani, K., Pandurangan, G., and Robinson, P. (2022, January 10\u201313). Awake-Efficient Distributed Algorithms for Maximal Independent Set. Proceedings of the 2022 IEEE 42nd International Conference on Distributed Computing Systems (ICDCS), Bologna, Italy.","DOI":"10.1109\/ICDCS54860.2022.00153"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Vaz, D., Matos, D.R., Pardal, M.L., and Correia, M. (2023, January 27\u201330). Automatic Generation of Distributed Algorithms with Generative AI. Proceedings of the 2023 53rd Annual IEEE\/IFIP International Conference on Dependable Systems and Networks\u2014Supplemental Volume (DSN-S), Porto, Portugal.","DOI":"10.1109\/DSN-S58398.2023.00037"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Haiyang, M., Changchun, Z., Guangshan, C., Chenglong, J., Yiyang, P., and Yangxiu, H. (2023, January 24\u201326). Research on Object Positioning Algorithm Based on Hybrid Monocular-Binocular. Proceedings of the 2023 42nd Chinese Control Conference (CCC), Tianjin, China.","DOI":"10.23919\/CCC58697.2023.10240081"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1789","DOI":"10.1109\/TCNS.2020.3000738","article-title":"Hierarchical Design for Position-Based Formation Control of Rotorcraft-Like Aerial Vehicles","volume":"7","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Control Netw. Syst."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Hui, Y., Jianxiong, W., Jianbo, S., Shiwei, F., Fei, Y., and Wenjun, H. (2021, January 22\u201324). Research on AUV Cooperative Positioning Technology Based on Improved-EKF With Error Estimation. Proceedings of the 2021 33rd Chinese Control and Decision Conference (CCDC), Kunming, China.","DOI":"10.1109\/CCDC52312.2021.9601673"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"12055","DOI":"10.1109\/JIOT.2021.3123626","article-title":"BCT: An Efficient and Fault Tolerance Blockchain Consensus Transform Mechanism for IoT","volume":"10","author":"Fu","year":"2023","journal-title":"IEEE Internet Things J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1109\/TNS.2019.2959975","article-title":"Applying Compiler-Automated Software Fault Tolerance to Multiple Processor Platforms","volume":"67","author":"James","year":"2020","journal-title":"IEEE Trans. Nucl. Sci."},{"key":"ref_19","unstructured":"Krishna, K.M., and Sarawadekar, K.P. (2021, January 19\u201321). Design of Concurrent Error Detection Techniques for FFT implemented on FPGA platform. Proceedings of the 2021 IEEE 18th India Council International Conference (INDICON), Guwahati, India."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1109\/LSSC.2020.3023501","article-title":"A Spatial\u2013Temporal Error Spreading Technique Based on Voltage Dithering Demonstrates a Power Savings of 35% in a Real-Time Video Processing Datapath Without Timing-Error Detection and Correction","volume":"3","author":"Huang","year":"2020","journal-title":"IEEE Solid-State Circuits Lett."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Liu, X., and Lyu, J. (2021, January 10\u201313). Design of Transponder Message Transmission Mechanism Based on Error Correction Code BCH. Proceedings of the 2021 7th International Conference on Computer and Communications (ICCC), Chengdu, China.","DOI":"10.1109\/ICCC54389.2021.9674680"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1964","DOI":"10.1109\/LCOMM.2023.3285404","article-title":"AES as Error Correction: Cryptosystems for Reliable Communication","volume":"27","author":"Cohen","year":"2023","journal-title":"IEEE Commun. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Nakahara, M., Hisano, D., Nishimura, M., Ushiku, Y., Maruta, K., and Nakayama, Y. (October, January 27). Retransmission Edge Computing System Conducting Adaptive Image Compression Based on Image Recognition Accuracy. Proceedings of the 2021 IEEE 94th Vehicular Technology Conference (VTC2021-Fall), Norman, OK, USA.","DOI":"10.1109\/VTC2021-Fall52928.2021.9625464"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"10302","DOI":"10.1109\/TVT.2023.3257424","article-title":"HARE: Hybrid ARQ-Based Adaptive Retransmission Control Scheme for Synchronous Multi-Link in Wireless LANs","volume":"72","author":"Song","year":"2023","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Cleveland-Slimming, M., and Leger, P. (2020, January 16\u201320). A Collaborative Learning Strategy in an MIS Development Course Using Case Method in Engineering in Information and Management Control. Proceedings of the 2020 39th International Conference of the Chilean Computer Science Society (SCCC), Coquimbo, Chile.","DOI":"10.1109\/SCCC51225.2020.9281192"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1288","DOI":"10.1109\/TASE.2020.3001183","article-title":"Robust Trajectory Tracking Control for Underactuated Autonomous Underwater Vehicles in Uncertain Environments","volume":"18","author":"Nikou","year":"2021","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1998","DOI":"10.1109\/TSG.2022.3211008","article-title":"Partitional Collaborative Mitigation Strategy of Distribution Network Harmonics Based on Distributed Model Predictive Control","volume":"14","author":"LLin","year":"2023","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Zhang, R., and Liu, Y. (2017, January 28\u201330). A new Barbalat\u2019s lemma and Lyapunov stability theorem for fractional order systems. Proceedings of the 2017 29th Chinese Control and Decision Conference (CCDC), Chongqing, China.","DOI":"10.1109\/CCDC.2017.7979143"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"6808","DOI":"10.1109\/TSMC.2020.2964057","article-title":"Admissibilization for Implicit Jump Systems with Mixed Retarded Delays Based on Reciprocally Convex Integral Inequality and Barbalat\u2019s Lemma","volume":"51","author":"Zhuang","year":"2021","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Liu, J., Song, H., Zhao, Z., Guerrero, J.M., and Qu, Y. (2022, January 21\u201323). L2-Gain Disturbance Attenuation-Based Decentralized Secondary Frequency Control in Autonomous Microgrids. Proceedings of the 2022 34th Chinese Control and Decision Conference (CCDC), Hefei, China.","DOI":"10.1109\/CCDC55256.2022.10033548"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Tao, D., Xiaoyu, G., and Wanquan, L. (2017, January 26\u201328). Disturbance attenuation and rejection for systems with unknown nonlinearity and missing measurements via DOBC approach. Proceedings of the 2017 36th Chinese Control Conference (CCC), Dalian, China.","DOI":"10.23919\/ChiCC.2017.8028627"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Liu, J., Song, H., Chen, C., Guerrero, J.M., Liu, M., and Qu, Y. (2022, January 1\u20133). A Non-linear Decentralized Secondary Frequency Control of islanded Microgrid via Adaptive L2-Gain Disturbance Attenuation. Proceedings of the 2022 IEEE 31st International Symposium on Industrial Electronics (ISIE), Anchorage, AK, USA.","DOI":"10.1109\/ISIE51582.2022.9831558"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Li, J., Zhou, T., and Cui, H. (2023). Brain-Inspired Deep Meta-Reinforcement Learning for Active Coordinated Fault-Tolerant Load Frequency Control of Multi-Area Grids. IEEE Trans. Autom. Sci. Eng., 1\u20133.","DOI":"10.1109\/TASE.2023.3263005"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Troubitsyna, E. (2022, January 1\u20133). Formal Model of Collaborative Fault Tolerant Planning in Multi-Robotic Systems. Proceedings of the 2022 8th International Conference on Control, Decision and Information Technologies (CoDIT), Istanbul, Turkey.","DOI":"10.1109\/CoDIT55151.2022.9804073"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/5\/582\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:42:05Z","timestamp":1760107325000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/5\/582"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,8]]},"references-count":34,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2024,5]]}},"alternative-id":["sym16050582"],"URL":"https:\/\/doi.org\/10.3390\/sym16050582","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,5,8]]}}}