{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:12:28Z","timestamp":1760242348676,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2017,4,28]],"date-time":"2017-04-28T00:00:00Z","timestamp":1493337600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61233005"],"award-info":[{"award-number":["61233005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National 973 Project","award":["2014CB744200"],"award-info":[{"award-number":["2014CB744200"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The mobile satcom antenna (MSA) enables a moving vehicle to communicate with a geostationary Earth orbit satellite. To realize continuous communication, the MSA should be aligned with the satellite in both sight and polarization all the time. Because of coupling effects, unknown disturbances, sensor noises and unmodeled dynamics existing in the system, the control system should have a strong adaptability. The significant features of terminal sliding mode control method are robustness and finite time convergence, but the robustness is related to the large switching control gain which is determined by uncertain issues and can lead to chattering phenomena. Neural networks can reduce the chattering and approximate nonlinear issues. In this work, a novel B-spline curve-based B-spline neural network (BSNN) is developed. The improved BSNN has the capability of shape changing and self-adaption. In addition, the output of the proposed BSNN is applied to approximate the nonlinear function in the system. The results of simulations and experiments are also compared with those of PID method, non-singularity fast terminal sliding mode (NFTSM) control and radial basis function (RBF) neural network-based NFTSM. It is shown that the proposed method has the best performance, with reliable control precision.<\/jats:p>","DOI":"10.3390\/s17050978","type":"journal-article","created":{"date-parts":[[2017,4,28]],"date-time":"2017-04-28T11:57:04Z","timestamp":1493380624000},"page":"978","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["An Adaptive B-Spline Neural Network and Its Application in Terminal Sliding Mode Control for a Mobile Satcom Antenna Inertially Stabilized Platform"],"prefix":"10.3390","volume":"17","author":[{"given":"Xiaolei","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Instrumentation Science and Opto-Electronics Engineering, Beihang University, Beijing 100191, China"}]},{"given":"Yan","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Instrumentation Science and Opto-Electronics Engineering, Beihang University, Beijing 100191, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4997-0345","authenticated-orcid":false,"given":"Kai","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Instrumentation Science and Opto-Electronics Engineering, Beihang University, Beijing 100191, China"}]},{"given":"Gaoliang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Instrumentation Science and Opto-Electronics Engineering, Beihang University, Beijing 100191, China"}]},{"given":"Nianmao","family":"Deng","sequence":"additional","affiliation":[{"name":"Beijing Institute of Control &amp; Electronic Technology, Beijing 100038, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,4,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1109\/25.260761","article-title":"A satellite-tracking k- and ka-band mobile vehicle antenna system","volume":"42","author":"Densmore","year":"1993","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_2","unstructured":"Cheng, W., Minzhe, T., and Weizhou, S. (2016, January 27\u201329). An h2\/h\u221e control design for mobile satcom antenna servo systems. Proceedings of the 2016 35th Chinese Control Conference (CCC), Chengdu, China."},{"key":"ref_3","unstructured":"Marsh, E.A. (2008). Inertially Stabilized Platforms for Satcom on-the-Move Applications: A Hybrid Open\/Closed-Loop Antenna Pointing Strategy. [Master\u2019s degree, Massachusetts Institute of Technology]."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1109\/MCS.2007.910205","article-title":"Control systems for mobile satcom antennas","volume":"28","author":"Debruin","year":"2008","journal-title":"IEEE Control Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/CC.2014.7022521","article-title":"A beam stabilization algorithm based on nonlinear observer for low cost satcom-on-the-move","volume":"11","author":"Tian","year":"2014","journal-title":"China Commun."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1109\/TAES.1969.309879","article-title":"Stabilization of precision electrooptical pointing and tracking systems","volume":"AES-5","author":"Rue","year":"1969","journal-title":"IEEE Trans. Aerosp. Electr. Syst."},{"key":"ref_7","first-page":"1606","article-title":"Modeling analysis on the gyro stabilized","volume":"241","author":"Shuang","year":"2011","journal-title":"Sci. Technol. Rev."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.mechatronics.2015.02.002","article-title":"An adaptive decoupling control for three-axis gyro stabilized platform based on neural networks","volume":"27","author":"Fang","year":"2015","journal-title":"Mechatronics"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Ito, K., Maebashi, W., Ikeda, J., and Iwasaki, M. (2011, January 7\u201310). Fast and precise positioning of rotary table systems by feedforward disturbance compensation considering interference force. Proceedings of the IECON 2011 37th Annual Conference on IEEE Industrial Electronics Society, Melbourne, Australia.","DOI":"10.1109\/IECON.2011.6119855"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"\u0158ez\u00e1\u010d, M., and Hur\u00e1k, Z. (2011, January 28\u201330). Vibration rejection for inertially stabilized double gimbal platform using acceleration feedforward. Proceedings of the IEEE International Conference on Control Applications (CCA), Denver, CO, USA.","DOI":"10.1109\/CCA.2011.6044442"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2014\/657985","article-title":"A RBFNN-based adaptive disturbance compensation approach applied to magnetic suspension inertially stabilized platform","volume":"2014","author":"Mu","year":"2014","journal-title":"Math. Probl. Eng."},{"key":"ref_12","first-page":"41","article-title":"H\u221e control law for line-of-sight stabilization for mobile land vehicles","volume":"41","author":"Moorty","year":"2002","journal-title":"Opt. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Li, S., Zhong, M., and Zhao, Y. (2014). Estimation and compensation of unknown disturbance in three-axis gyro-stabilized camera mount. Trans. Inst. Meas. Control.","DOI":"10.1177\/0142331214544498"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Ma, D., and Lin, H. (2016, January 27\u201329). Chattering-free nonsingular fast terminal sliding-mode control for permanent magnet synchronous motor servo system. Proceedings of the 35th Chinese Control Conference (CCC), Chengdu, China.","DOI":"10.1109\/ChiCC.2016.7553890"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2159","DOI":"10.1016\/S0005-1098(02)00147-4","article-title":"Non-singular terminal sliding mode control of rigid manipulators","volume":"38","author":"Feng","year":"2002","journal-title":"Automatica"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/0375-9601(88)90728-1","article-title":"Terminal attractors for addressable memory in neural networks","volume":"133","author":"Zak","year":"1988","journal-title":"Phys. Lett. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/S0167-6911(98)00036-X","article-title":"Terminal sliding mode control design for uncertain dynamic systems","volume":"34","author":"Wu","year":"1998","journal-title":"Syst. Control Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.mechatronics.2015.10.012","article-title":"Non-singular terminal sliding mode controller: Application to an actuated exoskeleton","volume":"33","author":"Madani","year":"2016","journal-title":"Mechatronics"},{"key":"ref_19","unstructured":"Yu, S., Yu, X., and Stonier, R. (2003, January 15\u201317). Continuous finite-time control for robotic manipulators with terminal sliding modes. Proceedings of the 6th International Conference of Information Fusion, Budapest, Hungary."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Ding, F., Cui, Y., Wang, C., and Zhang, X. (2016, January 27\u201329). Course control of air cushion vessel based on terminal sliding mode control with rbf neural network. Proceedings of the 35th Chinese Control Conference (CCC), Chengdu, China.","DOI":"10.1109\/ChiCC.2016.7553896"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Shtessel, Y., Edwards, C., Fridman, L., and Levant, A. (2015). Sliding Mode Control and Observation, Springer.","DOI":"10.1007\/978-0-8176-4893-0"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1447","DOI":"10.1109\/9.948475","article-title":"Universal single-input-single-output (siso) sliding-mode controllers with finite-time convergence","volume":"46","author":"Levant","year":"2001","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1744","DOI":"10.1080\/00207179.2013.796068","article-title":"Design of a chatter-free terminal sliding mode controller for nonlinear fractional-order dynamical systems","volume":"86","author":"Aghababa","year":"2013","journal-title":"Int. J. Control"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/j.neucom.2016.09.089","article-title":"Adaptive terminal sliding mode control of uncertain robotic manipulators based on local approximation of a dynamic system","volume":"228","author":"Tran","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Jia, T., and Kang, G. (2012, January 15\u201317). An rbf neural network-based nonsingular terminal sliding mode controller for robot manipulators. Proceedings of the 2012 Third International Conference on Intelligent Control and Information Processing (ICICIP), Dalian, China.","DOI":"10.1109\/ICICIP.2012.6391479"},{"key":"ref_26","unstructured":"Wang, H., Yang, Z., and Zhou, Z. (2016, January 28\u201330). Rbf-based terminal sliding mode control for a class of underactuated mechanical system. Proceedings of the 2016 Chinese Control and Decision Conference (CCDC), Yinchuan, China."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/00207179.2015.1012119","article-title":"Decoupling control based on terminal sliding mode and wavelet network for the speed and tension system of reversible cold strip rolling mill","volume":"88","author":"Fang","year":"2015","journal-title":"Int. J. Control"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1109\/TFUZZ.2006.879982","article-title":"Nonsingular terminal sliding mode control of robot manipulators using fuzzy wavelet networks","volume":"14","author":"Lin","year":"2006","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_29","unstructured":"Ferch, M., Zhang, J., and Knoll, A. (1999, January 10\u201315). Robot skill transfer based on B-Spline fuzzy controllers for force-control tasks. Proceedings of the 1999 IEEE International Conference on Robotics and Automation, Detroit, MI, USA."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.1109\/72.950131","article-title":"Nonlinear system modeling via knot-optimizing B-Spline networks","volume":"12","author":"Yiu","year":"2001","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_31","unstructured":"Cabrita, C., Ruano, A.E., and Fonseca, C.M. (2001, January 15\u201316). Single and multi-objective genetic programming design for B-Spline neural networks and Neuro-Fuzzy systems. Proceedings of the Ifac Workshop on Advanced Fuzzy-Neural Control, Valencia, Spain."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1513","DOI":"10.1016\/j.asoc.2007.10.015","article-title":"B-spline neural network design using improved differential evolution for identification of an experimental nonlinear process","volume":"8","author":"Leandro","year":"2008","journal-title":"Appl. Soft Comput."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Qamar, S., Khan, L., and Qamar, Z. (2013, January 16\u201318). Online adaptive full car active suspension control using b-spline fuzzy-neural network. Proceedings of the 2013 11th International Conference on Frontiers of Information Technology (FIT), Islamabad, Pakistan.","DOI":"10.1109\/FIT.2013.45"},{"key":"ref_34","first-page":"1348","article-title":"Adaptive B-Spline based Neuro-Fuzzy control for full car active suspension system","volume":"16","author":"Qamar","year":"2013","journal-title":"Middle East J. Sci. Res."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1109\/21.376496","article-title":"Fuzzy B-Spline membership function and its applications in Fuzzy-Neural control","volume":"25","author":"Wang","year":"1995","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"966","DOI":"10.1109\/TSMCB.2003.810872","article-title":"Evolutionary learning of BMF Fuzzy-Neural networks using a reduced-form genetic algorithm","volume":"33","author":"Mar","year":"2003","journal-title":"IEEE Trans. Syst. Man Cybern. Part B Cybern."},{"key":"ref_37","first-page":"2159","article-title":"Remote sensing images classification using fuzzy B-Spline function neural network","volume":"3","author":"Mao","year":"2002","journal-title":"J. Electr. Meas. Instrom."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2418","DOI":"10.1016\/j.ymssp.2009.01.013","article-title":"Nonlinear identification using a B-Spline neural network and chaotic immune approaches","volume":"23","author":"Coelho","year":"2009","journal-title":"Mech. Syst. Signal Proc."},{"key":"ref_39","unstructured":"Boor, C.D. (1985). A practical Guide to Splines\/Arl De Boor, Wiley."},{"key":"ref_40","unstructured":"(2017, January 01). B-Splines. Available online: http:\/\/web.mit.edu\/hyperbook\/Patrikalakis-Maekawa-Cho\/node16.html."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/5\/978\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:34:03Z","timestamp":1760207643000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/5\/978"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,28]]},"references-count":40,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2017,5]]}},"alternative-id":["s17050978"],"URL":"https:\/\/doi.org\/10.3390\/s17050978","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2017,4,28]]}}}