{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T06:33:57Z","timestamp":1777012437939,"version":"3.51.4"},"reference-count":35,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,6,11]],"date-time":"2020-06-11T00:00:00Z","timestamp":1591833600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"R&amp;D on soft-sensing and control of key parameters for microbial fermentation","award":["SH2017002"],"award-info":[{"award-number":["SH2017002"]}]},{"name":"The National Science Research Foundation of CHINA","award":["41376175"],"award-info":[{"award-number":["41376175"]}]},{"name":"The Natural Science Foundation of Jiangsu Province","award":["BK20140568, BK20151345"],"award-info":[{"award-number":["BK20140568, BK20151345"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>l-Lysine is produced by a complex non-linear fermentation process. A non-linear model predictive control (NMPC) scheme is proposed to control product concentration in real time for enhancing production. However, product concentration cannot be directly measured in real time. Least-square support vector machine (LSSVM) is used to predict product concentration in real time. Grey-Wolf Optimization (GWO) algorithm is used to optimize the key model parameters (penalty factor and kernel width) of LSSVM for increasing its prediction accuracy (GWO-LSSVM). The proposed optimal prediction model is used as a process model in the non-linear model predictive control to predict product concentration. GWO is also used to solve the non-convex optimization problem in non-linear model predictive control (GWO-NMPC) for calculating optimal future inputs. The proposed GWO-based prediction model (GWO-LSSVM) and non-linear model predictive control (GWO-NMPC) are compared with the Particle Swarm Optimization (PSO)-based prediction model (PSO-LSSVM) and non-linear model predictive control (PSO-NMPC) to validate their effectiveness. The comparative results show that the prediction accuracy, adaptability, real-time tracking ability, overall error and control precision of GWO-based predictive control is better compared to PSO-based predictive control.<\/jats:p>","DOI":"10.3390\/s20113335","type":"journal-article","created":{"date-parts":[[2020,6,15]],"date-time":"2020-06-15T05:56:27Z","timestamp":1592200587000},"page":"3335","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["A Non-linear Model Predictive Control Based on Grey-Wolf Optimization Using Least-Square Support Vector Machine for Product Concentration Control in l-Lysine Fermentation"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3472-9214","authenticated-orcid":false,"given":"Bo","family":"Wang","sequence":"first","affiliation":[{"name":"School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2414-5728","authenticated-orcid":false,"given":"Muhammad","family":"Shahzad","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2497-0653","authenticated-orcid":false,"given":"Xianglin","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5212-3115","authenticated-orcid":false,"given":"Khalil Ur","family":"Rehman","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6595-4169","authenticated-orcid":false,"given":"Saad","family":"Uddin","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Jiangsu University, Zhenjiang 212013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.2514\/1.G002507","article-title":"Model predictive control in aerospace systems: Current state and opportunities","volume":"40","author":"Eren","year":"2017","journal-title":"J. Guid. Control Dyn."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Muhammad, D., Ahmad, Z., and Aziz, N. (2019). Low density polyethylene tubular reactor control using state space model predictive control. Chem. Eng. Commun., 1\u201317.","DOI":"10.1080\/00986445.2019.1674816"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jenvman.2017.01.079","article-title":"Statistical monitoring and dynamic simulation of a wastewater treatment plant: A combined approach to achieve model predictive control","volume":"193","author":"Wang","year":"2017","journal-title":"J. Environ. Manag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1109\/TIE.2016.2625238","article-title":"Model predictive control for power converters and drives: Advances and trends","volume":"64","author":"Vazquez","year":"2016","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.enbuild.2017.02.012","article-title":"Artificial neural network (ANN) based model predictive control (MPC) and optimization of HVAC systems: A state of the art review and case study of a residential HVAC system","volume":"141","author":"Afram","year":"2017","journal-title":"Energy Build."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"133","DOI":"10.5004\/dwt.2020.24144","article-title":"Model predictive control for chlorine dosing of drinking water treatment based on support vector machine model","volume":"173","author":"Wang","year":"2020","journal-title":"Desalin. Water Treat."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Yokota, A., and Ikeda, M. (2017). Amino Acid Fermentation, Springer.","DOI":"10.1007\/978-4-431-56520-8"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1080\/07388551.2019.1663149","article-title":"l-Lysine production improvement: A review of the state of the art and patent landscape focusing on strain development and fermentation technologies","volume":"39","author":"Letti","year":"2019","journal-title":"Crit. Rev. Biotechnol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1007\/s13205-014-0252-7","article-title":"Optimization of fermentation upstream parameters and immobilization of Corynebacterium glutamicum MH 20-22 B cells to enhance the production of l-Lysine","volume":"5","author":"Razak","year":"2015","journal-title":"3 Biotech"},{"key":"ref_10","unstructured":"Gustavsson, R. (2018). Development of Soft Sensors for Monitoring and Control of Bioprocesses, Link\u00f6ping University Electronic Press."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Ahuja, K., and Pani, A.K. (2018, January 14\u201316). Software sensor development for product concentration monitoring in fed-batch fermentation process using dynamic principal component regression. Proceedings of the 2018 International Conference on Soft-computing and Network Security (ICSNS), Coimbatore, India.","DOI":"10.1109\/ICSNS.2018.8573661"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3168","DOI":"10.1109\/TII.2019.2902129","article-title":"Nonlinear dynamic soft sensor modeling with supervised long short-term memory network","volume":"16","author":"Yuan","year":"2020","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1016\/j.renene.2015.07.054","article-title":"Modelling and prediction of bioethanol production from intermediates and byproduct of sugar beet processing using neural networks","volume":"85","author":"Grahovac","year":"2016","journal-title":"Renew. Energy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4463","DOI":"10.1109\/JSEN.2019.2901453","article-title":"Impact Localization and Severity Estimation on Composite Structure Using Fiber Bragg Grating Sensors by Least Square Support Vector Regression","volume":"19","author":"Datta","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Wang, G., Xu, B., and Jiang, W. (, January 28\u201330). SVM modeling for glutamic acid fermentation process. Proceedings of the 2016 Chinese Control and Decision Conference (CCDC), Yinchuan, China.","DOI":"10.1109\/CCDC.2016.7531989"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1016\/j.energy.2018.11.128","article-title":"A novel combination forecasting model for wind power integrating least square support vector machine, deep belief network, singular spectrum analysis and locality-sensitive hashing","volume":"168","author":"Zhang","year":"2019","journal-title":"Energy"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2305","DOI":"10.1007\/s11063-019-09994-8","article-title":"Short-term traffic flow prediction based on least square support vector machine with hybrid optimization algorithm","volume":"50","author":"Luo","year":"2019","journal-title":"Neural Process. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Robles-Rodriguez, C.E., Bideaux, C., Roux, G., Molina-Jouve, C., and Aceves-Lara, C.A. (2016). Soft-sensors for lipid fermentation variables based on PSO Support Vector Machine (PSO-SVM). Distributed Computing and Artificial Intelligence, Proceedings of the 13th International Conference, Salamanca, Spain, 28\u201330 March 2020, Springer.","DOI":"10.1007\/978-3-319-40162-1_19"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.tust.2017.06.019","article-title":"Deformation evaluation on surrounding rocks of underground caverns based on PSO-LSSVM","volume":"69","author":"Xue","year":"2017","journal-title":"Tunn. Undergr. Space Technol."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Zhu, X., Rehman, K.U., Wang, B., and Shahzad, M. (2020). Modern Soft-Sensing Modeling Methods for Fermentation Processes. Sensors, 20.","DOI":"10.3390\/s20061771"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Saad, A.E.H., Dong, Z., and Karimi, M. (2017). A comparative study on recently-introduced nature-based global optimization methods in complex mechanical system design. Algorithms, 10.","DOI":"10.3390\/a10040120"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","article-title":"Grey wolf optimizer","volume":"69","author":"Mirjalili","year":"2014","journal-title":"Adv. Eng. Softw."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/4235.585893","article-title":"No free lunch theorems for optimization","volume":"1","author":"Wolpert","year":"1997","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2459","DOI":"10.1002\/fsn3.850","article-title":"The generalized predictive control of bacteria concentration in marine lysozyme fermentation process","volume":"6","author":"Zhu","year":"2018","journal-title":"Food Sci. Nutr."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Nisha, M.G., Prince, M.J.R., and Jones, A.J. (2019, January 7\u20138). Neural Network Predictive Control of Systems with Faster Dynamics using PSO. Proceedings of the 2019 International Conference on Recent Advances in Energy-Efficient Computing and Communication (ICRAECC), Nagercoil, India.","DOI":"10.1109\/ICRAECC43874.2019.8995025"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Ait Sahed, O., Kara, K., and Hadjili, M.L. (2015). Constrained fuzzy predictive control using particle swarm optimization. Appl. Comput. Intell. Soft Comput.","DOI":"10.1155\/2015\/437943"},{"key":"ref_27","first-page":"70","article-title":"Model Predictive Control Design Based on Particle Swarm Optimization","volume":"10","author":"Su","year":"2015","journal-title":"J. Converg. Inf. Technol."},{"key":"ref_28","unstructured":"Suthar, S., and Vishwakarma, D. (2020, June 08). A Fast Converging MPPT Control Technique (GWO) for PV Systems Adaptive to Fast Changing Irradiation and Partial Shading Conditions. Available online: https:\/\/d1wqtxts1xzle7.cloudfront.net\/60428554\/IRJET-V6I650220190829-75962-1sorde7.pdf."},{"key":"ref_29","first-page":"329","article-title":"Robust model predictive control for greenhouse temperature based on particle swarm optimization","volume":"5","author":"Chen","year":"2018","journal-title":"Inf. Process. Agric."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Kouvaritakis, B., and Cannon, M. (2016). Model Predictive Control, Springer International Publishing.","DOI":"10.1007\/978-3-319-24853-0"},{"key":"ref_31","unstructured":"Vapnik, V. (2013). The Nature of Statistical Learning Theory, Springer Science & Business Media."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1023\/A:1018628609742","article-title":"Least squares support vector machine classifiers","volume":"9","author":"Suykens","year":"1999","journal-title":"Neural Process. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1007\/s13201-019-0961-5","article-title":"Design of radial basis function-based support vector regression in predicting the discharge coefficient of a side weir in a trapezoidal channel","volume":"9","author":"Azimi","year":"2019","journal-title":"Appl. Water Sci."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Wang, X., Guo, T., Hao, W., and Guo, Q. (2019, January 27\u201330). Predicting Model based on LS-SVM for Inulinase Concentration during Pichia Pastoris\u2019 Fermentation Process. Proceedings of the 2019 Chinese Control Conference (CCC), Guangzhou, China.","DOI":"10.23919\/ChiCC.2019.8866656"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Huang, L., Wang, Z., and Ji, X. (2016). LS-SVM Generalized Predictive Control Based on PSO and Its Application of Fermentation Control. Proceedings of the 2015 Chinese Intelligent Systems Conference, Springer.","DOI":"10.1007\/978-3-662-48386-2_62"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/11\/3335\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:38:01Z","timestamp":1760175481000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/11\/3335"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,11]]},"references-count":35,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["s20113335"],"URL":"https:\/\/doi.org\/10.3390\/s20113335","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,11]]}}}