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To maximize the 1,3\u2010PD concentration at the terminal time, a constrained optimal control model is then presented. A solution approach is developed to seek the optimal feed rates based on control vector parametrization method and improved differential evolution algorithm. The proposed methodology yielded an increase by 32.17% of 1,3\u2010PD concentration at the terminal time.<\/jats:p>","DOI":"10.1155\/2012\/245315","type":"journal-article","created":{"date-parts":[[2012,3,8]],"date-time":"2012-03-08T21:01:03Z","timestamp":1331240463000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimal Control of a Fed\u2010Batch Fermentation Involving Multiple Feeds"],"prefix":"10.1155","volume":"2012","author":[{"given":"Chongyang","family":"Liu","sequence":"first","affiliation":[]},{"given":"Zhaohua","family":"Gong","sequence":"additional","affiliation":[]},{"given":"Zhaoyi","family":"Huo","sequence":"additional","affiliation":[]},{"given":"Bangyu","family":"Shen","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,3,8]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0141-0229(96)00087-7"},{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45736-4_11"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/bit.260440806"},{"key":"e_1_2_7_4_2","doi-asserted-by":"publisher","DOI":"10.3934\/jimo.2005.1.377"},{"key":"e_1_2_7_5_2","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.chaos.2005.05.027","article-title":"Nonlinear impulsive system of fed- batch culture in fermentative production and its properties","volume":"28","author":"Gao C.-X.","year":"2006","journal-title":"Chaos Solitons Fractals"},{"key":"e_1_2_7_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2009.12.011"},{"key":"e_1_2_7_7_2","series-title":"Measuring, Modelling and Control","first-page":"506","volume-title":"Biotechnology","author":"Lim H.-C.","year":"1991"},{"key":"e_1_2_7_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2009.06.006"},{"key":"e_1_2_7_9_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021708729556"},{"key":"e_1_2_7_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.compchemeng.2004.02.018"},{"key":"e_1_2_7_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.bej.2007.03.015"},{"key":"e_1_2_7_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2007.08.005"},{"key":"e_1_2_7_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2006.10.027"},{"key":"e_1_2_7_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2010.08.001"},{"key":"e_1_2_7_15_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207160.2011.553674"},{"key":"e_1_2_7_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2010.06.022"},{"key":"e_1_2_7_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2011.01.023"},{"key":"e_1_2_7_18_2","first-page":"383","article-title":"Optimization of biomass production in fed-batch culture by feed and dilution control actions","volume":"35","author":"Levi\u0161auskas D.","year":"2006","journal-title":"Information Technology and Control"},{"key":"e_1_2_7_19_2","doi-asserted-by":"publisher","DOI":"10.1021\/ie980731w"},{"key":"e_1_2_7_20_2","first-page":"428","article-title":"Mathematical modelling of kinetics and research on multiplicity of glyceroll bioconversion to 1,3-propanediol","volume":"4","author":"Xiu Z.-L.","year":"2000","journal-title":"Journal of Dalian University of Technology"},{"volume-title":"Ordinary Differential Equations","year":"1982","author":"Arrowsmith D.-K.","key":"e_1_2_7_21_2"},{"volume-title":"Advanced Process Control","year":"1981","author":"Ray W.-H.","key":"e_1_2_7_22_2"},{"volume-title":"A Unified Computational Approach to Optimal Control Problems","year":"1991","author":"Teo K.-L.","key":"e_1_2_7_23_2"},{"volume-title":"Applied Optimal Control","year":"1975","author":"Bryson A.","key":"e_1_2_7_24_2"},{"volume-title":"Adaptaion in Natural and Artificial Systems","year":"1975","author":"Holland J.-H.","key":"e_1_2_7_25_2"},{"volume-title":"Numerical Optimization of Computer Models","year":"1981","author":"Schwefel H.-P.","key":"e_1_2_7_26_2"},{"key":"e_1_2_7_27_2","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1126\/science.220.4598.671","article-title":"Optimization by simulated annealing","volume":"220","author":"Kirkpatrick S.","year":"1983","journal-title":"American Association for the Advancement of Science. 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