Optimal control of a batch fermentation process with nonlinear time-delay and free terminal time and cost sensitivity constraint
•An control problem is proposed to maximize the productivity of 1,3-PD.•The problem with free terminal time is transformed via a hybrid time-scaling strategy.•A parallel algorithm is proposed to solve the problem.•We consider a cost sensitivity constraint to reflect operational requirements. In this...
Saved in:
| Published in | Journal of process control Vol. 44; pp. 41 - 52 |
|---|---|
| Main Authors | , , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.08.2016
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | •An control problem is proposed to maximize the productivity of 1,3-PD.•The problem with free terminal time is transformed via a hybrid time-scaling strategy.•A parallel algorithm is proposed to solve the problem.•We consider a cost sensitivity constraint to reflect operational requirements.
In this paper, we consider a nonlinear time-delay dynamic system with uncertain system parameters to characterize the process of batch fermentation. Our goal is to design an optimal control scheme to maximize the productivity of 1,3-propanediol (1,3-PD). Accordingly, we introduce an optimal control problem governed by the nonlinear time-delay dynamic system, in which the control variables are the free terminal time of the batch fermentation process and the initial concentrations of biomass and glycerol. The optimal control problem is subject to a cost sensitivity constraint for ensuring that an acceptable level of the system performance is achieved and continuous state inequality constraints for ensuring that the concentrations of biomass, glycerol, 1,3-PD, acetate, ethanol lie within specified limits. Then, the optimal control problem with free terminal time is transformed, via a hybrid time-scaling strategy, into an equivalent problem with fixed terminal time, which is much preferred for numerical computation. Using the constraint transcription and local smoothing approximation techniques, we approximate these continuous state inequality constraints by conventional inequality constraints to yield an approximate optimal control problem. Because of the highly complex nature of this approximate problem, a parallel algorithm based on the filled function method is constructed to solve this approximate problem. Finally, it is observed that the optimal control obtained is satisfactory through numerical simulations. |
|---|---|
| AbstractList | •An control problem is proposed to maximize the productivity of 1,3-PD.•The problem with free terminal time is transformed via a hybrid time-scaling strategy.•A parallel algorithm is proposed to solve the problem.•We consider a cost sensitivity constraint to reflect operational requirements.
In this paper, we consider a nonlinear time-delay dynamic system with uncertain system parameters to characterize the process of batch fermentation. Our goal is to design an optimal control scheme to maximize the productivity of 1,3-propanediol (1,3-PD). Accordingly, we introduce an optimal control problem governed by the nonlinear time-delay dynamic system, in which the control variables are the free terminal time of the batch fermentation process and the initial concentrations of biomass and glycerol. The optimal control problem is subject to a cost sensitivity constraint for ensuring that an acceptable level of the system performance is achieved and continuous state inequality constraints for ensuring that the concentrations of biomass, glycerol, 1,3-PD, acetate, ethanol lie within specified limits. Then, the optimal control problem with free terminal time is transformed, via a hybrid time-scaling strategy, into an equivalent problem with fixed terminal time, which is much preferred for numerical computation. Using the constraint transcription and local smoothing approximation techniques, we approximate these continuous state inequality constraints by conventional inequality constraints to yield an approximate optimal control problem. Because of the highly complex nature of this approximate problem, a parallel algorithm based on the filled function method is constructed to solve this approximate problem. Finally, it is observed that the optimal control obtained is satisfactory through numerical simulations. |
| Author | Xie, Jun Xiu, Zhilong Yin, Hongchao Zhang, Xu Yuan, Jinlong Liu, Chongyang Feng, Enmin |
| Author_xml | – sequence: 1 givenname: Jinlong surname: Yuan fullname: Yuan, Jinlong email: yuanjinlong0613@163.com organization: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, PR China – sequence: 2 givenname: Chongyang surname: Liu fullname: Liu, Chongyang organization: School of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 264000, Shandong, PR China – sequence: 3 givenname: Xu surname: Zhang fullname: Zhang, Xu organization: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, PR China – sequence: 4 givenname: Jun surname: Xie fullname: Xie, Jun organization: Teaching and Research Office of Mathematics, Department of Basics, PLA Dalian Naval Academy, Dalian 116018, Liaoning, PR China – sequence: 5 givenname: Enmin surname: Feng fullname: Feng, Enmin organization: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, PR China – sequence: 6 givenname: Hongchao surname: Yin fullname: Yin, Hongchao email: hcyin@dlut.edu.cn organization: School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, Liaoning, PR China – sequence: 7 givenname: Zhilong surname: Xiu fullname: Xiu, Zhilong organization: School of Life Science and Biotechnology, Dalian University of Technology, Dalian 116024, Liaoning, PR China |
| BookMark | eNqFkM1OAyEUhYmpiW31FQwvMCMMM9BJXGga_5Im3eiaMMwlpZlCA6SmOx9dxurGTVfAvXzn3nNmaOK8A4RuKSkpofxuW273wWvvUlnld0makhB6gaZ0IVhRCUEnaErapi1oU9VXaBbjlhDCRMWn6Gu9T3anBjzywQ_YG6xwp5LeYANhBy6pZL3D4wiIEX_atMF5g8E6UAFnGIoeBnXEyvXYBACcMmdd1hybP2XtY8IRXLTJHmw6jtNiCsq6dI0ujRoi3Pyec_Tx_PS-fC1W65e35eOq0KxuU6FNY3i-6b7ruWoUFU21YB2jsIBa6NoQY2pgbd0yJZquZwwMV1Dlr4ID42yO-ElXBx9jACP3IRsPR0mJHHOUW_mXoxxzlKSROccM3v8DtT1lMhoYzuMPJxyyuYOFIKO24DT0NoBOsvf2nMQ3IM2agg |
| CitedBy_id | crossref_primary_10_3390_app9020337 crossref_primary_10_1016_j_jprocont_2018_10_001 crossref_primary_10_1016_j_cherd_2019_09_001 crossref_primary_10_1016_j_ijhydene_2018_11_053 crossref_primary_10_1109_ACCESS_2020_2976869 crossref_primary_10_3390_pr9050873 crossref_primary_10_3934_jimo_2021009 crossref_primary_10_1021_acs_iecr_2c02238 crossref_primary_10_1016_j_apm_2017_08_023 crossref_primary_10_1080_0305215X_2024_2349931 crossref_primary_10_1007_s11590_018_1375_2 crossref_primary_10_3934_era_2024312 |
| Cites_doi | 10.1002/(SICI)1097-0290(19980905)59:5<544::AID-BIT3>3.0.CO;2-A 10.1016/j.amc.2012.12.082 10.1016/j.apm.2015.04.051 10.1016/j.jprocont.2015.04.011 10.1016/j.jprocont.2009.03.006 10.1007/s12257-012-0290-0 10.1007/s002530051523 10.1016/j.sysconle.2014.07.001 10.1007/s11075-013-9746-3 10.1007/s10957-014-0654-z 10.1016/j.biotechadv.2009.07.003 10.1007/BF02172220 10.1016/j.copbio.2003.08.005 10.1016/j.amc.2014.01.027 10.1007/s10898-014-0245-4 10.3934/jimo.2014.10.275 10.3934/naco.2015.5.381 10.1016/j.amc.2011.01.039 10.3934/jimo.2013.9.471 10.1016/j.apm.2013.02.021 10.1007/BF00939433 10.1016/j.nahs.2014.08.004 10.1016/j.mcm.2011.03.005 10.1016/S0141-0229(96)00087-7 10.1002/bit.260460404 10.1007/s002530051251 10.1007/s40314-014-0160-9 10.1007/s00449-012-0800-7 10.1007/s10957-015-0783-z 10.1016/j.amc.2011.05.093 10.1016/j.cnsns.2013.10.021 10.1016/j.amc.2015.06.090 |
| ContentType | Journal Article |
| Copyright | 2016 Elsevier Ltd |
| Copyright_xml | – notice: 2016 Elsevier Ltd |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.jprocont.2016.05.001 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Computer Science |
| EISSN | 1873-2771 |
| EndPage | 52 |
| ExternalDocumentID | 10_1016_j_jprocont_2016_05_001 S0959152416300452 |
| GroupedDBID | --K --M .DC .~1 0R~ 1B1 1~. 1~5 29L 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABFNM ABFRF ABJNI ABMAC ABNUV ABTAH ABXDB ABYKQ ACDAQ ACGFO ACGFS ACNNM ACRLP ADBBV ADEWK ADEZE ADMUD ADTZH AEBSH AECPX AEFWE AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AHPOS AIEXJ AIKHN AITUG AJBFU AJOXV AKURH ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ASPBG AVWKF AXJTR AZFZN BBWZM BJAXD BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD ENUVR EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HLY HVGLF HZ~ IHE J1W JJJVA KOM LX7 LY7 M41 MO0 N9A NDZJH O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SCE SDF SDG SDP SES SET SEW SPC SPCBC SSG SST SSZ T5K UNMZH WUQ XFK ZMT ZY4 ~G- AATTM AAXKI AAYWO AAYXX ABWVN ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AFXIZ AGCQF AGQPQ AGRNS AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP BNPGV CITATION SSH |
| ID | FETCH-LOGICAL-c349t-cf5f6349cdbd6a5a175283b31e8e47c4f0ff4e39493a75bd33ef6ae2a5a76e363 |
| IEDL.DBID | .~1 |
| ISSN | 0959-1524 |
| IngestDate | Tue Jul 01 03:17:12 EDT 2025 Thu Apr 24 23:01:30 EDT 2025 Fri Feb 23 02:16:55 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Free terminal time Cost sensitivity constraint Parallel optimization Nonlinear time-delay system Optimal control Batch fermentation |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c349t-cf5f6349cdbd6a5a175283b31e8e47c4f0ff4e39493a75bd33ef6ae2a5a76e363 |
| PageCount | 12 |
| ParticipantIDs | crossref_primary_10_1016_j_jprocont_2016_05_001 crossref_citationtrail_10_1016_j_jprocont_2016_05_001 elsevier_sciencedirect_doi_10_1016_j_jprocont_2016_05_001 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2016-08-01 |
| PublicationDateYYYYMMDD | 2016-08-01 |
| PublicationDate_xml | – month: 08 year: 2016 text: 2016-08-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationTitle | Journal of process control |
| PublicationYear | 2016 |
| Publisher | Elsevier Ltd |
| Publisher_xml | – name: Elsevier Ltd |
| References | Yu (bib0125) 2014 Rehbock, Teo, Jennings (bib0130) 1992; 2 Saxena, Anand, Saran, Isar (bib0055) 2009; 27 Loxton, Lin, Teo (bib0145) 2014; 10 Polak (bib0160) 1997 Menzel, Zeng, Deckwer (bib0035) 1997; 20 Wei, Teo, Zhan (bib0135) 2011; 218 Biebl, Zeng, Menzel, Deckwer (bib0010) 1998; 50 Nakamura, Whited (bib0025) 2003; 14 Liu (bib0120) 2013; 37 Liu, Loxton, Teo (bib0155) 2014; 72 Lin, Gao, Wang (bib0175) 2014; 66 Wang, Lin, Loxton, Teo, Cheng (bib0050) 2015; 32 Cheng, Wang, Loxton, Lin (bib0115) 2014; 161 Wang, Wang, Zhao, Song, Ma (bib0105) 2015; 5 Wang (bib0040) 2013; 36 Yuan, Wang, Zhang, Feng, Yin, Xiu (bib0090) 2015; 62 Gao, Yang, You (bib0170) 2015; 268 Zeng, Biebl (bib0030) 2002; 74 Yuan, Zhang, Zhu, Feng, Yin, Xiu (bib0070) 2014; 19 Wang, Ye, Feng, Yin, Xiu (bib0100) 2011; 54 Yuan, Zhang, Zhu, Yin, Feng, Xiu, Tan (bib0085) 2015; 34 Ahrens, Menzel, Zeng, Deckwer (bib0020) 1998; 59 Biebl, Menzel, Zeng, Deckwer (bib0005) 1999; 52 Ashoori, Moshiri, Khaki-Sedigh, Bakhtiari (bib0045) 2009; 19 Yu, Lin, Loxton, Teo, Wang (bib0185) 2016; 169 Chai, Loxton, Teo, Yang (bib0180) 2013; 9 Zhu, Feng (bib0110) 2012; 17 Jiang, Yuan, Feng (bib0075) 2013; 219 Yuan, Zhang, Zhu, Feng, Yin, Xiu (bib0095) 2015; 15 Loxton, Teo, Rehbock (bib0140) 2011; 217 Lin, Loxton, Teo (bib0150) 2014; 10 Yuan, Zhu, Zhang, Yin, Feng, Xiu (bib0065) 2014; 232 Yin, Yuan, Zhang, Xie, Feng, Xiu (bib0080) 2016; 40 Zeng, Biebl (bib0015) 2002 Ge, Qin (bib0165) 1987; 54 Zeng (bib0060) 1995; 46 Zeng (10.1016/j.jprocont.2016.05.001_bib0030) 2002; 74 Wei (10.1016/j.jprocont.2016.05.001_bib0135) 2011; 218 Biebl (10.1016/j.jprocont.2016.05.001_bib0010) 1998; 50 Wang (10.1016/j.jprocont.2016.05.001_bib0050) 2015; 32 Yuan (10.1016/j.jprocont.2016.05.001_bib0085) 2015; 34 Yuan (10.1016/j.jprocont.2016.05.001_bib0090) 2015; 62 Cheng (10.1016/j.jprocont.2016.05.001_bib0115) 2014; 161 Saxena (10.1016/j.jprocont.2016.05.001_bib0055) 2009; 27 Yin (10.1016/j.jprocont.2016.05.001_bib0080) 2016; 40 Wang (10.1016/j.jprocont.2016.05.001_bib0100) 2011; 54 Loxton (10.1016/j.jprocont.2016.05.001_bib0145) 2014; 10 Chai (10.1016/j.jprocont.2016.05.001_bib0180) 2013; 9 Gao (10.1016/j.jprocont.2016.05.001_bib0170) 2015; 268 Jiang (10.1016/j.jprocont.2016.05.001_bib0075) 2013; 219 Yuan (10.1016/j.jprocont.2016.05.001_bib0095) 2015; 15 Lin (10.1016/j.jprocont.2016.05.001_bib0150) 2014; 10 Lin (10.1016/j.jprocont.2016.05.001_bib0175) 2014; 66 Ashoori (10.1016/j.jprocont.2016.05.001_bib0045) 2009; 19 Rehbock (10.1016/j.jprocont.2016.05.001_bib0130) 1992; 2 Zhu (10.1016/j.jprocont.2016.05.001_bib0110) 2012; 17 Yuan (10.1016/j.jprocont.2016.05.001_bib0070) 2014; 19 Polak (10.1016/j.jprocont.2016.05.001_bib0160) 1997 Yuan (10.1016/j.jprocont.2016.05.001_bib0065) 2014; 232 Wang (10.1016/j.jprocont.2016.05.001_bib0040) 2013; 36 Yu (10.1016/j.jprocont.2016.05.001_bib0125) 2014 Liu (10.1016/j.jprocont.2016.05.001_bib0155) 2014; 72 Zeng (10.1016/j.jprocont.2016.05.001_bib0015) 2002 Liu (10.1016/j.jprocont.2016.05.001_bib0120) 2013; 37 Loxton (10.1016/j.jprocont.2016.05.001_bib0140) 2011; 217 Zeng (10.1016/j.jprocont.2016.05.001_bib0060) 1995; 46 Biebl (10.1016/j.jprocont.2016.05.001_bib0005) 1999; 52 Ahrens (10.1016/j.jprocont.2016.05.001_bib0020) 1998; 59 Wang (10.1016/j.jprocont.2016.05.001_bib0105) 2015; 5 Ge (10.1016/j.jprocont.2016.05.001_bib0165) 1987; 54 Yu (10.1016/j.jprocont.2016.05.001_bib0185) 2016; 169 Menzel (10.1016/j.jprocont.2016.05.001_bib0035) 1997; 20 Nakamura (10.1016/j.jprocont.2016.05.001_bib0025) 2003; 14 |
| References_xml | – volume: 59 start-page: 544 year: 1998 end-page: 552 ident: bib0020 article-title: Kinetic, dynamic, and pathway studies of glycerol metabolism by publication-title: Biotechnol. Bioeng. – volume: 36 start-page: 433 year: 2013 end-page: 441 ident: bib0040 article-title: Determining the transport mechanism of an enzyme-catalytic complex metabolic network based on biological robustness publication-title: Bioprocess Biosyst. Eng. – volume: 32 start-page: 1 year: 2015 end-page: 9 ident: bib0050 article-title: Optimal 1,3-propanediol production: exploring the trade-off between process yield and feeding rate variation publication-title: J. Process Control – volume: 66 start-page: 511 year: 2014 end-page: 523 ident: bib0175 article-title: A continuously differentiable filled function method for global optimization publication-title: Numer. Algorithms – volume: 20 start-page: 82 year: 1997 end-page: 86 ident: bib0035 article-title: High concentration and productivity of 1,3-propanediol from continuous fermentation of glycerol by publication-title: Enzyme Microb. Technol. – volume: 74 start-page: 239 year: 2002 end-page: 259 ident: bib0030 article-title: Bulk chemicals from biotechnology: the case of 1,3-propanediol production and the new trends publication-title: Adv. Biochem. Eng. Biotechnol. – volume: 218 start-page: 1180 year: 2011 end-page: 1190 ident: bib0135 article-title: A numerical method for an optimal control problem with minimum sensitivity on coefficient variation publication-title: Appl. Math. Comput. – volume: 46 start-page: 314 year: 1995 end-page: 324 ident: bib0060 article-title: A kinetic model for product formation of microbial and mammalian cells publication-title: Biotechnol. Bioeng. – volume: 5 start-page: 381 year: 2015 end-page: 392 ident: bib0105 article-title: A stochastic model for microbial fermentation process under Gaussian white noise environment publication-title: Numer. Algebra Control Optim. – volume: 15 start-page: 112 year: 2015 end-page: 131 ident: bib0095 article-title: Pathway identification using parallel optimization for a nonlinear hybrid system in batch culture publication-title: Nonlinear Anal. Hybrid Syst. – volume: 34 start-page: 957 year: 2015 end-page: 978 ident: bib0085 article-title: Identification and robustness analysis of nonlinear multi-stage enzyme-catalytic dynamical system in batch culture publication-title: Comput. Appl. Math. – volume: 219 start-page: 6979 year: 2013 end-page: 6985 ident: bib0075 article-title: Robust identification and its properties of nonlinear bilevel multi-stage dynamic system publication-title: Appl. Math. Comput. – volume: 54 start-page: 241 year: 1987 end-page: 252 ident: bib0165 article-title: A class of filled functions for finding global minimizers of a function of several variables publication-title: J. Optim. Theory Appl. – volume: 40 start-page: 468 year: 2016 end-page: 484 ident: bib0080 article-title: Modeling and parameter identification for a nonlinear multi-stage system for DHA regulon in batch culture publication-title: Appl. Math. Model. – volume: 19 start-page: 1162 year: 2009 end-page: 1173 ident: bib0045 article-title: Optimal control of a nonlinear fed-batch fermentation process using model predictive approach publication-title: J. Process Control – volume: 72 start-page: 53 year: 2014 end-page: 60 ident: bib0155 article-title: A computational method for solving time-delay optimal control problems with free terminal time publication-title: Syst. Control Lett. – year: 1997 ident: bib0160 article-title: Optimization Algorithms and Consistent Approximations – volume: 232 start-page: 150 year: 2014 end-page: 163 ident: bib0065 article-title: Robust identification of enzymatic nonlinear dynamical systems for 1,3-propanediol transport mechanisms in microbial batch culture publication-title: Appl. Math. Comput. – volume: 268 start-page: 685 year: 2015 end-page: 695 ident: bib0170 article-title: A new filled function method for global optimization publication-title: Appl. Math. Comput. – volume: 10 start-page: 537 year: 2014 end-page: 560 ident: bib0145 article-title: Switching time optimization for nonlinear switched systems: direct optimization and the time-scaling transformation publication-title: Pac. J. Optim. – volume: 14 start-page: 454 year: 2003 end-page: 459 ident: bib0025 article-title: Metabolic engineering for the microbial production of 1,3-propanediol publication-title: Curr. Opin. Biotechnol. – volume: 62 start-page: 791 year: 2015 end-page: 810 ident: bib0090 article-title: Parameter identification for a nonlinear enzyme-catalytic dynamic system with time-delays publication-title: J. Glob. Optim. – volume: 27 start-page: 895 year: 2009 end-page: 913 ident: bib0055 article-title: Microbial production of 1,3-propanediol: recent developments and emerging opportunities publication-title: Biotechnol. Adv. – volume: 19 start-page: 2088 year: 2014 end-page: 2103 ident: bib0070 article-title: Modelling and pathway identification involving the transport mechanism of a complex metabolic system in batch culture publication-title: Commun. Nonlinear Sci. Numer. Simul. – volume: 217 start-page: 6566 year: 2011 end-page: 6576 ident: bib0140 article-title: Robust suboptimal control of nonlinear systems publication-title: Appl. Math. Comput. – year: 2014 ident: bib0125 article-title: Optimal control of a nonlinear time-delay system in batch fermentation process publication-title: Math. Probl. Eng. – volume: 10 start-page: 275 year: 2014 end-page: 309 ident: bib0150 article-title: The control parameterization method for nonlinear optimal control: a survey publication-title: J. Ind. Manag. Optim. – volume: 50 start-page: 24 year: 1998 end-page: 29 ident: bib0010 article-title: Fermentation of glycerol to 1,3-propanediol and 2,3-butanediol by publication-title: Appl. Microbiol. Biotechnol. – volume: 17 start-page: 1238 year: 2012 end-page: 1243 ident: bib0110 article-title: Joint estimation in batch culture by using unscented Kalman filter publication-title: Biotechnol. Bioprocess Eng. – volume: 161 start-page: 342 year: 2014 end-page: 362 ident: bib0115 article-title: Robust optimal control of a micro-bial batch culture process publication-title: J. Optim. Theory Appl. – volume: 37 start-page: 6899 year: 2013 end-page: 6908 ident: bib0120 article-title: Modelling and parameter identification for a nonlinear time-delay system in microbial batch fermentation publication-title: Appl. Math. Model. – volume: 54 start-page: 618 year: 2011 end-page: 624 ident: bib0100 article-title: Modeling and identification of a nonlinear hybrid dynamical system in batch fermentation of glycerol publication-title: Math. Comput. Model. – volume: 52 start-page: 289 year: 1999 end-page: 297 ident: bib0005 article-title: Microbial production of 1,3-propanediol publication-title: Appl. Microbiol. Biotechnol. – volume: 2 start-page: 331 year: 1992 end-page: 348 ident: bib0130 article-title: A computational procedure for suboptimal robust controls publication-title: Dynam. Control – start-page: 239 year: 2002 end-page: 259 ident: bib0015 article-title: Bulk chemicals from biotechnology: the case of 1,3-propanediol production and the new trends publication-title: Tools and Applications of Biochemical Engineering Science – volume: 9 start-page: 471 year: 2013 end-page: 486 ident: bib0180 article-title: A unified parameter identification method for nonlinear time-delay systems publication-title: J. Ind. Manag. Optim. – volume: 169 start-page: 876 year: 2016 end-page: 901 ident: bib0185 article-title: A hybrid time-scaling transformation for time-delay optimal control problems publication-title: J. Optim. Theory Appl. – volume: 59 start-page: 544 issue: 5 year: 1998 ident: 10.1016/j.jprocont.2016.05.001_bib0020 article-title: Kinetic, dynamic, and pathway studies of glycerol metabolism by Klebsiella pneumoniae in anaerobic continuous culture: III. Enzymes and fluxes of glycerol dissimilation and 1,3-propanediol formation publication-title: Biotechnol. Bioeng. doi: 10.1002/(SICI)1097-0290(19980905)59:5<544::AID-BIT3>3.0.CO;2-A – volume: 219 start-page: 6979 issue: 12 year: 2013 ident: 10.1016/j.jprocont.2016.05.001_bib0075 article-title: Robust identification and its properties of nonlinear bilevel multi-stage dynamic system publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2012.12.082 – volume: 40 start-page: 468 year: 2016 ident: 10.1016/j.jprocont.2016.05.001_bib0080 article-title: Modeling and parameter identification for a nonlinear multi-stage system for DHA regulon in batch culture publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2015.04.051 – volume: 10 start-page: 537 issue: 3 year: 2014 ident: 10.1016/j.jprocont.2016.05.001_bib0145 article-title: Switching time optimization for nonlinear switched systems: direct optimization and the time-scaling transformation publication-title: Pac. J. Optim. – volume: 32 start-page: 1 year: 2015 ident: 10.1016/j.jprocont.2016.05.001_bib0050 article-title: Optimal 1,3-propanediol production: exploring the trade-off between process yield and feeding rate variation publication-title: J. Process Control doi: 10.1016/j.jprocont.2015.04.011 – volume: 19 start-page: 1162 issue: 7 year: 2009 ident: 10.1016/j.jprocont.2016.05.001_bib0045 article-title: Optimal control of a nonlinear fed-batch fermentation process using model predictive approach publication-title: J. Process Control doi: 10.1016/j.jprocont.2009.03.006 – volume: 17 start-page: 1238 issue: 6 year: 2012 ident: 10.1016/j.jprocont.2016.05.001_bib0110 article-title: Joint estimation in batch culture by using unscented Kalman filter publication-title: Biotechnol. Bioprocess Eng. doi: 10.1007/s12257-012-0290-0 – volume: 52 start-page: 289 issue: 3 year: 1999 ident: 10.1016/j.jprocont.2016.05.001_bib0005 article-title: Microbial production of 1,3-propanediol publication-title: Appl. Microbiol. Biotechnol. doi: 10.1007/s002530051523 – volume: 72 start-page: 53 year: 2014 ident: 10.1016/j.jprocont.2016.05.001_bib0155 article-title: A computational method for solving time-delay optimal control problems with free terminal time publication-title: Syst. Control Lett. doi: 10.1016/j.sysconle.2014.07.001 – volume: 66 start-page: 511 year: 2014 ident: 10.1016/j.jprocont.2016.05.001_bib0175 article-title: A continuously differentiable filled function method for global optimization publication-title: Numer. Algorithms doi: 10.1007/s11075-013-9746-3 – volume: 161 start-page: 342 issue: 1 year: 2014 ident: 10.1016/j.jprocont.2016.05.001_bib0115 article-title: Robust optimal control of a micro-bial batch culture process publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-014-0654-z – volume: 27 start-page: 895 year: 2009 ident: 10.1016/j.jprocont.2016.05.001_bib0055 article-title: Microbial production of 1,3-propanediol: recent developments and emerging opportunities publication-title: Biotechnol. Adv. doi: 10.1016/j.biotechadv.2009.07.003 – volume: 2 start-page: 331 year: 1992 ident: 10.1016/j.jprocont.2016.05.001_bib0130 article-title: A computational procedure for suboptimal robust controls publication-title: Dynam. Control doi: 10.1007/BF02172220 – volume: 14 start-page: 454 issue: 15 year: 2003 ident: 10.1016/j.jprocont.2016.05.001_bib0025 article-title: Metabolic engineering for the microbial production of 1,3-propanediol publication-title: Curr. Opin. Biotechnol. doi: 10.1016/j.copbio.2003.08.005 – year: 2014 ident: 10.1016/j.jprocont.2016.05.001_bib0125 article-title: Optimal control of a nonlinear time-delay system in batch fermentation process publication-title: Math. Probl. Eng. – volume: 232 start-page: 150 year: 2014 ident: 10.1016/j.jprocont.2016.05.001_bib0065 article-title: Robust identification of enzymatic nonlinear dynamical systems for 1,3-propanediol transport mechanisms in microbial batch culture publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2014.01.027 – year: 1997 ident: 10.1016/j.jprocont.2016.05.001_bib0160 – volume: 62 start-page: 791 year: 2015 ident: 10.1016/j.jprocont.2016.05.001_bib0090 article-title: Parameter identification for a nonlinear enzyme-catalytic dynamic system with time-delays publication-title: J. Glob. Optim. doi: 10.1007/s10898-014-0245-4 – volume: 10 start-page: 275 issue: 1 year: 2014 ident: 10.1016/j.jprocont.2016.05.001_bib0150 article-title: The control parameterization method for nonlinear optimal control: a survey publication-title: J. Ind. Manag. Optim. doi: 10.3934/jimo.2014.10.275 – volume: 5 start-page: 381 issue: 4 year: 2015 ident: 10.1016/j.jprocont.2016.05.001_bib0105 article-title: A stochastic model for microbial fermentation process under Gaussian white noise environment publication-title: Numer. Algebra Control Optim. doi: 10.3934/naco.2015.5.381 – volume: 217 start-page: 6566 year: 2011 ident: 10.1016/j.jprocont.2016.05.001_bib0140 article-title: Robust suboptimal control of nonlinear systems publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2011.01.039 – volume: 9 start-page: 471 issue: 2 year: 2013 ident: 10.1016/j.jprocont.2016.05.001_bib0180 article-title: A unified parameter identification method for nonlinear time-delay systems publication-title: J. Ind. Manag. Optim. doi: 10.3934/jimo.2013.9.471 – start-page: 239 year: 2002 ident: 10.1016/j.jprocont.2016.05.001_bib0015 article-title: Bulk chemicals from biotechnology: the case of 1,3-propanediol production and the new trends – volume: 37 start-page: 6899 year: 2013 ident: 10.1016/j.jprocont.2016.05.001_bib0120 article-title: Modelling and parameter identification for a nonlinear time-delay system in microbial batch fermentation publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2013.02.021 – volume: 74 start-page: 239 year: 2002 ident: 10.1016/j.jprocont.2016.05.001_bib0030 article-title: Bulk chemicals from biotechnology: the case of 1,3-propanediol production and the new trends publication-title: Adv. Biochem. Eng. Biotechnol. – volume: 54 start-page: 241 issue: 2 year: 1987 ident: 10.1016/j.jprocont.2016.05.001_bib0165 article-title: A class of filled functions for finding global minimizers of a function of several variables publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00939433 – volume: 15 start-page: 112 year: 2015 ident: 10.1016/j.jprocont.2016.05.001_bib0095 article-title: Pathway identification using parallel optimization for a nonlinear hybrid system in batch culture publication-title: Nonlinear Anal. Hybrid Syst. doi: 10.1016/j.nahs.2014.08.004 – volume: 54 start-page: 618 year: 2011 ident: 10.1016/j.jprocont.2016.05.001_bib0100 article-title: Modeling and identification of a nonlinear hybrid dynamical system in batch fermentation of glycerol publication-title: Math. Comput. Model. doi: 10.1016/j.mcm.2011.03.005 – volume: 20 start-page: 82 issue: 2 year: 1997 ident: 10.1016/j.jprocont.2016.05.001_bib0035 article-title: High concentration and productivity of 1,3-propanediol from continuous fermentation of glycerol by Klebsiella pneumoniae publication-title: Enzyme Microb. Technol. doi: 10.1016/S0141-0229(96)00087-7 – volume: 46 start-page: 314 issue: 4 year: 1995 ident: 10.1016/j.jprocont.2016.05.001_bib0060 article-title: A kinetic model for product formation of microbial and mammalian cells publication-title: Biotechnol. Bioeng. doi: 10.1002/bit.260460404 – volume: 50 start-page: 24 issue: 1 year: 1998 ident: 10.1016/j.jprocont.2016.05.001_bib0010 article-title: Fermentation of glycerol to 1,3-propanediol and 2,3-butanediol by Klebsiella pneumoniae publication-title: Appl. Microbiol. Biotechnol. doi: 10.1007/s002530051251 – volume: 34 start-page: 957 year: 2015 ident: 10.1016/j.jprocont.2016.05.001_bib0085 article-title: Identification and robustness analysis of nonlinear multi-stage enzyme-catalytic dynamical system in batch culture publication-title: Comput. Appl. Math. doi: 10.1007/s40314-014-0160-9 – volume: 36 start-page: 433 issue: 4 year: 2013 ident: 10.1016/j.jprocont.2016.05.001_bib0040 article-title: Determining the transport mechanism of an enzyme-catalytic complex metabolic network based on biological robustness publication-title: Bioprocess Biosyst. Eng. doi: 10.1007/s00449-012-0800-7 – volume: 169 start-page: 876 issue: 3 year: 2016 ident: 10.1016/j.jprocont.2016.05.001_bib0185 article-title: A hybrid time-scaling transformation for time-delay optimal control problems publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-015-0783-z – volume: 218 start-page: 1180 year: 2011 ident: 10.1016/j.jprocont.2016.05.001_bib0135 article-title: A numerical method for an optimal control problem with minimum sensitivity on coefficient variation publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2011.05.093 – volume: 19 start-page: 2088 issue: 16 year: 2014 ident: 10.1016/j.jprocont.2016.05.001_bib0070 article-title: Modelling and pathway identification involving the transport mechanism of a complex metabolic system in batch culture publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2013.10.021 – volume: 268 start-page: 685 year: 2015 ident: 10.1016/j.jprocont.2016.05.001_bib0170 article-title: A new filled function method for global optimization publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2015.06.090 |
| SSID | ssj0003726 |
| Score | 2.2551723 |
| Snippet | •An control problem is proposed to maximize the productivity of 1,3-PD.•The problem with free terminal time is transformed via a hybrid time-scaling... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 41 |
| SubjectTerms | Batch fermentation Cost sensitivity constraint Free terminal time Nonlinear time-delay system Optimal control Parallel optimization |
| Title | Optimal control of a batch fermentation process with nonlinear time-delay and free terminal time and cost sensitivity constraint |
| URI | https://dx.doi.org/10.1016/j.jprocont.2016.05.001 |
| Volume | 44 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwED5VZYGBRwFRHpUH1vRlx2nHqqIqIMoAlbpFtmOLViWt2jCwIH46PseBIoYObHn4FMt27s7Wd98HcG0zEINE34ESwm5QNKdBRzIaGKWboZC8rdx5x8OID8fsbhJOStAvamEQVul9f-7Tnbf2Txp-NBvL6bTxhCdYNvpgRuGIwbGCnUW4yusfPzAPGjnJNXfcha03qoRn9RlGiUWKmMoWdwyeXhzmT4DaCDqDQ9j32SLp5R06gpJOK3BQKDEQ_2NWYG-DVvAYPh-tH3i1dh6HThaGCCKt030hxnpiX26UkmVeJUDwMJakOWmGWBHUmw-QPfKdiDQhZqU18aCZuXvpHqvFOiNrxL_nAhT4tbVTnMhOYDy4ee4PA6-0ECjKulmgTGi4vVKJTLgIhc0pbNohaUt3NIsUM01jmKZd1qUiCmVCqTZc6LZtGnFNOT2Fsu2lPgOCQuGyI1VCDWNMm46y-10hqU0rItOOVBXCYnhj5WnIsW_zuMCbzeJiWmKclrgZIvCuCo1vu2VOxLHVolvMXvxrScU2WmyxPf-H7QXs4l2OEryEcrZ601c2c8lkzS3NGuz0bu-Hoy_lJfKo |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwED6VdgAGHgXEGw-soaV2nHZEiKrQBwOt1C2yHVtQQVq1YWDjp-NznKqIoQNbZOcUy3buzqfP3wdwbTMQg0TfgRLCHlA0p0FTMhoYpeuhkLyhXL2jP-CdEXsah-MS3Bd3YRBW6X1_7tOdt_YtNT-btdnbW-0FK1g2-mBG4YjBN6CC7FRhGSp3j93OYOmQaeRU11zFCw1WLgpPbiYYKKYpwipvuSPx9Powf2LUStxp78GOTxjJXT6mfSjptAq7hRgD8f9mFbZXmAUP4PvZuoIPa-eh6GRqiCDS-t1XYqwz9jeOUjLLLwoQrMeSNOfNEHOCkvMBEkh-EZEmxMy1Jh438-46XbOaLjKyQAh8rkGBX1s40YnsEEbth-F9J_BiC4GirJUFyoSG2yeVyISLUNi0wmYekt7qpmaRYqZuDNO0xVpURKFMKNWGC92wr0ZcU06PoGxHqY-BoFa4bEqVUMMY06ap7JFXSGozi8g0InUCYTG9sfJM5Di297iAnE3iYlliXJa4HiL27gRqS7tZzsWx1qJVrF78a1fFNmCssT39h-0VbHaG_V7cexx0z2ALe3LQ4DmUs_mnvrCJTCYv_Ub9ASqB9Vk |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Optimal+control+of+a+batch+fermentation+process+with+nonlinear+time-delay+and+free+terminal+time+and+cost+sensitivity+constraint&rft.jtitle=Journal+of+process+control&rft.au=Yuan%2C+Jinlong&rft.au=Liu%2C+Chongyang&rft.au=Zhang%2C+Xu&rft.au=Xie%2C+Jun&rft.date=2016-08-01&rft.issn=0959-1524&rft.volume=44&rft.spage=41&rft.epage=52&rft_id=info:doi/10.1016%2Fj.jprocont.2016.05.001&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_jprocont_2016_05_001 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0959-1524&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0959-1524&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0959-1524&client=summon |