Nonlinear dynamical systems of fed-batch fermentation and their optimal control

References

• Ahmed , AU . 1974 . Existence of Optimal Controls with Frequency Constraints in the Absence of Convexity . International Journal of Systems Science , 5 : 1165 – 1178 .
   Web of Science ®Google Scholar
• Arrowsmith , DK and Place , CM . 1982 . Ordinary Differential Equations , London : Chapman and Hall .
   Google Scholar
• Bengea , SC and DeCarlo , RA . 2005 . Optimal Control of Switching Systems . Automatica , 41 : 11 – 27 .
   Web of Science ®Google Scholar
• Cesari , L . 1983 . Optimization-theory and Applications , New York : Springer-Verlag .
   Google Scholar
• Chen , X , Zhang , DJ , Qi , WT , Gao , SJ , Xiu , ZL and Xu , P . 2003 . Microbial Fed-batch Production of 1,3-propanediol by Klebsiella Pneumoniae under Microaerobic Conditions . Applied Microbiology and Biotechnology , 63 : 143 – 146 .
   PubMed Web of Science ®Google Scholar
• Gao , CX , Feng , EM , Wang , ZT and Xiu , ZL . 2005 . Nonlinear Dynamical Systems of Bio-dissimilation of Glycerol to 1,3-propanediol and Their Optimal Controls . Journal of Industrial and Management Optimization , 3 : 377 – 388 .
   Google Scholar
• Gao , CX , Li , KZ , Feng , EM and Xiu , ZL . 2006 . Nonlinear Impulsive System of Fed-batch Culture in Fermentative Production and its Properties . Chaos Solitions & Fractals , 28 : 271 – 277 .
   Web of Science ®Google Scholar
• Gong , ZH . 2010 . A Multistage System of Microbial Fed-batch Fermentation and its Parameter Identification . Mathematics and Computers in Simulation , 80 : 1903 – 1910 .
   Web of Science ®Google Scholar
• Gonzaga , G , Polak , E and Trahan , R . 1980 . An Improved Algorithm for Optimization Problems with Functional Inequality Constraints . IEEE Transactions on Automatic Control , AC-25 : 49 – 54 .
   Web of Science ®Google Scholar
• Gorbunov , VK and Lutoshkin , IV . 2004 . Development and Experience of using the Parameterization Method in Singular Problems of Dynamic Optimization . Journal of Computer and Systems Sciences International , 43 : 725 – 742 .
   Web of Science ®Google Scholar
• Ferreira , MMA . 2006 . On the Regularity of Optimal Controls for a Class of Problems with State Constraints . International Journal of Systems Science , 37 : 495 – 502 .
   Web of Science ®Google Scholar
• Homann , T , Tag , C , Biebl , H , Deckwer , WD and Schink , B . 1990 . Fermentation of Glycerol to 1,3-propanediol by Klebsiella and Citrobacter Strains . Applied Microbiology and Biotechnology , 33 : 121 – 126 .
   Web of Science ®Google Scholar
• Jennings , LS and Teo , KL . 1990 . A Computational Algorithm for Functional Inequality Constrained Optimization Problems . Automatica , 26 : 371 – 375 .
   Web of Science ®Google Scholar
• Liu , CY . 2009 . Optimal Control for Nonlinear Dynamical System of Microbial Fed-batch Culture . Journal of Computational and Applied Mathematics , 232 : 252 – 261 .
   Web of Science ®Google Scholar
• Liu , CY . and Feng, E.M. (2010), ‘Optimal Control of Switched Autonomous Systems in Microbial Fed-batch Cultures’, International Journal of Computer Mathematics (in press)
   Google Scholar
• Liu , CY , Feng , EM and Yin , HC . 2008 . Optimal Switching Control for Microbial Fed-batch Culture . Nonlinear Analysis: Hybrid Systems , 2 : 1168 – 1174 .
   Google Scholar
• Liu , CY , Gong , ZH , Feng , EM and Yin , HC . 2009 . Modelling and Optimal Control for Nonlinear Multistage Dynamical System of Microbial Fed-batch Culture . Journal of Industrial and Management Optimization , 5 : 835 – 850 .
   Web of Science ®Google Scholar
• Menzel , K , Zeng , AP and Deckwer , WD . 1997 . High Concentration and Productivity of 1,3-propanediol from Continuous Fermentation of Glycerol by Klebsiella Pneumoniae . Enzyme Microbial Technology , 20 : 82 – 86 .
   Web of Science ®Google Scholar
• Nocedal , J and Wright , SJ . 1999 . Numerical Optimization , New York : Springer-Verlag .
   Google Scholar
• Paschedag , T , Giua , A and Seatzu , C . 2010 . Constrained Optimal Control: an Application to Semiactive Suspension Systems . International Journal of Systems Science , 41 : 797 – 811 .
   Web of Science ®Google Scholar
• Polak , E and Myne , DQ . 1976 . An Algorithm for Optimization Problems with Functional Inequality Constraints . IEEE Transactions on Automatic Control , AC-21 : 184 – 193 .
   Web of Science ®Google Scholar
• Polak , E and Wardi , Y . 1982 . Nondifferentiable Optimization Algorithm for Designing Control Systems Having Singular Value Inequalities . Automatica , 18 : 267 – 283 .
   Web of Science ®Google Scholar
• Sakawaa , M and Sawaragi , Y . 1975 . State-space Constrained Optimal Control Problems with Control Variables Appearing Linearly . International Journal of Systems Science , 6 : 1185 – 1194 .
   Web of Science ®Google Scholar
• Seatze , C , Corona , D , Giua , A and Bemporad , A . 2006 . Optimal Control of Continuous-time Switched Affine Systems . IEEE Transactions on Automatic Control , 51 : 726 – 741 .
   Web of Science ®Google Scholar
• Teo , KL , Rehbock , V and Jennings , LS . 1993 . A New Computational Algorithm for Functional Inequality Constrained Optimization Problems . Automatica , 29 : 789 – 792 .
   Web of Science ®Google Scholar
• Wang , G , Feng , EM and Xiu , ZL . 2008a . Modeling and Parameter Identification of Microbial Biconversion in Fed-batch Cultures . Journal of Process Control , 18 : 458 – 464 .
   Web of Science ®Google Scholar
• Wang , HY , Feng , EM and Xiu , ZL . 2008b . Optimality Condition of the Nonlinear Impulsive System in Fed-batch Fermentation . Nonlinear Analysis: Real World Applications , 68 : 12 – 23 .
   Web of Science ®Google Scholar
• Warschat , J and Wunderlich , HJ . 1994 . Time-optimal Control Policies for Cascaded Production-inventory Systems with Control and State Constraints . International Journal of Systems Science , 15 : 513 – 524 .
   Google Scholar
• Xiu , ZL , Zeng , AP and An , LJ . 2000 . Mathematical Modelling of Kinetics and Research on Multiplicity of Glycerol Bioconversion to 1,3-propanediol . Journal of Dalian University of Technology , 4 : 428 – 433 .
   Google Scholar
• Xu , X and Antasaklis , PJ . 2004 . Optimal Control of Switched Systems Based on Parameterization of the Switching Instants . IEEE Transactions on Automatic Control , 49 : 2 – 16 .
   Web of Science ®Google Scholar
• Zeng , AP . 1996 . Pathway and Kinetic Analysis of 1,3-propanediol Production from Glycerol Fermentation by Clostridium Butyricum . Bioprocess Engineering , 14 : 169 – 175 .
   Google Scholar
• Zeng , AP and Biebl , H . 2002 . Bulk-chemicals from Biotechnology: the Case of Microbial Production of 1,3-propanediol and the New Trends . Advances in Biochemical Engineering/Biotechnology , 74 : 239 – 259 .
   PubMedGoogle Scholar
• Zeng , AP , Rose , A , Biebl , H , Tag , C , Guenzel , B and Deckwer , WD . 1994 . Multiple Product Inhibition and Growth Modeling of Clostridium Butyricum and Klebsiella Pneumoniae in Glycerol Fermentation . Biotechnology and Bioengineering , 44 : 902 – 911 .
   PubMed Web of Science ®Google Scholar