84
Views
8
CrossRef citations to date
0
Altmetric
Section B

Optimal control of switched autonomous systems in microbial fed-batch cultures

&
Pages 396-407 | Received 23 Apr 2009, Accepted 25 Oct 2009, Published online: 26 Nov 2010

References

  • Arrowsmith , D. K. and Place , C. M. 1982 . Ordinary Differential Equations , London : Chapman and Hall .
  • Bengea , S. C. and DeCarlo , R. A. 2005 . Optimal control of switching systems . Automatica , 41 : 11 – 27 .
  • Bibel , H. , Memzel , K. and Zeng , A. P. 1999 . Microbial production of 1,3-propanediol . Appl. Microbiol. Biotechnol. , 52 : 289 – 297 .
  • Chen , X. , Zhang , D. J. , Qi , W. T. , Gao , S. J. , Xiu , Z. L. and Xu , P. 2003 . Microbial fed-batch production of 1,3-propanediol by Klebsiella pneumoniae under microaerobic conditions . Appl. Microbiol. Biotechnol. , 63 : 143 – 146 .
  • Egerstedt , M. , Wardi , Y. and Delmotte , F. Proceding of the 42nd IEEE CDC . Maui, Hawaii, USA. Optimal control of switching times in switched dynamical systems ,
  • Gao , C. X. , Feng , E. M. , Wang , Z. T. and Xiu , Z. L. 2005 . Nonlinear dynamical systems of bio-dissimilation of glycerol to 1,3-propanediol and their optimal controls . J. Ind. Manage. Optim. , 3 : 377 – 388 .
  • Gao , C. X. , Li , K. Z. , Feng , E. M. and Xiu , Z. L. 2006 . Nonlinear impulsive system of fed-batch culture in fermentative production and its properties . Chaos Solut. Fractals. , 28 : 271 – 277 .
  • Gao , C. X. , Wang , Z. T. , Feng , E. M. and Xiu , Z. L. 2006 . Parameter identification and optimization of process for bio-dissimilation of glycerol to 1,3-propanediol in batch culture . J. Dalian Univ. Technol. , 46 : 771 – 774 .
  • Gill , P. E. and Murray , W. 1974 . Newton-type methods for unconstrained and linearly constrained optimization . Math. Program. , 7 : 311 – 350 .
  • Giua , A. , Seatze , C. and Van Der Mee , C. Optimal control of autonomous linear systems switched with a preassigned finite sequence . Procedings of the 2001 IEEE ISIC . México City, México.
  • Giua , A. , Seatze , C. and Van Der Mee , C. Optimal control of autonomous linear systems . Procedings of the 40th IEEE CDC . Orlando, FL, USA.
  • Lenhart , S. M. , Seidman , T. I. and Yong , J. M. 2001 . Optimal control of a bioreactor with modal switching . Math. Models. Methods. Appl. Sci. , 6 : 933 – 949 .
  • Liu , C. Y. 2009 . Optimal control for nonlinear dynamical system of microbial fed-batch cultures . J. Comput. and Appl. Math. , 232 : 252 – 261 .
  • Liu , C. Y. , Feng , E. M. and Yin , H. C. 2008 . Optimal switching control for microbial fed-batch culture . Nonlinear Anal. Hybrid Syst. , 2 : 1168 – 1174 .
  • Liu , C. Y. , Gong , Z. H. , Feng , E. M. and Yin , H. C. 2009 . Modelling and optimal control for nonlinear multistage dynamical system of microbial fed-batch culture . J. Ind. Manage Optim. , 5 : 835 – 850 .
  • Menzel , K. , Zeng , A. P. and Deckwer , W. D. 1997 . High concentration and productivity of 1,3-propanediol from continuous fermentation of glycerol by Klebsiella pneumoniae . Enzyme Microb. Technol. , 20 : 82 – 86 .
  • Seatzu , C. , Corona , D. , Giua , A. and Bemporad , A. 2006 . Optimal conrol of continous-time switched affine systems . IEEE Trans. Autom. Control , 51 : 726 – 741 .
  • T.I. Seidman, Switching systems: Thermostats and periodicity, MRR 83–07, UMBC, 1983
  • Seidman , T. I. 1987 . Optimal control for switching systems Baltimore, , MD, USA Proc. 21st Ann. Conf. on Inf. Sci. and Syst
  • Spinelli , W. , Bolzern , P. and Colaneri , P. A note on optimal control of autonomous switched systems on a finite time interval . Procedings of the 2006 ACC . Minneapolis, MN, USA.
  • Teo , K. L. , Rehbock , V. and Jennings , L. S. 1993 . A new computational algorithm for functional inequality constrained optimization problems . Automatica , 29 : 789 – 792 .
  • Wang , L. Y. , Beydoun , A. , Cook , J. , Sun , J. and Kolmanovsky , I. 1997 . “ Optimal hybrid control with applications to automotive powertrain systems ” . In Control Using Logic-based Switching , Edited by: Stephen Morse , A. 190 – 200 . London : Springer-Verlag .
  • Wang , G. , Feng , E. M. and Xiu , Z. L. 2008 . Modelling and parameter identification of microbial biconversion in fed-batch cultures . J. Process Control , 18 : 458 – 464 .
  • Wang , H. Y. , Feng , E. M. and Xiu , Z. L. 2008 . Optimality condition of the nonlinear impulsive system in fed-batch fermentation . Nonlinear Anal. Real World Appl. , 68 : 12 – 23 .
  • Xiu , Z. L. , Zeng , A. P. and An , L. J. 2000 . Mathematical modelling of kinetics and research on multiplicity of glyceroll bioconversion to 1,3-propanediol . J. Dalian Univ. Technol. , 4 : 428 – 433 .
  • Xu , X. and Antsaklis , P. J. Optimal control of switched autonomous systems . Procedings of the 41st IEEE CDC . Las Vegas, NV, USA.
  • Xu , X. and Antsaklis , P. J. 2004 . Optimal control of switched systems based on parameterization of the switching instants . IEEE Trans. Autom. Control , 49 : 2 – 16 .
  • Zeng , A. P. 1996 . Pathway and kinetic analysis of 1,3-propanediol production from glycerol fermentation by Clostridium butyricum . Bioprocess Eng. , 14 : 169 – 175 .
  • Zeng , A. P. and Biebl , H. 2002 . Bulk-chemicals from biotechnology: The case of microbial production of 1,3-propanediol and the new trends . Adv. Biochem. Eng. Biotechnol. , 74 : 239 – 259 .
  • Zeng , A. P. , Rose , A. , Biebl , H. , Tag , C. , Guenzel , B. and Deckwer , W. D. 1994 . Multiple product inhibition and growth modeling of Clostridium butyricum and Klebsiella pneumoniae in glycerol fermentation . Biotechnol. Bioeng. , 44 : 902 – 911 .
  • Zhang , L. , Chen , Y. and Cui , P. 2005 . Stabilization for a class of second-order switched systems . Nonlinear Anal. , 62 : 1527 – 1535 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.