Sensitivity analysis and parameter identification for a nonlinear time-delay system in microbial fed-batch process

Applied Mathematical Modelling

Volumn 38, Issue 4, 2014, Pages 1449-1463

  Liu, Chongyang ^a  

^a SHANDONG INSTITUTE OF BUSINESS AND TECHNOLOGY   (China)

Author keywords

Fed batch fermentation; Nonlinear time delay system; Optimization algorithm; Parameter identification; Sensitivity analysis

Indexed keywords

FED-BATCH FERMENTATION; GLOBAL OPTIMIZATION METHOD; GLYCEROL BIOCONVERSIONS; MICROBIAL METABOLISM; NONLINEAR TIME-DELAY SYSTEMS; OPTIMIZATION ALGORITHMS; PARAMETER IDENTIFICATION MODEL; PARAMETRIC SENSITIVITY ANALYSIS;

ALGORITHMS; BATCH DATA PROCESSING; DELAY CONTROL SYSTEMS; FERMENTATION; GLOBAL OPTIMIZATION; IDENTIFICATION (CONTROL SYSTEMS); OPTIMIZATION; PROCESS CONTROL; SENSITIVITY ANALYSIS;

TIME DELAY;

EID: 84893766610     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2013.07.039     Document Type: Article

References (45)

1. Baker C.T.H., Bocharov G.A., Paul C.A.H., Rihan F.A. Modelling and analysis of time-lags in some basic patterns of cell proliferation. J. Math. Biol. 1998, 37:341-371.
2. Richard J.P. Time-delay systems: an overview of some recent advances and open problems. Automatica 2003, 39:1667-1694.
3. S.M. Verduyn-Lunel, Identification problems in functional differential equations, in: Proceedings of the 36th IEEE Conference on Decision and Control, San Diego, CA, Dec. 1997, pp. 4409-4413.
4. Banks H.T., Lamm P.K.D. Estimation of delays and other parameters in nonlinear functional differential equations. SIAM J. Control Optim. 1983, 21:895-915.
5. Gawthrop P.J., Nihtila M.T. Identification of time-delays using polynomial identification method. Syst. Control Lett. 1985, 5:267-271.
6. Murphy K.A. Estimation of time-dependent and state-dependent delays and other parameters in functional-differential equations. SIAM J. Appl. Math. 1990, 50:972-1000.
7. C.T.H. Baker, G.A. Bocharov, F.A. Rihan, A report on the use of delay differential equations in numerical modelling in the biosciences, MCCM Tech. Rep., vol. 343, 1999, Manchester, ISSN 1936-1725.
8. Biebl H., Memzel K., Zeng A.P. Microbial production of 1,3-propanediol. Appl. Microbiol. Biotechnol. 1999, 52:289-297.
9. Menzel K., Zeng A.P., Deckwer W.D. High concentration and productivity of 1,3-propanediol from continuous fermentation of glycerol by Klebsiella pneumoniae. Enzym. Microbiol. Technol. 1997, 20:82-86.
10. Zeng A.P., Biebl H. Bulk-chemicals from biotechnology: the case of microbial production of 1,3-propanediol and the new trends. Adv. Biochem. Eng. Biotechnol. 2002, 74:239-259.
11. Liu C.Y., Gong Z.H., Feng E.M., Yin H.C. Modelling and optimal control for nonlinear multistage dynamical system of microbial fed-batch culture. J. Ind. Manage. Optim. 2009, 5:835-850.
12. Xiu Z.L., Song B.H., Wang Z.T., Sun L.H., Feng E.M., Zeng A.P. Optimization of biodissimilation of glycerol to 1,3-propanediol by Klebsiella pneumoniae in one-stage and two-stage anaerobic cultures. Biochem. Eng. J. 2004, 19:189-197.
13. Xiu Z.L., Zeng A.P., An L.J. Mathematical modelling of kinetics and research on multiplicity of glyceroll bioconversion to 1,3-propanediol. J. Dalian Univ. Technol. 2000, 4:428-433.
14. Menzel K., Zeng A.P., Biebl H., Deckwer W.D. Kinetic, dynamic, and pathway studies of glycerol metabolism by Klebsiella pneumoniae in anaerobic continuous culture: I. the phenomena and characterization of oscillation and hysteresis. Biotechnol. Bioeng. 1996, 52:549-560.
15. Xiu Z.L., Song B.H., Sun L.H., Zeng A.P. Theoretical analysis of effects of metabolic overflow and time delay on the performance and dynamic behavior of a two-stage fermentation process. Biochem. Eng. J. 2002, 11:101-109.
16. MacDonald N. Time-lags in biological models. Lect. Notes in Biomath. 1979, vol. 27. Springer, Berlin.
17. an der Heiden U. Delays in physiological systems. J. Math. Biol. 1979, 8:345-364.
18. Chen C.T., Hwang C. Optimal control computation for differential-algebraic process systems with general constraints. Chem. Eng. Commun. 1990, 97:9-26.
19. Luus R. Application of dynamic programming to differential-algebraic process systems. Comput. Chem. Eng. 1993, 17:373-377.
20. Oberle H.J., Sothmann B. Numerical computation of optimal feed rates for a fed-batch fermentation model. J. Optim. Theory Appl. 1999, 100:1-13.
21. Shin H.S., Lim H.C. Optimization of metabolite production in fed-batch cultures: use of sufficiency and characteristics of singular arc and properties of adjoint vector in numerical computation. Ind. Eng. Chem. Res. 2007, 46:2526-2534.
22. Gao C.X., Feng E.M., Wang Z.T., Xiu Z.L. Nonlinear dynamical systems of bio-dissimilation of glycerol to 1,3-propanediol and their optimal controls. J. Ind. Manage. Optim. 2005, 3:377-388.
23. Gao C.X., Li K.Z., Feng E.M., Xiu Z.L. Nonlinear impulsive system of fed-batch culture in fermentative production and its properties. Chaos Solution Fract. 2006, 28:271-277.
24. Wang G., Feng E.M., Xiu Z.L. Modelling and parameter identification of microbial biconversion in fed-batch cultures. J. Process Control 2008, 18:458-464.
25. Liu C.Y. Optimal control for nonlinear dynamical system of microbial fed-batch cultures. J. Comput. Appl. Math. 2009, 232:252-261.
26. Liu C.Y., Gong Z.H., Shen B.Y., Feng E.M. Modelling and optimal control for a fed-batch process. Appl. Math. Model. 2013, 37:695-706.
27. Gong Z.H. A multistage system of microbial fed-batch fermentation and its parameter identification. Math. Comput. Simul. 2010, 80:1903-1910.
28. Liu C.Y. Modelling and parameter identification for a nonlinear time-delay system in microbial batch fermentation. Appl. Math. Model. 2013, 37:6899-6908.
29. Eslami M. Theory of Sensitivity in Dynamic Systems 1994, Springer-Verlag, New York.
30. O'Sullivan F. Sensitivity analysis for regularized estimation in some system identification problems. SIAM J. Sci. Stat. Comput. 1991, 12:1266-1283.
31. Azema P., Durante C., Roubellat F., Sevely Y. Study of the sensitivity of systems to time-delay variations. Electron. Lett. 1967, 3:171-172.
32. Banks H.T., Bortz D.M. A parameter sensitivity methodology in the context of HIV delay equation models. J. Math. Biol. 2005, 50:607-625.
33. Koda M. Sensitivity analysis of time-delay systems. Int. J. Syst. Sci. 1981, 12:1389-1397.
34. Rihan F.A. Sensitivity analysis for dynamic systems with time-lags. J. Comput. Appl. Math. 2003, 151:445-462.
35. Liu C.Y., Feng E.M., Yin H.C. Optimal switching control for microbial fed-batch culture. Nonlinear Anal. 2008, 2:1168-1174.
36. Hale J.K., Verduyn Lunel S.M. Introduction to Functional Differential Equations 1993, Springer, Berlin.
37. Shampine L.F., Thompson S. Solving DDEs in matlab. Appl. Numer. Math. 2001, 37:441-458.
38. Stoer J., Bulirsch R. Introduction to Numerical Analysis 1980, Springer-Verlag, New York.
39. Teo K.L., Goh C.J., Wong K.H. A Unified Computational Approach to Optimal Control Problems 1991, Long Scientific Technical, Essex.
40. Mendes P., Kell D.B. Nonlinear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation. Bioinformatics 1998, 14:869-883.
41. Moles C.G., Mendes P., Banga J.R. Parameter estimation in biochemical pathways: a comparison of global optimization methods. Genome Res. 2003, 13:2467-2474.
42. J. Kennedy, R.C. Eberhart, Particle swarm optimization, in: Proceedings of the 1995 IEEE International Conference on Neural Networks, Perth, Australia, Nov. 1995, pp. 1942-1948.
43. C.A. Coello Coello, A survey of constraint handling techniques used with evolutionary algorithms, Technical Report Lania-RI-99-04, Laboratorio Nacional de Informática Avanzada Xalapa, Veracruz, México, 1999.
44. Michalewicz Z. A survey of constraint handling techniques in evolutionary computation methods. Proceedings of the 4th Annual Conference on Evolutionary Programming 1995, 135-155. MIT Press, Cambridge, MA.
45. Mu Y., Xiu Z.L., Zhang D.J. A combined bioprocess of biodiesel production by lipase with microbial production of 1,3-propanediol by Klebsiella pneumoniae. Biochem. Eng. J. 2008, 40:537-541.