Structural identifiability of the yield coefficients in bioprocess models when the reaction rates are unknown. (English) Zbl 0839.92010
Summary: The identification problem of bioprocesses in a stirred tank reactor essentially concerns the determination of the yield coefficients and the reaction rates involved in a general state-space model. This paper deals with the analysis of structural identifiability of the yield coefficients issuing from a two-step identification procedure. In fact, the identification of the yield coefficients can be completely decoupled from that of the reaction rates by means of an appropriate transformation of the dynamical model. It is shown that the identifiability properties of these coefficients can be drawn from the structure of the underlying reaction network. Necessary and sufficient identifiability conditions are given in the form of some simple algebraic tests.
MSC:
| 92C40 | Biochemistry, molecular biology |
| 93B30 | System identification |
| 93C15 | Control/observation systems governed by ordinary differential equations |
Keywords:
biotechnological reactors; mass balance differential equations; bioprocesses; stirred tank reactor; yield coefficients; reaction rates; general state-space model; structural identifiability; two-step identification procedure; reaction networkReferences:
| [1] | Chen, L.; Bastin, G.; Dochain, D., Structural identifiability of the yield parameters in nonlinear compartmental models for bioprocesses, (29th IEEE Conf. Decision and Control. 29th IEEE Conf. Decision and Control, Honolulu (December 1990)), 1074-1079 |
| [2] | Bonvin, D.; Rippin, D. W.T., Target factor analysis for the identification of stoichiometric models, Chem. Eng. Sci., 49, 3417-3426 (1990) |
| [3] | Chen, L.; Bastin, G., On the model identifiability of stirred tank bioreactors, (Proc. First Eur. Control Conf.. Proc. First Eur. Control Conf., Grenoble, France (July 1991)), 243-247 |
| [4] | Saner, U. M., Modelling and on-line estimation in a batch culture of Bacillus subtilis, (Ph.D. Thesis (1991), Swiss Federal Inst. Technology: Swiss Federal Inst. Technology Zurich, Switzerland) |
| [5] | Chen, L., Modelling, identifiability and control of complex biotechnological systems, (Ph.D. Thesis (1992), CESAME, Louvain Univ: CESAME, Louvain Univ Belgium) |
| [6] | Bastin, G.; Chen, L.; Chotteau, V., Can we identify biotechnological processes?, (Proc. ICCAF-4/IFAC-BIO-2 Symp. Modelling and Control of Biol. Processes. Proc. ICCAF-4/IFAC-BIO-2 Symp. Modelling and Control of Biol. Processes, Keystone, CO (April 1992)), 83-88 |
| [7] | Aris, R.; Mah, R. H.S., Independence of chemical reactions, Ind. Eng. Chem. Fundam., 2, 90-94 (1963) |
| [8] | Vajda, S.; Rabitz, H.; Walter, E.; Lecourtier, Y., Quantitative and qualitative identifiability analysis of nonlinear chemical kinetic models, Chem. Eng. Commun., 83, 191-219 (1989) |
| [9] | Erdi, P.; Toth, J., Mathematical Models of Chemical Reactions: Theory and Application of Deterministic and Stochastic Models (1989), Manchester Univ. Press · Zbl 0696.92027 |
| [10] | Chotteau, V.; Bastin, G., Identification of mathematical models for biotechnological processes: recipe and application to a culture of animal cells, (Proc. 6th Eur. Congr. Biotechnology (1993)), 837-844 |
| [11] | Walter, E., Identifiability of State Space Models, (Lect. Notes Biomath., 46 (1982), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0508.93001 |
| [12] | Vajda, S.; Godfrey, K.; Rabitz, H., Similarity transformation approach to identifiability analysis of nonlinear compartmental models, Math. Biosci., 93, 217-248 (1989) · Zbl 0696.92001 |
| [13] | Glad, S. T.; Ljung, L., Model structure of identifiability and persistence of excitation, (29th IEEE Conf. Decision and Control. 29th IEEE Conf. Decision and Control, Honolulu (December 1990)), 3236-3240 |
| [14] | Chapell, M. J.; Godfrey, K., Structural identifiability of nonlinear systems: application to a batch reactor, identification and system parameter estimation, (9th IFAC/IFORS Symp.. 9th IFAC/IFORS Symp., Budapest, Hungary (July 1991)), 492-497 |
| [15] | (Walter, E., Identifiability of Parametric Models (1987), Pergamon: Pergamon Oxford) · Zbl 0644.00033 |
| [16] | Bastin, G.; Dochain, D., On-Line Estimation and Adaptive Control of Bioreactors (1990), Elsevier: Elsevier New York |
| [17] | Robust, J.; Valero, F.; del Rio, J. L.; Sol, M. C.; Cheruy, A., Mathematical modelling of lipase production by Candida rugosa: calibration and application to continuous start-up, (5th Eur. Congr. Biotechnol.. 5th Eur. Congr. Biotechnol., Copenhagen (July 8-13, 1990)) |
| [18] | Bastin, G.; Bitmead, R. R.; Campion, G.; Gevers, M., Identification of linearly overparametrized nonlinear systems, IEEE Trans. Autom. Control, 37, 7, 1073-1078 (1992) · Zbl 0767.93010 |
| [19] | Dasgupta, S.; Anderson, B. D.O.; Kaye, R. J., Identification of physical parameters in structured systems, Automatica, 24, 217-225 (March 1988) · Zbl 0663.93072 |
| [20] | Grewal, M. S.; Glover, K., Identifiability of linear and nonlinear dynamical systems, IEEE Trans. Autom. Control, 21, 833-837 (December 1976) · Zbl 0344.93022 |
| [21] | Walter, E.; Lecourtier, Y.; Happel, J., On the structural distinguishability of parametric models and its relations with structural identifiability, IEEE Trans. Autom. Control, AC-29, 1, 56-57 (1984) · Zbl 0529.93023 |
| [22] | Feinberg, M., Chemical reaction network structure and the stability of complex isothermal reactors. I. The deficiency zero and deficiency one theorems, Chem. Eng. Sci., 42, 10, 2229-2268 (1987) |
| [23] | Munack, A., Optimal feeding strategy for identification of Monod-type models by fed-batch experiments, (SCI Fourth Int. Congr. Comput. Appl. Fermentation Technol.: Modelling and Control of Biotechnological Processes. SCI Fourth Int. Congr. Comput. Appl. Fermentation Technol.: Modelling and Control of Biotechnological Processes, Univ. Cambridge, U.K. (September 1988)), 25-29 |
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