Singular perturbation based solution to optimal microalgal growth problem and its infinite time horizon analysis

IEEE Transactions on Automatic Control

Volumn 55, Issue 3, 2010, Pages 767-772

  Celikovsky, Sergej ^a   Papacek, Â Štěpán ^b   Cervantes Herrera, Alejandro ^c   Ruiz León, Javier ^c  

^a INSTITUTE OF INFORMATION THEORY AND AUTOMATION   (Czech Republic)

^b UNIVERSITY OF SOUTH BOHEMIA   (Czech Republic)

^c DEPARTAMENTO DE FÍSICA   (Mexico)

Author keywords

Photosynthetic factory (PSF)

Indexed keywords

ANALYTICAL SOLUTIONS; INFINITE HORIZONS; INFINITE TIME HORIZON; MICRO-ALGAE; MICROALGAL GROWTH; OPTIMAL CONTROL PROBLEM; OPTIMAL SOLUTIONS; OPTIMAL STEADY STATE; PHOTOSYNTHETIC PRODUCTION; SINGULAR PERTURBATIONS; SPECIFIC GROWTH RATE; TIME INTERVAL;

OPTICAL TRANSFER FUNCTION;

OPTIMIZATION;

EID: 77949424085     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2040498     Document Type: Article

References (17)

1. S. Čelikovský, "On the continuous dependence of trajectories of bilinear systems on controls and its applications," Kybernetika, vol.24, pp. 278-292, 1988.
2. P. H. C. Eilers and J. C. H. Peeters, "A model for the relationship between light intensity and the rate of photosynthesis in phytoplankton," Ecol. Model., vol.42, pp. 199-215, 1988.
3. P. H. C. Eilers and J. C. H. Peeters, "Dynamic behaviour of a model for photosynthesis and photoinhibition," Ecol. Model., vol.69, pp. 113-133, 1993.
4. M. Janssen, P. Slenders, J. Tramper, L. R. Mur, and R. H. Wijffels, "Photosynthetic efficiency of Dunaliella tertiolecta under short light/ dark cycles," Enzyme Microb. Technol., vol.29, pp. 298-305, 2001.
5. T. Kmet', M. Strǎskraba, and P. Mauersberger, "A mechanistic model of the adaptation of phytoplankton photosynthesis," Bull. Math. Biol., vol.55, pp. 259-275, 1993.
6. H. K. Khalil, "Stability analysis of singularly perturbed systems," in Singular Perturbations and Asymptotic Analysis in Control Systems. Berlin, Germany: Springer, 1987.
7. J. Masojídek, S. Papá̌cek, V. Jirka, J. Červený, J. Kunc, J. Korěcko, M. Sergejevová, O. Verbovikova, J. Kopecký, D. Štys, and G. Torzillo, "A closed solar photobioreactor for cultivation of microalgae under suprahigh irradiances: Basic design and performance of pilot plant," J. Appl. Phycol., vol.15, pp. 239-248, 2003.
8. L. Nedbal, V. Tichý, F. Xiong, and J. U. Grobbelaar, "Microscopic green algae and cyanobacteria in high-frequency intermittent light," J. Appl. Phycol., vol.8, pp. 325-333, 1996.
9. Š. Papáček, S. Čelikovský, D. Štys, and J. Ruiz-León, "Bilinear system as modelling framework for analysis of microalgal growth," Kybernetika vol. 43, pp. 1-20, 2007.
10. S. Papáček, S. Č elikovský, and J. Ruiz-León, "Optimal feedback control of microalgal growth based on the slow reduction," in Proc. IFAC World Congress, Seoul, Korea, Jul. 2008, pp. 14588-14593.
11. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mischenko, The Mathematical Theory of Optimal Processes. New York: Wiley, 1962.
12. B. Rehák, S. Čelikovský, and Š. Papáček, "Model for photosynthesis and photoinhibition: Parameter identification based on the harmonic irradiation response measurement," Joint Spec. Issue Syst. Biol., IEEE Trans. Circuits Syst. I & IEEE Trans. Autom. Control, vol.54, no. 1, pp. 101-108, Jan. 2008.
13. R. Rosello Sastre, Z. Csögör, I. Perner-Nochta, P. Fleck-Schneider, and C. Posten, "Scale-down of microalgae cultivations in tubular photo-bioreactors-A conceptual approach," J. Biotechnol., vol.132, pp. 127-133, 2007.
14. K. Schugerl and K.-H. Bellgardt, Bioreaction Engineering, Modeling and Control. Berlin, Germany: Springer-Verlag, 2000.
15. K. L. Terry, "Photosynthesis in modulated light: Quantitative dependence of photosynthetic enhancement on flashing rate," Biotechnol. Bioeng., vol.28, pp. 988-995, 1986.
16. A. Vigodner, "Limits of singularly perturbed control problems with statistical dynamics of fast motions," SIAM J. Control Optim, vol.35, pp. 1-27, 1997.
17. X.Wu and J. C. Merchuk, "A model integrating fluid dynamics in photosynthesis and photoinhibition processes," Chem. Eng. Sci., vol.56, pp. 3527-3538, 2001.