J. R. Banga, E. B. Canto, C. G. Moles, and A. A. Alonso, Dynamic optimization of bioreactors -a review, Proceedings of the Indian Academy of Sciences

T. T. Lee, F. Y. Wang, and R. B. Newell, Robust multivariable control of complex biological processes, Journal of Process Control, vol.14, issue.2, pp.193-209, 2004.
DOI : 10.1016/S0959-1524(03)00037-4

R. Yamuna and V. S. Ramachandra, Control of fermenters ??? a review, Bioprocess Engineering, vol.21, issue.1, pp.77-88, 1999.
DOI : 10.1007/PL00009066

I. Y. Smets, J. E. Claes, E. J. November, G. P. Bastin, and J. F. Impe, Optimal adaptive control of (bio)chemical reactors: past, present and future, Journal of Process Control, vol.14, issue.7, pp.795-805, 2004.
DOI : 10.1016/j.jprocont.2003.12.005

J. G. Na, Y. Chang, B. Chung, and H. Lim, Adaptive optimization of fed-batch culture of yeast by using genetic algorithms, Bioprocess and Biosystems Engineering, vol.24, issue.5, pp.299-308, 2002.
DOI : 10.1007/s004490100251

S. K. Nguang, L. Chen, and X. D. Chen, Optimisation of fed-batch culture of hybridoma cells using genetic algorithms, ISA Transactions, vol.40, issue.4, pp.381-389, 2001.
DOI : 10.1016/S0019-0578(01)00005-2

M. Ronen, Y. Shabtai, and H. Guterman, Optimization of feeding profile for a fed-batch bioreactor by an evolutionary algorithm, Journal of Biotechnology, vol.97, issue.3, pp.253-263, 2002.
DOI : 10.1016/S0168-1656(02)00106-2

J. A. Roubos, G. Van-straten, and A. J. Van-boxtel, An evolutionary strategy for fed-batch bioreactor optimization; concepts and performance, Journal of Biotechnology, vol.67, issue.2-3, pp.173-187, 1999.
DOI : 10.1016/S0168-1656(98)00174-6

J. Chiou and F. Wang, Hybrid method of evolutionary algorithms for static and dynamic optimization problems with application to a fed-batch fermentation process, Computers & Chemical Engineering, vol.23, issue.9, pp.1277-1291, 1999.
DOI : 10.1016/S0098-1354(99)00290-2

D. Herbert, R. Elsworth, and R. C. Telling, The Continuous Culture of Bacteria; a Theoretical and Experimental Study, Journal of General Microbiology, vol.14, issue.3, pp.601-622, 1956.
DOI : 10.1099/00221287-14-3-601

N. I. Marcos, M. Guay, D. Dochain, and T. Zhang, Adaptive extremum-seeking control of a continuous stirred tank bioreactor with Haldane's Kinetics, Journal of Process Control, vol.14, issue.3, pp.317-328, 2004.
DOI : 10.1016/S0959-1524(03)00070-2

J. Monod, LA TECHNIQUE DE CULTURE CONTINUE TH??ORIE ET APPLICATIONS, Annales de l´Institutl´Institut Pasteur, vol.79, pp.390-410, 1950.
DOI : 10.1016/B978-0-12-460482-7.50023-3

J. Moreno, Optimal time control of bioreactors for the wastewater treatment, Optimal Control Applications and Methods, vol.20, issue.3, pp.145-164, 1999.
DOI : 10.1002/(SICI)1099-1514(199905/06)20:3<145::AID-OCA651>3.0.CO;2-J

G. D. 'ans, P. Kokotovic, and D. Gottlieb, A nonlinear regulator problem for a model of biological waste treatment, IEEE Transactions. Automatic Control, vol.16, pp.341-347, 1971.

P. Gajardo, J. Harmand, H. R. , and A. Rapaport, Minimal time bioremediation of natural water resources, Automatica, vol.47, issue.8, pp.1764-1769, 2011.
DOI : 10.1016/j.automatica.2011.03.001

URL : https://hal.archives-ouvertes.fr/hal-00521118

P. L. Mccarty, Anaerobic waste treatment fundamentals 107-112 Part I, Chemistry and Microbiology Part II, vol.95, issue.99911, pp.123-126, 1964.

J. P. Grivet, Nonlinear population dynamics in the chemostat, Computing in Science & Engineering, vol.3, issue.1, pp.48-55, 2001.
DOI : 10.1109/5992.895187

H. Smith and . Waltman, The theory of the Chemostat, In Cambridge studies in Mathematical biology, vol.13, 1995.
DOI : 10.1017/CBO9780511530043

M. Crespo, Mathematical optimization in industrial processes, Master's thesis, 2013.

A. K. Dramé, A semilinear parabolic boundary-value problem in bioreactors theory, Electronic Journal of Differential Equations, vol.129, pp.1-13, 2004.

A. K. Dramé, C. Lobry, J. Harmand, A. Rapaport, and F. Mazenc, Multiple stable equilibrium profiles in tubular bioreactors, Mathematical and Computer Modelling, vol.48, issue.11-12, pp.11-12, 2008.
DOI : 10.1016/j.mcm.2008.05.008

L. Dung and H. L. Smith, A Parabolic System Modeling Microbial Competition in an Unmixed Bio-reactor, Journal of Differential Equations, vol.130, issue.1, pp.59-91, 1996.
DOI : 10.1006/jdeq.1996.0132

S. Hsu, Steady States of a System of Partial Differential Equations Modeling Microbial Ecology, SIAM Journal on Mathematical Analysis, vol.14, issue.6, pp.1130-1138, 1983.
DOI : 10.1137/0514087

C. M. Kung and B. C. Baltzis, The growth of pure and simple microbial competitors in a moving distributed medium, Mathematical Biosciences, vol.111, issue.2, pp.295-313, 1992.
DOI : 10.1016/0025-5564(92)90076-9

J. W. So and P. Waltman, A nonlinear boundary value problem arising from competition in the chemostat, Applied Mathematics and Computation, vol.32, issue.2-3, pp.169-183, 1989.
DOI : 10.1016/0096-3003(89)90092-1

D. Dochain and P. Vanrolleghem, Dynamical Modelling & Estimation in Wastewater Treatment Processes, Water Intelligence Online, vol.4, issue.0, 2001.
DOI : 10.2166/9781780403045

B. Ivorra, J. L. Redondo, J. G. Santiago, P. M. Ortigosa, and A. M. Ramos, Two- and three-dimensional modeling and optimization applied to the design of a fast hydrodynamic focusing microfluidic mixer for protein folding, Physics of Fluids, vol.241, issue.13, p.32001, 2013.
DOI : 10.1007/s10898-007-9221-6

A. J. Chorin and J. E. Marsden, A Mathematical Introduction to Fluid Mechanics, Texts in Applied Mathematics, 2013.

G. B. Marin, Advances in Chemical Engineering: Multiscale Analysis, Advances in Chemical Engineering, 2005.

R. J. Leveque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, 2007.
DOI : 10.1137/1.9780898717839

F. N. Fritsch and R. E. Carlson, Monotone Piecewise Cubic Interpolation, SIAM Journal on Numerical Analysis, vol.17, issue.2, pp.238-246, 1980.
DOI : 10.1137/0717021

B. Ivorra, B. Mohammadi, and A. M. Ramos, A multi-layer line search method to improve the initialization of optimization algorithms, European Journal of Operational Research, vol.247, issue.3, pp.711-720, 2015.
DOI : 10.1016/j.ejor.2015.06.044

URL : https://hal.archives-ouvertes.fr/hal-01206339

P. Gajardo, H. Ramirez, V. Riquelme, and A. Rapaport, BIOREMEDIATION OF NATURAL WATER RESOURCES VIA OPTIMAL CONTROL TECHNIQUES, Biomat 2011 -International Symposium on Mathematical and Computational Biology, pp.178-190, 2012.
DOI : 10.1142/9789814397711_0012

URL : https://hal.archives-ouvertes.fr/hal-01001374

S. J. Pirt, Principles of microbe and cell cultivation, 1975.

J. R. Banga, E. B. Canto, C. G. Moles, and A. A. Alonso, Dynamic optimization of bioreactors -a review, Proceedings of the Indian Academy of Sciences

T. T. Lee, F. Y. Wang, and R. B. Newell, Robust multivariable control of complex biological processes, Journal of Process Control, vol.14, issue.2, pp.193-209, 2004.
DOI : 10.1016/S0959-1524(03)00037-4

R. Yamuna and V. S. Ramachandra, Control of fermenters ??? a review, Bioprocess Engineering, vol.21, issue.1, pp.77-88, 1999.
DOI : 10.1007/PL00009066

I. Y. Smets, J. E. Claes, E. J. November, G. P. Bastin, and J. F. Impe, Optimal adaptive control of (bio)chemical reactors: past, present and future, Journal of Process Control, vol.14, issue.7, pp.795-805, 2004.
DOI : 10.1016/j.jprocont.2003.12.005

J. G. Na, Y. Chang, B. Chung, and H. Lim, Adaptive optimization of fed-batch culture of yeast by using genetic algorithms, Bioprocess and Biosystems Engineering, vol.24, issue.5, pp.299-308, 2002.
DOI : 10.1007/s004490100251

S. K. Nguang, L. Chen, and X. D. Chen, Optimisation of fed-batch culture of hybridoma cells using genetic algorithms, ISA Transactions, vol.40, issue.4, pp.381-389, 2001.
DOI : 10.1016/S0019-0578(01)00005-2

M. Ronen, Y. Shabtai, and H. Guterman, Optimization of feeding profile for a fed-batch bioreactor by an evolutionary algorithm, Journal of Biotechnology, vol.97, issue.3, pp.253-263, 2002.
DOI : 10.1016/S0168-1656(02)00106-2

J. A. Roubos, G. Van-straten, and A. J. Van-boxtel, An evolutionary strategy for fed-batch bioreactor optimization; concepts and performance, Journal of Biotechnology, vol.67, issue.2-3, pp.173-187, 1999.
DOI : 10.1016/S0168-1656(98)00174-6

URL : http://dutera.et.tudelft.nl/~roubos/pubs/jbiotech99.pdf

J. Chiou and F. Wang, Hybrid method of evolutionary algorithms for static and dynamic optimization problems with application to a fed-batch fermentation process, Computers & Chemical Engineering, vol.23, issue.9, pp.1277-1291, 1999.
DOI : 10.1016/S0098-1354(99)00290-2

D. Herbert, R. Elsworth, and R. C. Telling, The Continuous Culture of Bacteria; a Theoretical and Experimental Study, Journal of General Microbiology, vol.14, issue.3, pp.601-622, 1956.
DOI : 10.1099/00221287-14-3-601

N. I. Marcos, M. Guay, D. Dochain, and T. Zhang, Adaptive extremum-seeking control of a continuous stirred tank bioreactor with Haldane's Kinetics, Journal of Process Control, vol.14, issue.3, pp.317-328, 2004.
DOI : 10.1016/S0959-1524(03)00070-2

J. Monod, LA TECHNIQUE DE CULTURE CONTINUE TH??ORIE ET APPLICATIONS, Annales de l´Institutl´Institut Pasteur, vol.79, pp.390-410, 1950.
DOI : 10.1016/B978-0-12-460482-7.50023-3

J. Moreno, Optimal time control of bioreactors for the wastewater treatment, Optimal Control Applications and Methods, vol.20, issue.3, pp.145-164, 1999.
DOI : 10.1002/(SICI)1099-1514(199905/06)20:3<145::AID-OCA651>3.0.CO;2-J

G. D. 'ans, P. Kokotovic, and D. Gottlieb, A nonlinear regulator problem for a model of biological waste treatment, IEEE Transactions. Automatic Control, vol.16, pp.341-347, 1971.

P. Gajardo, J. Harmand, H. R. , and A. Rapaport, Minimal time bioremediation of natural water resources, Automatica, vol.47, issue.8, pp.1764-1769, 2011.
DOI : 10.1016/j.automatica.2011.03.001

URL : https://hal.archives-ouvertes.fr/hal-00521118

P. L. Mccarty, Anaerobic waste treatment fundamentals 107-112 Part I, Chemistry and Microbiology Part II, vol.95, issue.99911, pp.123-126, 1964.

P. Gajardo, H. Ramirez, V. Riquelme, and A. Rapaport, BIOREMEDIATION OF NATURAL WATER RESOURCES VIA OPTIMAL CONTROL TECHNIQUES, Biomat 2011 -International Symposium on Mathematical and Computational Biology, pp.178-190, 2012.
DOI : 10.1142/9789814397711_0012

URL : https://hal.archives-ouvertes.fr/hal-01001374

H. Ramirez, A. Rapaport, and V. Riquelme, Minimal time bioremediation of water resources with two patches, SIAM Conference on Control & Applications CT15, pp.8-10, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01154435

J. P. Grivet, Nonlinear population dynamics in the chemostat, Computing in Science & Engineering, vol.3, issue.1, pp.48-55, 2001.
DOI : 10.1109/5992.895187

H. Smith and . Waltman, The theory of the Chemostat, In Cambridge studies in Mathematical biology, vol.13, 1995.
DOI : 10.1017/CBO9780511530043

M. Crespo, Mathematical optimization in industrial processes, Master's thesis, 2013.

A. K. Dramé, A semilinear parabolic boundary-value problem in bioreactors theory, Electronic Journal of Differential Equations, vol.129, pp.1-13, 2004.

A. K. Dramé, C. Lobry, J. Harmand, A. Rapaport, and F. Mazenc, Multiple stable equilibrium profiles in tubular bioreactors, Mathematical and Computer Modelling, vol.48, issue.11-12, pp.11-12, 2008.
DOI : 10.1016/j.mcm.2008.05.008

L. Dung and H. L. Smith, A Parabolic System Modeling Microbial Competition in an Unmixed Bio-reactor, Journal of Differential Equations, vol.130, issue.1, pp.59-91, 1996.
DOI : 10.1006/jdeq.1996.0132

S. Hsu, Steady States of a System of Partial Differential Equations Modeling Microbial Ecology, SIAM Journal on Mathematical Analysis, vol.14, issue.6, pp.1130-1138, 1983.
DOI : 10.1137/0514087

C. M. Kung and B. C. Baltzis, The growth of pure and simple microbial competitors in a moving distributed medium, Mathematical Biosciences, vol.111, issue.2, pp.295-313, 1992.
DOI : 10.1016/0025-5564(92)90076-9

J. W. So and P. Waltman, A nonlinear boundary value problem arising from competition in the chemostat, Applied Mathematics and Computation, vol.32, issue.2-3, pp.169-183, 1989.
DOI : 10.1016/0096-3003(89)90092-1

D. Dochain and P. Vanrolleghem, Dynamical Modelling & Estimation in Wastewater Treatment Processes, Water Intelligence Online, vol.4, issue.0, 2001.
DOI : 10.2166/9781780403045

B. Ivorra, J. L. Redondo, J. G. Santiago, P. M. Ortigosa, and A. M. Ramos, Two- and three-dimensional modeling and optimization applied to the design of a fast hydrodynamic focusing microfluidic mixer for protein folding, Physics of Fluids, vol.241, issue.13, p.32001, 2013.
DOI : 10.1007/s10898-007-9221-6

M. Crespo, B. Ivorra, and A. M. Ramos, Existence and uniqueness of solution of a continuous flow bioreactor model with two species, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, pp.1-21, 2015.
DOI : 10.1017/CBO9780511530043

A. J. Chorin and J. E. Marsden, A Mathematical Introduction to Fluid Mechanics, Texts in Applied Mathematics, 2013.

G. B. Marin, Advances in Chemical Engineering: Multiscale Analysis, Advances in Chemical Engineering, 2005.

R. J. Leveque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems, 2007.
DOI : 10.1137/1.9780898717839

F. N. Fritsch and R. E. Carlson, Monotone Piecewise Cubic Interpolation, SIAM Journal on Numerical Analysis, vol.17, issue.2, pp.238-246, 1980.
DOI : 10.1137/0717021

B. Ivorra, B. Mohammadi, and A. M. Ramos, A multi-layer line search method to improve the initialization of optimization algorithms, European Journal of Operational Research, vol.247, issue.3, pp.711-720, 2015.
DOI : 10.1016/j.ejor.2015.06.044

URL : https://hal.archives-ouvertes.fr/hal-01206339