N. Venayak, N. Anesiadis, W. R. Cluett, and R. Mahadevan, Engineering metabolism through dynamic control, Current Opinion in Biotechnology, vol.34, pp.142-152, 2015.
DOI : 10.1016/j.copbio.2014.12.022

J. Izard, C. D. Gomez-balderas, D. Ropers, S. Lacour, X. Song et al., A synthetic growth switch based on controlled expression of RNA polymerase, Molecular Systems Biology, vol.11, issue.11, p.840, 2015.
DOI : 10.15252/msb.20156382
URL : https://hal.archives-ouvertes.fr/hal-01247993

A. Varma and B. Palsson, Stoichiometric flux balance models quantitatively predict growth and metabolic by-product secretion in wild-type Escherichia coli W3110, Applied Environmental Microbiology, vol.60, issue.10, pp.3724-3731, 1994.

R. Mahadevan, J. S. Edwards, I. Doyle, and F. J. , Dynamic Flux Balance Analysis of Diauxic Growth in Escherichia coli, Biophysical Journal, vol.83, issue.3, pp.1331-1340, 2002.
DOI : 10.1016/S0006-3495(02)73903-9

R. Schuetz, N. Zamboni, M. Zampieri, M. Heinemann, and U. Sauer, Multidimensional Optimality of Microbial Metabolism, Science, vol.224, issue.1, pp.601-604, 2012.
DOI : 10.1016/S0022-5193(03)00146-2

E. Bosdriesz, D. Molenaar, B. Teusink, and F. J. Bruggeman, How fast-growing bacteria robustly tune their ribosome concentration to approximate growth-rate maximization, FEBS Journal, vol.42, issue.10, pp.2029-2044, 2015.
DOI : 10.1016/j.molcel.2011.05.004

N. Giordano, F. Mairet, J. Gouzé, J. Geiselmann, and H. De-jong, Dynamical Allocation of Cellular Resources as an Optimal Control Problem: Novel Insights into Microbial Growth Strategies, PLOS Computational Biology, vol.31, issue.3, 2016.
DOI : 10.1371/journal.pcbi.1004802.s006
URL : https://hal.archives-ouvertes.fr/hal-01332394

R. Schuetz, L. Kuepfer, and U. Sauer, Systematic evaluation of objective functions for predicting intracellular fluxes in Escherichia coli, Molecular Systems Biology, vol.101, p.119, 2007.
DOI : 10.1042/bj2380781

A. Goelzer, V. Fromion, and G. Scorletti, Cell design in bacteria as a convex optimization problem, Automatica, vol.47, issue.6, pp.1210-1218, 2011.
DOI : 10.1016/j.automatica.2011.02.038
URL : https://hal.archives-ouvertes.fr/hal-00593415

O. 'brien, E. J. Lerman, J. A. Chang, R. L. Hyduke, D. R. Palsson et al., Genome-scale models of metabolism and gene expression extend and refine growth phenotype prediction, Molecular Systems Biology, vol.160, issue.1, p.693, 2013.
DOI : 10.1038/msb.2011.34

S. Waldherr, D. A. Oyarzún, and A. Bockmayr, Dynamic optimization of metabolic networks coupled with gene expression, Journal of Theoretical Biology, vol.365, pp.469-485, 2015.
DOI : 10.1016/j.jtbi.2014.10.035

D. Molenaar, R. Van-berlo, D. De-ridder, and B. Teusink, Shifts in growth strategies reflect tradeoffs in cellular economics, Molecular Systems Biology, vol.8, p.323, 2009.
DOI : 10.1099/00221287-19-3-592

H. A. Van-den-berg, Y. N. Kiselev, S. A. Kooijman, and M. V. Orlov, Optimal allocation between nutrient uptake and growth in a microbial trichome, Journal of Mathematical Biology, vol.37, issue.1, pp.28-48, 1998.
DOI : 10.1007/s002850050118

H. A. Van-den-berg, Y. N. Kiselev, and M. V. Orlov, Optimal allocation of building blocks between nutrient uptake systems in a microbe, Journal of Mathematical Biology, vol.44, issue.3, pp.276-296, 2002.
DOI : 10.1007/s002850100123

M. Scott, C. W. Gunderson, E. M. Mateescu, Z. Zhang, H. et al., Interdependence of Cell Growth and Gene Expression: Origins and Consequences, Science, vol.73, issue.12, pp.1099-1102, 2010.
DOI : 10.1016/0300-9084(91)90190-C

I. Yegorov, F. Mairet, and J. Gouzé, Optimal resource allocation for bacterial growth with degradation, To appear in Proceedings of IFAC 2017 World Congress. URL
URL : https://hal.archives-ouvertes.fr/hal-01524917

F. H. Johnson and I. Lewin, The growth rate of E. coli in relation to temperature, quinine and coenzyme, Journal of Cellular and Comparative Physiology, vol.28, issue.1, pp.47-75, 1946.
DOI : 10.1042/bj0281463

A. Farewell and F. Neidhardt, Effect of temperature on in vivo protein synthetic capacity in Escherichia coli, Journal of Bacteriology, vol.180, issue.17, pp.4704-4710, 1998.

G. M. Grimaud, F. Mairet, and O. Bernard, Modelling thermal adaptation in microalgae: an adaptive dynamics point of view, IFAC Proceedings Volumes, vol.47, issue.3, pp.4376-4381, 2014.
DOI : 10.3182/20140824-6-ZA-1003.00982
URL : https://hal.archives-ouvertes.fr/hal-01094700

G. M. Grimaud, L. Guennec, V. Ayata, S. Mairet, F. Sciandra et al., Modelling the effect of temperature on phytoplankton growth across the global ocean???, 8th Vienna International Conference on Mathematical Modelling ? MATHMOD 2015, pp.228-233
DOI : 10.1016/j.ifacol.2015.05.059
URL : https://hal.archives-ouvertes.fr/hal-01245890

M. I. Zelikin and V. F. Borisov, Theory of Chattering Control with Applications to Astronautics, Robotics, Economics, and Engineering, 1994.

H. Schattler and U. Ledzewicz, Geometric Optimal Control: Theory, Methods and Examples
DOI : 10.1007/978-1-4614-3834-2

T. Kalisky, E. Dekel, and U. And-alon, Cost???benefit theory and optimal design of gene regulation functions, Physical Biology, vol.4, issue.4, pp.229-245, 2007.
DOI : 10.1088/1478-3975/4/4/001

F. J. Poelwijk, M. G. De-vos, and S. J. Tans, Tradeoffs and Optimality in the Evolution of Gene Regulation, Cell, vol.146, issue.3, pp.462-470, 2011.
DOI : 10.1016/j.cell.2011.06.035

S. C. Makrides, Strategies for achieving high-level expression of genes in Escherichia coli, Microbiological Reviews, vol.60, issue.3, pp.512-538, 1996.

M. Ehrenberg, H. Bremer, D. , and P. P. , Medium-dependent control of the bacterial growth rate, Biochimie, vol.95, issue.4, pp.643-658, 2013.
DOI : 10.1016/j.biochi.2012.11.012

D. A. Carlson, A. B. Haurie, and A. Leizarowitz, Infinite Horizon Optimal Control: Deterministic and Stochastic Systems, 1991.

E. Trélat and E. Zuazua, The turnpike property in finite-dimensional nonlinear optimal control, Journal of Differential Equations, vol.258, issue.1, pp.81-114, 2015.
DOI : 10.1016/j.jde.2014.09.005

C. W. Clark, Mathematical Bioeconomics: The Optimal Management of Renewable Resources., Biometrics, vol.49, issue.2, 1990.
DOI : 10.2307/2532591

F. H. Clarke, Y. S. Ledyaev, R. J. Stern, and P. Wolenski, Nonsmooth Analysis and Control Theory, 1998.
URL : https://hal.archives-ouvertes.fr/hal-00863298

V. Lakshmikantham and S. Leela, Differential and Integral Inequalities: Theory and Applications. Volume I: Ordinary Differential Equations, 1969.

E. Borek, L. Ponticorvo, R. , and D. , PROTEIN TURNOVER IN MICRO-ORGANISMS, Proceedings of the National Academy of Sciences, vol.44, issue.5, pp.369-374, 1958.
DOI : 10.1073/pnas.44.5.369

F. Neidhardt, The Regulation of RNA Synthesis in Bacteria, Progress in Nucleic Acid Research and Molecular Biology, vol.3, pp.145-181, 1964.
DOI : 10.1016/S0079-6603(08)60741-2

M. P. Deutscher, Degradation of Stable RNA in Bacteria, Journal of Biological Chemistry, vol.163, issue.46, pp.45041-45044, 2003.
DOI : 10.1016/S0079-6603(08)60100-2

V. N. Afanas-'ev, V. B. Kolmanovskii, and V. R. Nosov, Mathematical Theory of Control Systems Design, 1996.

E. B. Lee and L. Markus, Foundations of Optimal Control Theory, 1986.

L. Perko, Differential Equations and Dynamical Systems, 2001.

R. Gabasov and F. M. Kirillova, Singular Optimal Control, 1982.

A. A. Melikyan, Generalized Characteristics of First Order PDEs: Application in Optimal Control and Differential Games, 1998.
DOI : 10.1007/978-1-4612-1758-9

B. Bonnard and M. Chyba, Singular Trajectories and their Role in Control Theory, Mathématiques & Applications, vol.40, 2003.

M. I. Zelikin and V. F. Borisov, Singular Optimal Regimes in Problems of Mathematical Economics, Journal of Mathematical Sciences, vol.37, issue.9, pp.4409-4570, 2005.
DOI : 10.1090/conm/209/02774

H. Schattler and U. Ledzewicz, Optimal Control for Mathematical Models of Cancer Therapies: An Application of Geometric Methods, Interdisciplinary Applied Mathematics, vol.42, 2015.
DOI : 10.1007/978-1-4939-2972-6

G. Naumov, Construction of the switching curve for optimal control problems with chattering control, Izvestiya RAN: Teoriya i Sistemy Upravleniya, vol.3, pp.46-51, 2003.

A. Filippov, Differential Equations with Discontinuous Right-hand Sides. Kluwer Academic: Dordrecht, 1988.

V. I. Blagodatskikh and A. F. Filippov, Differential inclusions and optimal control, Proceedings of the Steklov Institute of Mathematics, vol.169, pp.199-259, 1986.

F. Bonnans, P. Martinon, D. Giorgi, V. Grélard, S. Maindrault et al., ? User Guide, 2017.

J. Zhu, E. Trélat, and M. Cerf, Minimum Time Control of the Rocket Attitude Reorientation Associated with Orbit Dynamics, SIAM Journal on Control and Optimization, vol.54, issue.1, pp.391-422, 2016.
DOI : 10.1137/15M1028716
URL : https://hal.archives-ouvertes.fr/hal-01170274

J. Zhu, E. Trélat, and M. Cerf, Planar tilting maneuver of a spacecraft: Singular arcs in the minimum time problem and chattering, Discrete and Continuous Dynamical Systems - Series B, vol.21, issue.4, pp.1347-1388, 2016.
DOI : 10.3934/dcdsb.2016.21.1347
URL : https://hal.archives-ouvertes.fr/hal-01145876

A. Bratus, I. Yegorov, Y. , and D. , Optimal investment strategies in a certain class of stochastic Merton???s terminal wealth problems, International Journal of Dynamics and Control, vol.62, issue.1, 2016.
DOI : 10.1016/j.sysconle.2012.11.008

A. Bratus, I. Yegorov, Y. , and D. , Optimal bounded noisy feedback control for damping random vibrations, Journal of Vibration and Control, pp.10-1177, 2016.
DOI : 10.1177/1077546316670072

G. Kolosov, Optimal Design of Control Systems: Stochastic and Deterministic Problems, 1999.

J. Yong, X. Jou, and . Yu, Stochastic Controls: Hamiltonian Systems and HJB Equations, 1999.
DOI : 10.1007/978-1-4612-1466-3