Terence Bayen Homepage

Topics of interest
- Optimal Control Theory, Pontryagin Maximum Principle, Singular arcs, Viability.
- Modelling, Optimal synthesis, Bioprocesses, Biology, Resource-consumer models.
- Optimization, Shape Optimization, Convexity Constraints, Calculus of Variation.
The research I intend to follow is concerned with optimal control theory and shape optimization. One main issue in optimal control theory is to find properties of optimal trajectories for differential controlled systems (in terms of optimal feedback control laws) via Pontryagin maximum principle and Hamilton-Jacobi Equation. Several differential systems (in connection with bioprocesses) for which singular strategies can be defined lead to interesting studies. The second aspect I intend to develop deals with non standard shape optimization problems (for instance involving convex constraints) for which standard methods (such as Euler-Lagrange equation in calculus of variation) cannot be applied. One interesting issue is to find adequate way to formulate convexity constraints within an optimization problem.
Publications (journal)

Minimal time crisis versus minimum time to reach a viability kernel : a case study in the prey-predator model, Optimal Control Appl. Methods, 2019, vol. 40, 2, pp. 330--350 (with A. Rapaport).
On the steady state optimization of the biogas production in a two-stage anaerobic digestion model, J. Math. Biol., 2019, Vol. 78, 4, pp. 1067--1087 (with P. Gajardo).
Optimal control of membrane filtration systems, IEEE Trans. Automat. Control, in press, 64 (5), pp. 8704--8709, 2019 (with N. Kalbussi, A. Rapaport, N. Benamar, F. Ellouze and J. Harmand).
Analysis of an optimal control problem related to anaerobic digestion process, Journal of Optim. Theory and Applications, August 2018, Volume 178, Issue 2, pp 627–659 (with O. Cots and P. Gajardo).
Optimal control of backwash strategy - towards the enhancement of membrane filtration system performance, Journal of Membrane Science, Vol. 545, 1 Jan. 2018, pp. 38--48 (with N. Kalbussi, A. Rapaport, N. Benamar, F. Ellouze and J. Harmand).
Time-optimal control of concentrations changes in the chemostat with one single species, Applied Mathematical Modelling, vol. 50, 2017, pp. 257-278, (with J. Harmand and M. Sebbah).
Optimization of strain selection in evolutionary continuous culture, International Journal of Control, vol. 90, issue 12, 2017, pp. 2748--2759 (with F. Mairet).
De l'importance d'être constant...dans sa largeur, Dossier N°91 / avril-juin 2016 / © POUR LA SCIENCE (avec J.-B. Hiriart-Urruty).
Second order analysis for strong solutions in the optimal control of parabolic equations, SIAM J. Control Optim. 54-2 (2016), pp. 819-844 (with F. Silva).
Dynamical modelling and optimal control of landfills, Mathematical Models and Methods in Applied Sciences, vol. 26, No. 05, pp. 901-929, 2016 (with A. Rapaport, M. Sebbah, A. Donoso, A. Torrico).
About Moreau-Yosida regularization of the minimal time crisis problem, Journal of Convex Analysis 23 (2016), No. 1, 263-290 (with A. Rapaport).
Analysis of an optimal control problem connected to bioprocesses involving a saturated singular arc, DCDS, series B, vol. 20, 1, pp.39--58, 2015 (with F. Mairet and M. Mazade).
Analysis of a periodic optimal control problem connected to microalgae anaerobic digestion, Optimal Control and Applications Methods, vol. 36, 6, pp. 750--773, 2015 (with F. Mairet, P. Martinon and M. Sebbah).
Optimal feeding strategy for the minimal time problem of a fed-batch bioreactor with mortality rate, Optimal Control and Applications Methods, vol. 36, 1, pp. 77--92, 2015 (with F. Mairet, M. Mazade).
Minimal time control of the two tanks gradostat model under a cascade inputs constraint, SIAM J. Control Optim., Vol. 52, No. 4, pp. 2568--2594, 2014 (with A. Rapaport, M. Sebbah).
Optimization of the separation of two species in a chemostat, Automatica, vol. 50, 4, April 2014, Pages 1243--1248 (with F. Mairet).
Characterization of local quadratic growth for strong minima in the optimal control of semi-linear elliptic equations, Trans. Amer. Math. Soc. 366 (2014), 2063-2087 (with F. Bonnans and F. Silva).
Minimal time control of fed-batch bioreactor with product inhibition, Bioprocess and Biosystems Engineering 36, 10, pp. 1485-1496, 2013 (with F. Mairet).
Optimal synthesis for the minimum time control problems of fed-batch bioprocesses for growth functions with two maxima, Journal of Optim. Theory and Applications, vol. 158, 2, pp. 521-553, 2013 (with P. Gajardo, F. Mairet).
Semidefinite programming for optimizing convex bodies under width constraints, Optimization Methods and Software, 27, 6, pp. 1073-1099, 2012 (with D. Henrion).
Objets convexes de largeur constante (en 2D) ou d'epaisseur constante (en 3D) : du neuf avec du vieux, Ann. Sci. Math. Quebec 36, 1, pp. 17-42, 2012 (with J.-B. Hiriart-Urruty).
Analytical Parameterization of Rotors and Proof of a Goldberg conjecture by Optimal Control Theory, SIAM J. Control Optim. 47, 6, pp. 3007-3036, 2009.
Analytic parametrization of three dimensional bodies of constant width , Archive Rational Mechanics Analysis, 186, 2, pp. 225-249, 2007 (with T. Lachand-Robert, E. Oudet).

Recent preprints and submitted papers
- Weak resilience of the chemostat model to a species invasion with non-autonomous removal rates, preprint HAL, march 2019 (with A. Rapaport and F.-Z. Tani).
- About the prior-saturation phenomenon for minimal time problems in the plane, preprint, march 2019 (with O. Cots).
- Second-order analysis for the time crisis problem, submitted feb. 2019 (with L. Pfeiffer).
- Optimal periodic control for scalar dynamics under integral constraint on the input, submitted feb. 2018 (with A. Rapaport, F.-Z. Tani).
- Analysis of a stated constrained optimal control problem related to the modelling of a coastal lagoon, preprint, february 2017 (with L. Dagnas, Hector Ramirez, Alain Rapaport, A. Rousseau, M. Sebbah).

Referred conference publications

About optimal periodic control of the chemostat with Contois growth function, IFAC 2018, 9th Vienna International Conf. on Mathematical Modelling (with A. Rapaport, F.-Z. Tani).
About the minimal time crisis problem, ESAIM: Proceedings and Surveys, EDP Sciences, Vol. 57, p. 1-11, 2017 (with A. Rapaport).
Optimal control of a membrane filtration system, IFAC 2017, 20th World Congress of the International Federation of Automatic Control (with N. Kalbussi, A. Rapaport, T. Bayen, N. Benamar, F. Ellouze, J. Harmand).
About the minimal time crisis problem and applications, IFAC 2017, Toulouse, 20th World Congress of the International Federation of Automatic Control (with A. Rapaport).
Analysis of an optimal control problem connected to microorganisms selection, IFAC 2017, 20th World Congress of the International Federation of Automatic Control (with F. Mairet).
Minimal time problem for a chemostat model with growth rate of Haldane Type, European Control Conference 2014, ECC14, Strasbourg, 24-27 june 2014, 6 pages (with J. Harmand).
Minimal time control of the two tanks gradostat model under a cascade inputs constraint, European Control Conference 2014, ECC14, Strasbourg, 24-27 june 2014, 6 pages (with A. Rapaport, M. Sebbah).
Minimal time problem for a fed-batch bioreactor with a non-admissible singular arc, European Control Conference 2014, ECC14, Strasbourg, 24-27 june 2014, 6 pages (with F. Mairet, M. Mazade).
Weak and strong minima : from calculus of variation toward PDE optimization, accepted in 1st IFAC Workshop on Control of Systems Modeled by Partial Differential Equations (CPDE 2013), Paris, France, Septembre 25-27, 2013, 4 pages (with F. Silva).
Fed-batch bioreactor with mortality rate, 9th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2013), Toulouse, September 4-6, 2013, 6 pages (with F. Mairet, M. Mazade).
Optimizing the anaerobic digestion of microalgae in a coupled process, European Control Conference 2013, ECC13, Zurich, 17-19 july 2013, 6 pages (with F. Mairet, P. Martinon, M. Sebbah).
Minimal time control of fed-batch bioreactor with product inhibition, 20th Mediterranean Conference on Control & Automation (MED) 2012, 6 pages (with F. Mairet, P. Gajardo).
Parametrization of a Convex Optimization Problem by Optimal Control Theory and Proof of a Goldberg Conjecture, 48th IEEE Conference on Decision and Control, Shangai, 2009, 6 pages.
Asymptotic analysis of an optimal control problem connected to the human locomotion, 48th IEEE Conference on Decision and Control, Shangai, 2009, 6 pages (with Y. Chitour, F. Jean, P. Mason).

Other reports or preprint

On the degree of the polynomial defining planar algebraic curves of constant width, preprint 2013 (with M. Bardet).

Study of a controlled Kolmogorov periodic equation connected to the optimization of periodic bioprocess, preprint 2013 (with F. Mairet and M. Sebbah).

Thesis and Habilitation

Optimisation de forme dans la classe des corps de largeur constante (PhD Thesis, University Paris 6, 2007).
Etude de quelques problemes de controle optimal issus des EDP et des EDO (HDR, University Montpellier 2, 2013).

Poster

Poster PGMO (FMJH) for the project OPTIBIO (2014-2016).

Some communications

Workshop in Nonsmooth and Variational Analysis, ESI Vienna, January 28 - February 1, 2019.
ORCOS 2018 (14th Viennese Conference on Optimal Control and Dynamic Games), Vienna, july 2018.
Control and Optimization Conference, Palaiseau, Nov. 2017. On the occasion of Frédéric Bonnans 60th birthday.
IFAC 2017, Toulouse
ETAMM 2016 (Emerging Trends in applied Mathematics and Mechanics), Perpignan, june 2016.
EURO 2015 (Euro Conference in Optimization), Glasgow, july 2015.
SIAM Conference on Control, Paris, july 2015.
PGMO days (october 2015, ENSTA)
EUROPT14 (12th workshop on advances in continuous optimization), Perpignan july 2014.
International Conference on Variational Analysis and Optimization (dedicated to Lionel Thibault), Santiago, Chili, janvier 2014.
ECC 2014 (European Control Conference), Strasbourg.
NOLCOS Ifac, Toulouse, 3-5 september 2013.
ICCOPT Lisbonne, 27 july - 1 august 2013.
Workshop bioprocesses, Pucon, Chile, 16-17 january 2012.
AFG2011 (15th Austrian-French-German Conference on Optimization), Toulouse, september 2011.
Journées MODE (Autrans 2018, Toulouse 2016, Rennes 2014, Dijon 2012, Limoges 2010, Clermont-Ferrand 2008, CODE 2007, IHP Paris)
BFG2009 (14th Belgian-French-German Conference on Optimization), Louvain Belgique, 2009.
CDC 2009 (Control Decision Conference), Shangai, 2009.

Ph.D. Supervision

Ph.D. Student supervision : Kenza BOUMAZA (2018-2021) ; co-advisor : Alain Rapaport, Sébastien Roux. PhD. title: Commande optimale pour l'utilisation rationnelle de l'eau.
Ph.D. Student supervision : Fatima Zahra TANI (2016-2019) ; co-advisor : Alain Rapaport. Ph.D. title: Commande périodique de bioréacteurs multi-spécifiques en vue de l’optimisation de leur rendements.
Ph.D. Student supervision : Matthieu SEBBAH (Graduation july 2012) ; co-advisor : L. Thibault. Ph.D. title : Stability of variational inequalities and prox-regularity, Controlled Kolmogorov Periodic Equations.

Other activities (past)

Member of groupe MODE (research group in optimization) 2010-2016. In charge of broader impact and communication activities and webmaster of groupe MODE from 2009 to 2016. The groupe MODE focuses on applied and industrial mathematics in areas such as nonlinear analysis, optimization, discrete mathematics, operations research, mathematical modeling in economy, finance and social sciences.

Ph.D. Thesis Referee Committees: in the thesis exam commitee of :

Walid Bouhaf (february 2016, ENIT, Tunisie) : Optimisation de bioréacteurs séquentiels discontinus.
Hayk Sedrakyan (december 2014, Université Paris 6) : Comportement limite des systèmes singuliers et les limites de fonctions valeur en contrôle optimal.

Ph.D. Thesis Examination Committees: in the thesis exam commitee of :

David Salas (décembre 2016, University of Montpellier).

Sylvain Prigent (september 2015, IMT Toulouse).
Amel Ghouali (december 2015, INRA Montpellier).
Radhouane Fekih Salem (september 2013, INRA Montpellier).
Miled El Hajji (december 2010, INRA Montpellier).
Ihab Haidar (december 2011, INRA Montpellier).

Co-organizer of the conference EUROPT 2014 (12th EUROPT Workshop on Advances in Continuous Optimization, Perpignan Juillet, 2014).

Research

Topics of interest

Publications (journal)

Recent preprints and submitted papers

Referred conference publications

Ph.D. Supervision

Other activities (past)