Aziz Belmiloudi, PhD hab.

Senior Associate Professor (Aziz. Belmiloudi at math.cnrs.fr)

IRMAR (Institut de Recherche Mathématique de Rennes)



 




 

Topics : PDEs/ODEs, Control theory, Coupled Systems, Hybrid Systems, Time-delay Systems, Applied analysis and Mathematical modelling As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality.» Albert Einstein

 

Special Issues: Biomedical Dynamical Systems In Mathematical Biosciences and Engineering(SCIE; IF=1.285, Q2 (JCR))

The deadline for manuscript submission is 15 August 2021

Scientific Publications :

Books:


74. A. Belmiloudi. Stabilization, Optimal and Robust Control. Theory and Applications in Biological and Physical Sciences, 526 pages, Springer-Verlag, London, Berlin, 2008. http://dx.doi.org/10.1007/978-1-84800-344-6

http://www.springer.com/engineering/robotics/book/978-1-84800-343-9 Reviews: R. M. Bianchini (Firenze, Ulisse Dini) in: Zentralblatt MATH; D. O. Welch (Brookhaven National Laboratory) in: JOM Journal of TMS (http://www.tms.org/pubs/journals/JOM/reviews/153.htm) ; J.P. Raymond (Toulouse,MIP) in: MathematicalReviews

Edited Books:


73. A. Belmiloudi. Heat Transfer. Mathematical Modelling, Numerical Methods and Information Technology, 642 pages, INTECH, Vienna, 2011. http://dx.doi.org/10.5772/569

http://www.intechopen.com/books/heat-transfer-mathematical-modelling-numerical-methods-and-information-technolog

 

 


72. A. Belmiloudi. Heat Transfer. Theoretical Analysis, Experimental Investigations and Industrial Systems, 654 pages, INTECH, Vienna, 2011. http://dx.doi.org/10.5772/1756

http://www.intechopen.com/books/heat-transfer-theoretical-analysis-experimental-investigations-and-industrial-systems

Invited Book Chapters:

71. A. Belmiloudi, Coupled PDEs and Control systems arising in Climate Dynamics: Ocean-Atmosphere Interactions and Tropical Instability Waves. In Edited Book:Mathematical Research Summaries (Matthew A. Rowe ed.), Vol. 1, Chapter 105, Nova Science Publishers, New York, 2017.

70. S. Corre, A. Belmiloudi. Coupled Lattice Boltzmann Modeling of Bidomain type models in Cardiac Electrophisiology. Mathematical and Computational Approaches in Advancing Modern Science and Engineering (eds. J. Bélair, I. Frigaard, H. Kunze, R., Melnik, J. Spiteri), Springer cham, Switzerland, 2016. Book link

69. A. Belmiloudi. Coupled PDEs and Control systems arising in Climate Dynamics: Ocean-Atmosphere Interactions and Tropical Instability Waves. In Edited Book: Partial Differential Equations: Classification, Properties and Applications (D.E. Richards ed.), Chapter 2, Nova Science Publishers, New York, 15-71, 2015. Book link

68. A. Belmiloudi. Nonlinear robust control and regulation problems for biomedical dynamical systems. In. Interdisciplinary Topics in Applied Mathematics, Modeling, and Computational Science (eds. M. Cojocaru, I.S. Kotsireas, R. Makarov, R. Melnik, H. Shodiev), Vol. 117, Chapter 8, Serie Springer Proceedings in Mathematics and Statistics, Springer Berlin Heidelberg, 49-56, 2015. Book link

67. A. Belmiloudi. Stabilization, Regulation and Robust Control of Uncertain processes and parameters in Porous Medium systems with Applications. In Edited Book: Focus on Porous Media Research (C. Zhao ed.), Chapter 6, Nova Science Publishers, New York, 165-228, 2013 . Book link

66. A. Belmiloudi. Thermal Therapy: Stabilization and Identification. In Edited Book: Heat Transfer-Mathematical Modelling, Numerical Methods and Information Technology (A. Belmiloudi ed.), Chapter 2, INTECH, Vienna, 33-76, 2011. http://dx.doi.org/10.5772/14450

International Refereed Journals Articles:

65. A. Belmiloudi, Cardiac memory phenomenon, time-fractional order nonlinear system and bidomain-torso type model in electrocardiology, AIMS Mathematics, vol. 6, No.1, 821-867, 2021.

64. S. Corre, A. Belmiloudi, Coupled lattice Boltzmann simulation method for bidomain type models in cardiac electrophysiology with multiple time-delays, Mathematical Modelling of Natural Phenomena, vol. 14, No. 2, pp. 27., 2019.

63. A. Belmiloudi, Time-varying delays in electrophysiological wave propagation along cardiac tissue and minimax control problems associated with uncertain bidomain type models, AIMS Mathematics, vol. 4, No. 3, 928-983, 2019.

62. A. Belmiloudi, S. Corre , Mathematical modeling and analysis of dynamic effects of multiple time-varying delays on electrophysiological wave propagation in the heart, Nonlinear Analysis Series B: Real World Applications, vol. 47, 18-44, 2019.

61. A. Belmiloudi. Optimal control for chemotaxis systems and adjoint-based optimization with multiple-relaxation-time lattice Boltzmann models, Journal of Mathematics and Biostatistics, vol. 1, No. 1, 32-67, 2018 (by invitation for the launch of  the journal)

60. A. Belmiloudi. Mathematical modeling and optimal control problems in brain tumor targeted drug delivery strategies, International Journal of Biomathematics, vol. 10, 1750056, [62 pages], 2017.

59. S. Corre, A. Belmiloudi. Coupled lattice Boltzmann method for numerical simulations of fully coupled heart and torso bidomain system in electrocardiology, Journal of Coupled Systems and Multiscale Dynamics, vol. 4, No. 3, 207-229, 2016.

58. M. Penet, H. Guéguen, A. Belmiloudi. Saddle Point MPC Approach to Nonlinear Robust Sampled Data Control problem, International Journal of Control, Automation and Systems, vol. 14, issue 1, 222-233, 2016.

57. A. Belmiloudi. Dynamical behavior of nonlinear impulsive abstract partial differential equations on networks with multiple time-varying delays and mixed boundary conditions involving time-varying delays, Journal of Dynamical and Control Systems, vol. 21, No 1, 95-146, 2015.

56. A. Belmiloudi, F. Mahé. On nonlinear inverse problems of heat transfer with radiation boundary conditions. Application to dehydratation of gypsum plasterboards exposed to fire, Advance in Numerical Analysis, vol. 2014, Article ID 634712, 18 pages, 2014.

55. A. Belmiloudi. Robust control problem of uncertain bidomain models in cardiac electrophysiology, Journal of Coupled Systems and Multiscale Dynamics, vol. 1, No. 3, 332-350, 2013.

54. A. Rasheed, A. Belmiloudi. Mathematical modelling and numerical simulation of dendrite growth using phase-field method with a magnetic field effect, Communications in Computational Physics, vol. 14, No. 2, 477-508, 2013.

53. A. Rasheed, A. Belmiloudi. An analysis of a phase-field model for isothermal binary alloy solidification with convection under the influence of magnetic field, Journal of Mathematical Analysis and Applications, vol. 390, 244-273, 2012.

52. A. Rasheed, A. Belmiloudi, F. Mahé. Dynamics of dendrite growth in a binary alloy with magnetic field effect, Discrete and Continuous Dynamical Systems, vol. 2011, special issue, 1224-1233, 2011.

51. A. Belmiloudi. Parameter identication problems and analysis of the impact of porous media in biofluid heat transfer in biological tissues during thermal therapy, Nonlinear Analysis Series B: Real World Applications, vol. 11, No.3, 1345-1363, 2010. (Highlighted by Health and Medicine Week, July 26, 2010, p.2636, ISSN: 15316459).

50. A. Belmiloudi. Analysis of the impact of nonlinear heat transfer laws on temperature distribution in irradiated biological tissues: mathematical models and optimal controls, Journal of Dynamical and Control Systems, vol. 13, No. 2, 217-254, 2007.

49. A. Belmiloudi. Bilinear minimax control problems for a class of parabolic systems with applications to control of nuclear reactors, Journal of Mathematical Analysis and Applications, vol. 327, No. 1, 620-642, 2007.

48. A. Belmiloudi. Robust control problems of vortex dynamics in superconducting films with Ginzburg-Landau complex systems, Abstract and Applied Analysis, vol. 2006, Article ID 26724, 43 pages, 2006.

47. A. Belmiloudi. On some control problems for heat transfer systems in perfused biological tissues, WSEAS Transactions on Systems, vol.5, No.1, 17-25, 2006.

46. A. Belmiloudi. Minimax control problem of periodic competing parabolic systems with logistic growth terms, International Journal of Control, vol.79, No.2, 150-161, 2006.

45. A. Belmiloudi, J.P. Yvon. Robust control of a non-isothermal solidification model, WSEAS Transactions on Systems, vol.4, No.12, 2291-2300, 2005.

44. A. Belmiloudi. Nonlinear optimal control problems of degenerate parabolic equations with logistic time-varying delays of convolution type, Nonlinear Analysis Series A: Theory, Methods & Applications, vol. 63, 1126-1152, 2005.

43. A. Belmiloudi, G. Le Meur. Mathematical and numerical analysis of dehydratation of gypsum plasterboards exposed to fire, Applied Mathematics and Computation, vol.163, No.3, 1023-1042, 2005.

42. A. Belmiloudi. Optimal control problems of nonlinear degenerate parabolic differential systems with logistic time-varying delays, IMA Journal of Mathematical Control and Information, vol.22, No.1, 88-108, 2005.

41. A. Belmiloudi. Robust and optimal control problems to a phase-field model for the solidification of a binary alloy with a constant temperature, Journal of Dynamical and Control Systems, vol.10, No.2,453-499, 2004.

40. A. Belmiloudi. On some robust control problems for nonlinear parabolic equations, International Journal of Pure and Applied Mathematics, vol.11, No.2, 119-151, 2004.

39. A. Belmiloudi. Robust control problems associated with time-varying delays nonlinear parabolic equations, IMA Journal of Mathematical Control and Information, vol.20, No.3, 305-334, 2003.

38. A. Belmiloudi. Nonlinear robust control problems of parabolic type equations with time-varying delays given in the integral form, Journal of Dynamical and Control Systems, vol.9, No.4, 469-512, 2003.

37. A. Belmiloudi. Mathematical analysis and optimal control problems for the perturbation of the primitive equations of the ocean with vertical viscosity, Journal of Applied Analysis, vol.8, No.2, 153-200, 2002.

36. A. Belmiloudi. Robin-type boundary control problems for the nonlinear Boussinesq type equations, Journal of Mathematical Analysis and Applications, vol.273, No.2, 428-456, 2002.

35. A. Belmiloudi. Existence and characterization of an optimal control for the problem of long waves in a Shallow-Water model, SIAM Journal on Control and Optimization, vol.39, No.5, 1558-1584, 2001.

34. A. Belmiloudi. Asymptotic behaviour of the perturbation of the primitive equations of the ocean with vertical viscosity, Canadian Applied Mathematics Quarterly, vol.8, No.2, 97-140, 2000.

33. A. Belmiloudi. Regularity results and optimal control problems for the perturbation of Boussinesq equations of the ocean, Numerical Functional Analysis and Optimization, vol.21, No 5&6, 623-651, 2000.

32. A. Belmiloudi, F. Brossier, L. Monier. Mathematical and numerical modelization of large-scale oceanic waves, Mathematical Methods in the Applied Sciences, vol.22, 967-999, 1999.

31. A. Belmiloudi. A nonlinear optimal control problem for assimilation of surface data in a Navier-Stokes type equations related to oceanography, Numerical Functional Analysis and Optimization, vol.20, No 1&2, 1-26, 1999.

30. A. Belmiloudi, F. Brossier. Regularity results for a Navier-Stokes type problem related to oceanography, Acta Applicandae Mathematicae, vol.48, No.3, 299-316, 1997.

29. A. Belmiloudi, F. Brossier. A control method for assimilation of surface data in a linearized Navier-Stokes type problem related to oceanography, SIAM Journal on Control and Optimization, vol.35, No.6, 2183-2197, 1997.

International Conference Proceedings (with Referee) :

28. M. Penet, H. Guéguen, A. Belmiloudi. Artificial Blood Glucose Control Using a DDE Modelling Approach, In. Proceeding of 19th IFAC World Congress, pp. 2076– 2081, Vol. 19, Capetown, 2014 (ISBN: 978-3-902823-62-5).

27. M. Penel, H. Guéguen and A. Belmiloudi. A Robust Receding Horizon Control Approach to Artificial Glucose Control for Type 1 Diabetes In. 9th IFAC Symposium on Nonlinear Control Systems, IFAC-papersOnline, (eds. S. Tarbouriech, M.Krstic), pp. 833-838, 2013 (ISBN: 978-3-902823-47-2).

26. R. Bourdais, H. Guéguen and A. Belmiloudi. Distributed model predictive control for a class of hybrid system based on Lagrangian relaxation, In. Analysis and Design of Hybrid Systems, IFAC-papersOnline, (eds. M. Heemels, B. De Schutter, M. Lazar), pp. 46-51, 2012 (ISBN 978-3-902823-00-7).

25. M. Penet, H. Guéguen et A. Belmiloudi. Regulation Artificielle de la Glycemie : Developpement d'une commande robuste, In. Proceedings of the 7th IEEE Conférence Internationale Francophone d'Automatique (CIFA), pp. 425-430, 2012.

24. A. Maalouf, C. Bastianelli, F. Mahé, A. Belmiloudi, M. Gadonna and D. Bosc. Improved integrated resonators in polymer technology for tunable filter, In. Silicon Photonics and Photonic Integrated Circuits III, Vol. 8431, SPIE Proceedings, (eds., L. Vivien, S.K. Honkanen, L. Pavesi, S. Pelli), (ISBN 9780819491237), pp. 843124/1-843124/15, 2012 (supported by ANR, Images&Reseaux cluster and Brittany Region).

23. A. Belmiloudi. Regulation of uncertain nonlinear systems: a differential equation approach to robust control design with applications to biological systems, International Congress of Mathematicians, Hyderabad, India, (eds., R. Bhatia et al.), Hindustan Book Agency, pp. 466-467, 2010 (supported by French National Committee of Mathematicians (CNFM)).

22. A. Rasheed, A. Belmiloudi. Phase-field method for computationally efficient modeling of the solidification of binary alloy with magnetic field effect, In. Proceedings of the NumAn2010 Conference in Numerical Analysis; Recent Approaches to Numerical Analysis: Theory, Methods and Applications, (eds., V. Dougalis, E. Gallopoulos, A. Hadjidimos et al.), pp. 222-230, 2010 (ISBN 978-960-8475-14-4).

21. A. Belmiloudi, J.P. Yvon. Optimal control of a non-isothermal solidification model, In. Proceedings of the WSEAS Inter. Conf. on Dynamical System and Control, pp. 1-6, 2005 (ISBN:960-8457-37-8), Invited paper.

20. A. Belmiloudi. Optimal control related to effects of microwave heating on thermal states of biological bodies, In. Proceedings of the WSEAS Inter. Conf. on Dynamical System and Control, pp. 7-12, 2005 (ISBN:960-8457-37-8), Invited paper.

19. A. Belmiloudi. Analysis of robust control problems for a quasilinear parabolic equations, In. Proceedings of the 9th IEEE MMAR, "Optimisation of Infinite Dimensional Systems" (eds., R. Kaszynski), Wydawnictwo Uczelniane Politechniki Szczecinskiej, pp. 99-108, 2003 (ISBN: 83-88764-82-9), Invited paper.

18. A. Belmiloudi. Mathematical and computional methods of an optimal control for the primitive equations in a coupled atmosphere-ocean model, In. Proceedings of the 9th IEEE MMAR, "Optimisation of Infinite Dimensional Systems" (eds., R. Kaszynski), Wydawnictwo Uczelniane Politechniki Szczecinskiej, pp. 87-96, 2003, (ISBN: 83-88764-82-9), Invited paper.

17. A. Belmiloudi. Studies in Robin-type boundary control problems for the primitive equation of the ocean, In. Proceedings of the 8th IEEE MMAR, "Optimisation of Infinite Dimensional Systems" (eds., S. Domek and R. Kaszynski), Wydawnictwo Uczelniane Politechniki Szczecinskiej, pp. 159-166, 2002 (ISBN: 83-88764-61-6), Invited paper.

16. A. Belmiloudi. On some control problems in a shallow-water model, In. Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, Florida, IEEE Control Society, pp. 4956-4961, 2001 (ISBN:0-7803-7061-9), Paper proposed by SIAM.

15. A. Belmiloudi. Studies in linear and nonlinear optimal control problems for viscous flows equations, Application of mathematics in Engineering and Business Sozopol. In. Proceedings of the XXVI Summer School Sozopol (eds., B.I. Cheshankov and M.D. Todorov), Heron Press, Sofia, 181-188, 2001 (ISBN: 954-580-094-1) .

14. A. Belmiloudi. Resolution of optimal control problem for a perturbation linearized Navier-Stokes type equations, Application of mathematics in Engineering and Business Sozopol. In. Proceedings of the XXII Summer School, Sofia University Press, pp. 39-51, 1996 (Invited paper).

13. A. Belmiloudi. Method of characteristics and error estimates of the perturbation of given mean flow, Application of mathematics in Engineering and Business Sozopol. In. Proceedings of the XXII Summer School, Sofia University Press, pp. 25-38, 1996 (Invited paper).

Abstract of International Conferences (with Referee):

12. A. Belmiloudi, F. Mahé, Optimal control and parameter estimation in some epidemiological models, 21th International Epidemiological Association (IEA) World Congress of Epidemology (WCE), August 19-22, Tokyo Area, Japan, 2017.

11. S. Corre, A. Belmiloudi. Mathematical modeling and lattice Bolzmann simulation method for bidomain type models in cardiac electrophysiology with time-varying delays. Conference on Complex Dynamical Systems in Life Sciences: Modeling and Analysis, October 26-28, Agadir, Morocco, 2016.

10. A. Rasheed, A. Belmiloudi. Optimal control of dendrite structure using magnetic field, in Special Session : Nonlinear evolution PDEs, interface and applications (Organizers. A. Miranville, G. Caginalp and M. Grasselli), AIMS Conferences on Dynamical Systems, Differential Equations and Applications, July 1- 5, Orlando, Florida, USA, 2016.

9. M. Penet, H. Guéguen, A. Belmiloudi, J.Y Poirier and I. Guilhem. A robust receding horizon approach for blood glucose control in type 1 diabetes, International Conference on Advanced Technologies and Treatments for Diabetes (ATTD), Barcelona, Spain, 2012.

8. A. Belmiloudi, F. Mahé. Numerical resolution of long waves in a Shallow-Water type model, International Symposium on Nonlinear Dynamics, Shanghai, China, 2005.

7. A. Belmiloudi. Optimal control problems of nonlinear parabolic systems with logistic time-varying delays, International Workshop on Shape optimization in life sciences and environment, Toulouse, France, 2004.

Other articles (Technical reports and non-peer reviewed publications):

6. A. Belmiloudi, J-L. Merrien. New collocation methods for differential equations, Laboratory LANS publication, 2000 (18 pp).

5. A. Belmiloudi, F. Brossier. Numerical study of a control method computing an oceanic circulation from the observed surface pressure, Laboratory IRMAR publication, rapport 00-53, 2000, (25 pp).

4. A. Belmiloudi. Discretization of the perturbation of a given mean flow: convergence, stability and error estimates. Laboratory LANS publication, vol.66, 1996, (37 pp).

Habilitation to direct research :

3. Etudes théoriques et numériques de méthodes de contrôle optimal pour des équations primitives de l'océan et de l'atmosphère. Soutenue le 10 Juin 2002 (University de Rennes I). Jury : T. Colin (rapporteur), F.X. Le Dimet (rapporteur), E. Zuazua (rapporteur), G. Caloz, M. Crouzeix, M. Pierre, J.P. Yvon.

PhD Thesis (Allocataire moniteur ):

2. Développement d'une méthode de contrôle optimal pour un problème de type Navier-Stokes: Application à la modélisation des courants océaniques par assimilation de mesures altimétriques. Soutenue le 20 Janvier 1995, Mention Très honorable). Jury : J. Blum (rapporteur), O. Pironneau (rapporteur), F. Brossier, G. Caloz, M. Crepon, M. Crouzeix, J. Rappaz.

Master Thesis :

1. Discrétisation du problème PNS incompressible par une méthode d'éléments finis discontinus (P1-P2) [1]xQ1, 1991, Ecole Polytechnique Fédérale de Lausanne, EPFL (from Mathematics Institute of Computational Science and Engineering, Funded by Swiss metallurgical company Alusuisse-Lonza Group).

Activities of general interest:

and other activities as member of the Executive Committee of the Institute IRMAR (2012-2017), board member of IRMAR (2012-2017), member of the working group2 for HRS4R labeling of INSA-Rennes (2019-2020), responsibilities within the different recruitment commissions, scientific or organizing committee member of several international conferences,...

Editorial Topic Member of Axioms

Editorial board member of the following journals:

- Applied Mathematics

- Research & Reviews: Discrete Mathematical Structures

- International Journal of Advanced Mathematical Sciences

- Journal of Advances in Shell Programming

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Guest Editor of Special Issue « Biomathematics », Applied Mathematics, 2013.

N.B. I am also continuously reviewer of international research projects and scientific journals

Recent «ANR» Research Projects:


MIHMES :

Multi-scale modelling, from animal Intra-Host to Metapopulation, of mechanisms of pathogen spread to Evaluate control Strategies, ANR Bioinformatique, 2011-2017. (Partners : BioEpAR-INRA-Nantes, MIA-INRA-Jouy-en-Josas, MYRIADS-INRIA-Rennes, IRMAR-Rennes, EBEP-ANSESPloufragan, National Veterinary Institute SVA (Sweden)).

Hjnet :

Hamilton-Jacobi equations on heterogeneous structures and networks, ANR Blanc, 2012-2016. (Partners: IRMAR-Rennes, LJLL-Paris 7, CERMICS-ENPC, LMPT-Tours)

PhD students:

- Amer Rasheed : "Dendritic Solidification of Binary Mixtures of Metals under the action of Magnetic Field: Modeling, Mathematical and Numerical Analysis", PhD Thesis Defended October 14th, 2010. Actually A. Rasheed is "Assistant Professor" at LUMS Lahore University of Management Sciences, Department of Mathematics, Punjab, Pakistan.

- Maxime Penet: "Commande Prédictive nonlinéaire robuste par méthode de point selle en optimisation sous contraintes. Analyse de stabilité et application au diabète de type 1", PhD Thesis Defended October 10th, 2013. Actually M. Penet is Senior Research Engineer (before that he was Assistant Professor at Supelec).

- Samuel Corre: ''Méthodes de Boltzmann sur réseau pour la simulation numérique de certains systèmes d'advection-réaction-diffusion provenant de la physique et de la biologie, et analyse mathématique et numérique de problèmes issus du domaine biomédical cardio-vasculaire'', PhD Thesis Defended October 19th, 2018.

N.B. I have also supervised and co-supervised some thirty of Master students.

Education:

- Classes préparatoires aux grandes écoles (CPGE,) : MALHERBE High School in Caen; - Magistère of mathematics of Rennes and Master of mathematics and applications (Rennes1).