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I started my academic journey by obtaining a Bachelor's degree in Pure Mathematics from the Lebanese University in Beirut, Lebanon in 2012. Following this, I pursued a Master's degree in Pure Mathematics at the same institution from 2012 to 2013, and then a Master's degree in Mathematics and Applications at the Université de Rennes 1 in Rennes, France, from 2013 to 2014. I was awarded an excellence scholarship from France to pursue this degree. Finally, I completed my Ph.D. in Mathematics from the Université de Bretagne Occidentale in Brest, France, from 2014 to 2017, with a focus on "Optimality conditions for optimal control problems and applications." After completing my Ph.D., I gained diverse professional experience in teaching and research across various worldwide institutions. I worked as a teaching assistant at the Université de Bretagne Occidentale in Brest, France in 2017, where I taught, in French, vector calculus and complex analysis to undergraduate mathematicians. Following this, I worked as a research and teaching assistant at the Université de Paris Nanterre from 2017 to 2018, where I pursued my research on control systems featuring uncertainties, with applications to aerospace engineering. I also lectured, in French, on topics such as Statistics applied to Business Management, Statistics methods, Optimization, and Measure Methodology. In 2018, I moved to Portugal and worked as a postdoctoral research fellow at the Department of Electrical Engineering at the Universidade do Porto, where I worked on implementing computational methods to solve optimal control problems subject to constraints and applying it to autonomous underwater vehicles. Since then, I have been working as a junior researcher at the same department, where I focus on building a strong research portfolio in areas related to control theory, optimal control, nonsmooth analysis, computational methods, and designing control techniques to model constrained structured crowd motion management problem. In addition to my research, I have also lectured on Numerical Methods and Algebra in Portuguese at the same department. During my academic career, I have made significant contributions to the field of mathematics by publishing a wide range of research papers, including a doctoral thesis, 15 articles in peer-reviewed journals, 4 conference proceedings, and two book chapters. In addition to my publications, I have also actively shared my research with the wider academic community by presenting at various international conferences. I was invited to speak at 10 congresses, and I gave presentations at 13 other conferences. Over the past years, I have established a strong reputation in the academic community for my contributions to research, particularly through my involvement in visiting positions and mentoring. Between September 2015 and June 2016, and after receiving three mobility grants from France and Italy, I worked, as a visiting Ph.D. student at the Università di Padova in Italy, on a new class of state-constrained control systems. In December 2019, during a collaboration stay as an invited researcher at Université de Bretagne Occidentale in Brest, France, I co-led a research project studying optimal control problems where the model design takes into account uncertainties and state constraints. Furthermore, between October 2022 and January 2023, during a stay at the Universidad Autónoma Metropolitana in Mexico City, I played a leading role in a collaborative project on sweeping process problems subject to mixed constraints. During my visit, I also delivered seminars to undergraduate students. Additionally, in February 2023, I was invited as a lecturer at a PhD program at the Indian Institute of Technology in Mumbai, India. In that program, I taught a course on how to model constrained structured crowd motion management problem, using control theory and advanced optimization techniques. I have provided also feedback on the students' research work.
Identification

Personal identification

Full name
Nathalie Khalil

Citation names

  • Khalil, Nathalie

Author identifiers

Ciência ID
2A11-A1FC-67CA
ORCID iD
0000-0002-4761-5868

Websites

Knowledge fields

  • Exact Sciences - Mathematics - Pure Mathematics
  • Exact Sciences - Mathematics - Applied Mathematics

Languages

Language Speaking Reading Writing Listening Peer-review
English Advanced (C1) Advanced (C1) Advanced (C1) Advanced (C1)
French Proficiency (C2) Proficiency (C2) Proficiency (C2) Proficiency (C2) Proficiency (C2)
Italian Intermediate (B1) Intermediate (B1) Intermediate (B1) Intermediate (B1)
Portuguese Upper intermediate (B2) Upper intermediate (B2) Upper intermediate (B2) Advanced (C1) Upper intermediate (B2)
Arab (Mother tongue)
Spanish; Castilian Intermediate (B1) Intermediate (B1) Intermediate (B1) Intermediate (B1) Intermediate (B1)
Education
Degree Classification
2017/11/17
Concluded
Ph.D. (Doctor of Philosophy)
Major in Mathematics and its Applications
Universite de Bretagne Occidentale Département de Mathématiques, France
"Optimality conditions for optimal control problems and applications" (THESIS/DISSERTATION)
N/A
2014/07
Concluded
Master 2 (MSc) (Master)
Major in Mathematics and Applications; Fundamental Mathematics
Université de Rennes 1, France
"Normality conditions for problems in Calculus of Variations subject to state constraints." (THESIS/DISSERTATION)
2013/07
Concluded
Master 1 (MSc) (Master)
Major in Pure Mathematics
Université Libanaise Faculté des Sciences 2, Lebanon
"N/A" (THESIS/DISSERTATION)
N/A
2012/07
Concluded
Bachelor (BSc) (Bachelor)
Major in Pure Mathematics
Université Libanaise Faculté des Sciences 2, Lebanon
"N/A" (THESIS/DISSERTATION)
N/A
Affiliation

Science

Category
Host institution
Employer
2018/12/20 - Current Researcher (Research) Universidade do Porto Faculdade de Engenharia, Portugal
Universidade do Porto Faculdade de Engenharia, Portugal
2022/10/06 - 2023/01/31 Visiting Researcher (Research) Universidade do Porto Faculdade de Engenharia, Portugal
Universidad Autónoma Metropolitana Departamento de Matemáticas, Mexico
2019/12/03 - 2019/12/07 Visiting Researcher (Research) Universidade do Porto Faculdade de Engenharia, Portugal
Universite de Bretagne Occidentale Département de Mathématiques, France
2018/09/03 - 2018/12/19 Postdoc (Research) Universidade do Porto Faculdade de Engenharia, Portugal
Universidade do Porto Faculdade de Engenharia, Portugal
2017/09/01 - 2018/08/31 Research Assistant (Research) Université Paris-Nanterre UFR Sciences économiques gestion mathématiques informatique, France
Université Paris-Nanterre UFR Sciences économiques gestion mathématiques informatique, France
2015/09/01 - 2016/06/30 Visiting Researcher (Research) Universite de Bretagne Occidentale Département de Mathématiques, France
Università degli Studi di Padova Dipartimento di Matematica Tullio Levi-Civita, Italy

Teaching in Higher Education

Category
Host institution
Employer
2023/02/13 - 2023/02/17 Tutor (University Teacher) Universidade do Porto Faculdade de Engenharia, Portugal
Indian Institute of Technology Bombay, India
2021/10/01 - 2022/01/31 Assistant (University Teacher) Universidade do Porto Faculdade de Engenharia, Portugal
Universidade do Porto Faculdade de Engenharia, Portugal
2017/09/01 - 2018/08/31 Assistant (University Teacher) Université Paris-Nanterre UFR Sciences économiques gestion mathématiques informatique, France
Université Paris-Nanterre UFR Sciences économiques gestion mathématiques informatique, France
2017/01/01 - 2017/06/01 Assistant (University Teacher) Universite de Bretagne Occidentale Département de Mathématiques, France
Universite de Bretagne Occidentale Département de Mathématiques, France
Projects

Grant

Designation Funders
2018/09/03 - 2018/12/20 STRIDE
Post-doc Fellow
Universidade do Porto Faculdade de Engenharia, Portugal
Comissao de Coordenacao e Desenvolvimento Regional do Norte
Concluded
Outputs

Publications

Book chapter
  1. Chertovskih, Roman; Khalil, Nathalie; Lobo Pereira, Fernando. "Time-optimal control problem with state constraints in a time-periodic flow field". In International Conference on Optimization and Applications OPTIMA 2019: Optimization and Applications, 340-354. Springer International Publishing, 2020.
    Published • 10.1007/978-3-030-38603-0_25
  2. Bettiol, Piernicola; Khalil, Nathalie. "9. Non-degenerate forms of the generalized Euler–Lagrange condition for state-constrained optimal control problems". In Variational Methods, 295-313. De Gruyter, 2016.
    Published • 10.1515/9783110430394-009
Conference paper
  1. Khalil, Nathalie; Lobo Pereira, Fernando. "Necessary conditions of optimality in the Gamkrelidze's form for general dynamic control systems with state and mixed constraints". Paper presented in 2021 American Control Conference (ACC), New Orleans, LA, 2021.
    Published • 10.23919/acc50511.2021.9483201
  2. Khalil, Nathalie; Lobo Pereira, Fernando. "A framework for the control of bilevel sweeping processes". Paper presented in 2019 IEEE 58th Conference on Decision and Control (CDC), Nice, 2019.
    Published • 10.1109/cdc40024.2019.9029270
  3. Lobo Pereira, Fernando; Khalil, Nathalie; F51A-0488-0C69. "Optimal path planning of AUVs operating in flows influenced by tidal currents". Paper presented in PhysCon2019, Moscovo, 2019.
  4. Chertovskih, Roman; Karamzin, Dmitry; Khalil, Nathalie; Lobo Pereira, Fernando. "Path-constrained trajectory time-optimization in a three-dimensional steady flow field". Paper presented in 2019 18th European Control Conference (ECC), Naples, 2019.
    Published • 10.23919/ecc.2019.8796083
  5. Chertovskih, Roman; Karamzin, Dmitry; Khalil, Nathalie; Lobo Pereira, Fernando. "An indirect numerical method for a time-optimal state-constrained control problem in a steady two-dimensional fluid flow". Paper presented in 2018 IEEE/OES Autonomous Underwater Vehicle Workshop (AUV), Porto, 2018.
    Published • 10.1109/auv.2018.8729750
Journal article
  1. Khalil, Nathalie; Karla L. Cortez; António Pedro Aguiar. Corresponding author: Khalil, Nathalie. "A Non-Regular Mixed Constrained Problem Involving Sweeping Processes". IEEE Control Systems Letters 7 (2023): 3860-3865. https://doi.org/10.1109/LCSYS.2023.3343989.
    Published • 10.1109/LCSYS.2023.3343989
  2. Bettiol, Piernicola; Khalil, Nathalie. "Average cost minimization problem subject to state constraints". SIAM Journal on Control and Optimization (SICON) (2023):
    Under revision
  3. Cortez, Karla L.; Khalil, Nathalie; Solis, Julio E.. "A sweeping process control problem subject to mixed constraints". IFAC PapersOnLine 56 2 (2023): 1223-1228. https://doi.org/10.1016/j.ifacol.2023.10.1741.
    Open access • Published
  4. Colombo, Giovanni; Khalil, Nathalie; Rampazzo, Franco. "State constraints, higher order inward pointing conditions, and neighboring feasible trajectories". SIAM Journal on Control and Optimization 60 6 (2022): 3326-3357. http://dx.doi.org/10.1137/21m1468796.
    Published • 10.1137/21m1468796
  5. Khalil, Nathalie; Lobo Pereira, Fernando. "A Maximum Principle for state-constrained optimal sweeping control problems". IEEE Control Systems Letters 7 (2022): 43-48. https://doi.org/10.1109/LCSYS.2022.3186615.
    Published • 10.1109/LCSYS.2022.3186615
  6. Fernando Lobo Pereira; Nathalie T. Khalil. "A Maximum Principle for a Time-Optimal Bilevel Sweeping Control Problem". Journal of Optimization Theory and Applications 192 3 (2022): 1022-1051. http://dx.doi.org/10.1007/s10957-022-02004-3.
    Published • 10.1007/s10957-022-02004-3
  7. Cao, Tan H. ; Khalil, Nathalie; Lobo Pereira, Fernando; Mordukhovich, Boris S.; Nguyen, Dao. "Crowd motion paradigm modeled by a bilevel sweeping control problem". IEEE Control Systems Letters 6 (2021): 385-390. https://doi.org/10.1109/LCSYS.2021.3077446.
    Published • 10.1109/LCSYS.2021.3077446
  8. Chertovskih, Roman; Karamzin, Dmitry; Khalil, Nathalie; Lobo Pereira, Fernando. "An indirect method for regular state-constrained optimal control problems in flow fields". IEEE Transactions on Automatic Control 66 2 (2021): 787-793. http://dx.doi.org/10.1109/tac.2020.2986179.
    Published • 10.1109/tac.2020.2986179
  9. Cao, Tan H. ; Khalil, Nathalie; Lobo Pereira, Fernando; Boris S. Mordukhovich; Nguyen, Dao; Nguyen, Trang. "Optimization of controlled free-time sweeping processes with applications to marine surface vehicle modeling". IEEE Control Systems Letters 6 (2021): 782-787. https://doi.org/10.1109/LCSYS.2021.3085900.
    Published • 10.1109/LCSYS.2021.3085900
  10. Chertovskih, Roman; Karamzin, Dmitry; Khalil, Nathalie; Lobo Pereira, Fernando. "Regular path-constrained time-optimal control problems in three-dimensional flow fields". European Journal of Control 56 (2020): 98-106. http://dx.doi.org/10.1016/j.ejcon.2020.02.003.
    Published • 10.1016/j.ejcon.2020.02.003
  11. Khalil, Nathalie; Lobo Pereira, Fernando. "Necessary conditions of optimality in the Gamkrelidze's form for state constrained problems with differential inclusion". IEEE Control Systems Letters 4 4 (2020): 958-963. http://dx.doi.org/10.1109/lcsys.2020.2997672.
    Published • 10.1109/lcsys.2020.2997672
  12. Khalil, Nathalie; Lobo Pereira, Fernando. "Necessary conditions of optimality for a time-optimal bi-level sweeping control problem". IFAC-PapersOnLine 53 2 (2020): 6831-6836. http://dx.doi.org/10.1016/j.ifacol.2020.12.338.
    Published • 10.1016/j.ifacol.2020.12.338
  13. Bettiol, Piernicola; Khalil, Nathalie. "Necessary optimality conditions for average cost minimization problems". Discrete & Continuous Dynamical Systems - B 24 5 (2019): 2093-2124. http://dx.doi.org/10.3934/dcdsb.2019086.
    Published • 10.3934/dcdsb.2019086
  14. Khalil, Nathalie; Lopes, Sofia. "Normality of necessary optimality conditions for calculus of variations problems with state constraints". Set-Valued and Variational Analysis 27 2 (2019): 503-521. http://dx.doi.org/10.1007/s11228-018-0498-z.
    Published • 10.1007/s11228-018-0498-z
  15. Bettiol, Piernicola; Khalil, Nathalie; Vinter, Richard B.. "Normality of generalized euler-lagrange conditions for state constrained optimal control problems". Journal of Convex Analysis 23 1 (2016): 291-311. http://www.scopus.com/inward/record.url?eid=2-s2.0-85028810464&partnerID=MN8TOARS.
    Published
Activities

Oral presentation

Presentation title Event name
Host (Event location)
2023/12 Crowd motion paradigm modeled by a bilevel sweeping control problem Workshop on Optimal Control Theory and Related Fields
University of Santa Maria (Valparaiso, Chile)
2023/08 Crowd motion paradigm modeled by a bilevel sweeping control problem International Conference on Bilevel Optimization
University of Southampton (Southampton, United Kingdom)
2023/07 A sweeping process control problem subject to mixed constraints International Federation of Automatic Control World Congress (IFAC)
(Yokohama, Japan)
2022/12 State-constrained sweeping control problems 2022 Control and Decision Conference (CDC)
(Cancun, Mexico)
2022/05 State-constrained sweeping control problems French German Portuguese Conference on Optimization
(Porto, Portugal)
2022/05 State-constrained average cost problems French German Portuguese Conference on Optimization
(Porto, Portugal)
2021/12 Crowd motion paradigm modeled by a bilevel sweeping control problem 2021 Control and Decision Conference (CDC) (virtual)
(Austin, Texas, United States)
2021/12 Optimization of controlled free-time sweeping processes with applications to marine surface vehicle modeling 2021 Control and Decision Conference (CDC)
( Austin, Texas, United States)
2021/11 Crowd motion paradigm modeled by a bilevel sweeping control problem Seminar, Universidad Autónoma Metropolitana, Iztapalapa México (virtual)
(Mexico City, Iztapalapa, Mexico)
2021/05 Necessary conditions of optimality in the Gamkrelidze's form for general dynamic control systems with state and mixed constraints 2021 American Control Conference (ACC)
(New Orleans, Louisiana, United States)
2020/11 A novel paradigm for bilevel sweeping control problems Seminar of the Systems and Control Group, University of Aveiro, Portugal
(Aveiro, Portugal)
2020/07 Necessary conditions of optimality for a time-optimal bilevel sweeping control problem 21st IFAC World Congress (virtual)
(Berlin, Germany)
2019/12 A framework for the control of bilevel sweeping processes 2019 IEEE 58th Conference on Decision and Control (CDC)
(Nice, France)
2019/12 Some questions on bilevel optimal control sweeping process problems Seminar, Department of Mathematics, Brest France
(Brest, France)
2019/09 Violated classical inward pointing condition Control of State-Constrained Dynamical Systems
(Valparaiso, Chile)
2019/08 Numerical solutions for regular state-constrained optimal control problems via an indirect approach International Conference on Continuous Optimization
(Berlin, Germany)
2019/06 Path-constrained trajectory time-optimization in a three-dimensional steady flow field 2019 European Control Conference (ECC'19)
(Naples, Italy)
2019/04 On the development of a bilevel optimal control sweeping process problem Lebanese International Conference on Mathematics and Applications
(Beirut, Lebanon)
2018/11 An indirect numerical method for a time-optimal state-constrained control problem in a steady two-dimensional fluid flow (Poster) IEEE OES Autonomous Underwater Vehicle Symposium
(Porto, Portugal)
2018/07 Average cost minimization problems: necessary optimality conditions 14th Viennese Conference on Optimal Control and Dynamic Games
(Vienna, Austria)
2018/04 Necessary optimality conditions for average cost minimization problems Training School on Optimal Control Theory and Mosquito Control Strategies: Mathematical Modelling in Epidemiology and Control,
(Aveiro, Portugal)
2017/09 Necessary optimality conditions for average cost minimization problems Control of State Constrained Dynamical Systems
(Padua, Italy)
2016/06 Normality of generalized Euler-Lagrange condition for nonsmooth state constrained optimal control problems Recent Trends in Differential Equations
(Aveiro, Portugal)
2016/03 When the generalized Euler-Lagrange condition is normal for nonsmooth state constrained optimal control problems? Journées MODE, Société de mathématiques appliquées industrielles
ENSEEIHT (Toulouse, France)
2015/09 Normality of necessary conditions for calculus of variations problems with state constraints Symposium on Nonlinear Analysis
(Torun, Poland)
2014/11 Necessary conditions in normal form for calculus of variations problems (Poster) Special Semester on New Trends in Calculus of Variations
(Linz, Austria)

Course / Discipline taught

Academic session Degree Subject (Type) Institution / Organization
2023/02/13 - 2023/02/17 In February 2023, I was invited to give a lecture at a PhD program at the Institute of Technology in Mumbai, India. During my time there, I taught the PhD students how to model the operation of crowd motion populations with a defined structure using control theory and advanced optimization techniques, while also providing constructive feedback on their research work. Optimal control and application to crowd motion problems (Doctor of Philosophy) Indian Institute of Technology Bombay, India
2021/10/01 - 2022/01/31 In parallel with my research, in 2021, I lectured, in Portuguese, a course on Numerical Methods at the department of Electrical Engineering of Universidade do Porto, Portugal, aiming second year undergraduate. Numerical Methods (Licenciatura) Universidade do Porto Faculdade de Engenharia, Portugal
2017/09/01 - 2018/08/31 After concluding my Ph.D., I was contracted as a teaching and research assistant where I taught, in French, Statistics applied to Business Management to 3rd-year undergraduates in Economics. Statistics applied to Business Management (Licence) Université Paris-Nanterre UFR Sciences économiques gestion mathématiques informatique, France
2017/09/01 - 2018/08/31 After concluding my Ph.D., I was contracted as a teaching and research assistant where I taught, in French, Statistics methods to 2nd-year undergraduates in Economics. Statistics methods (Licence) Université Paris-Nanterre UFR Sciences économiques gestion mathématiques informatique, France
2017/09/01 - 2018/08/31 After concluding my Ph.D., I was contracted as a teaching and research assistant where I taught, in French, Statistics 1 to 1st-year undergraduates in Economics. Statistics 1 (Licence) Université Paris-Nanterre UFR Sciences économiques gestion mathématiques informatique, France
2017/09/01 - 2018/08/31 After concluding my Ph.D., I was contracted as a teaching and research assistant where I taught, in French, Optimization 1st-year undergraduates in Engineering. Optimization (Licence) Université Paris-Nanterre UFR Sciences économiques gestion mathématiques informatique, France
2017/09/01 - 2018/08/31 After concluding my Ph.D., I was contracted as a teaching and research assistant where I taught, in French, Measure Methodology to 1st-year undergraduates in Psychology. Measure Methodology (Licence) Université Paris-Nanterre UFR Sciences économiques gestion mathématiques informatique, France
2017/01/01 - 2017/06/30 In 2017, while concluding my Ph.D., I worked as a teaching assistant, where I lectured, in French, on vector calculus and complex analysis to a group of undergraduates in mathematics. Vector calculus and complex analysis (Licence) Universite de Bretagne Occidentale Département de Mathématiques, France
Distinctions

Award

2013 Excellency prize (rank 1/24 in the Master 1)
Université Libanaise Faculté des Sciences 2, Lebanon
2012 Excellency prize (rank 2/134 in the BSc degree)
Université Libanaise Faculté des Sciences 2, Lebanon

Other distinction

2023 Travel Grant
University of Southampton, United Kingdom
2020 Accreditation for Tenure-Eligible Lecturer
Agencia para la Calidad del Sistema Universitario de Cataluna, Spain
2019 Qualification `Maître de Conférences' (Associate Professor)
French National University Council (CNU), France
2019 Travel Grant
The Sixth International Conference on Continuous Optimization, Germany
2018 Qualification `Maître de Conférences' (Associate Professor)
French National University Council (CNU), France
2018 Trainee Grant
COST Action CA16227 European Cooperation of Science and Technology, Portugal
2018 Postdoctoral Research Grant
Project STRIDE, ref. NORTE-01-0145-FEDER-000033, Portugal
2016 Mobility grant (1 month)
Department of Mathematics, University of Padua, Italy
2016 Mobility grant for Ph.D. students (2 months)
Université de Bretagne Loire, France
2015 Mobility grant for Ph.D. students (3 months)
Université de Bretagne Occidentale, France
2014 Ph.D. Scholarship
Université de Bretagne Occidentale, France
2013 Master 2 excellency scholarship
Henri Lebesgue Research Center,, France