ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 102 Hours of tutorials: 6 Expository Class: 18 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Applied Mathematics, External department linked to the degrees
Areas: Applied Mathematics, Área externa M.U en Matemática Industrial
Center Faculty of Mathematics
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
Introduce the student in the mathematical modeling and in the numerical resolution of different problems of optimization and optimal control that arise in the field of engineering and industry.
Part I: Numerical Methods in Optimization (21h)
- Introduction (3h) – Practical examples with MATLAB
- Global and multi-objective optimization (3h) – Practical examples with MATLAB
- Optimization applied to mathematical modelling (3h)
- Practical case of industrial interest (3h)
- AMIGO2 sofware as a tool for dynamical systems optimization (9h)
Part II: Optimal Control (21h)
- Introduction: Constrained optimization and control (4h)
- Optimal control problems governed by discrete systems (5h)
- Optimal control problems governed by ordinary differential equations (8h)
- Optimal control problems governed by partial differential equations: elliptic and parabolic systems (4h)
Basic references on optimization:
D. Bertsekas (1999): Nonlinear Programming, Athena Scientific.
Basic references on control:
D. Bertsekas (2005): Dynamic Programming and Optimal Control, Athena Scientific.
Complementary references on optimization:
J. Nocedal, S.J. Wright (2006): Numerical Optimization, Springer.
E. Walter, L. Pronzato (1997): Identification of parametric models from experimental data. Springer.
Complementary references on control:
E. Cerdá Tena (2001): Optimización dinámica, Prentice Hall.
K. Ogata (2010): Ingeniería de control moderna, Pearson-Prentice-Hall.
E. Trelat (2007): Contrôle optimal, Notes de cours, Master de Mathématiques, Univ. De Orléans.
F. Tröltzsch (2010): Optimal Control of Partial Differential Equations: Theory, Methods and Applications, AMS (Graduate Studies in Mathematics, Vol 112).
Basic:
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- CG1: To have knowledge that provide a basis or opportunity for originality in developing and / or applying ideas, often within a research context, knowing how to translate industrial needs in terms of R & D in the field of mathematics Industrial.
- CG4: To have the ability to communicate the findings to specialist and non-specialist audiences in a clear and unambiguous way.
- CG5: To have the appropriate learning skills to enable them to continue studying in a way that will be largely self-directed or autonomous, and also to be able to successfully undertake doctoral studies.
Specific:
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- CE2: To model specific ingredients and make appropriate simplifications in the model to facilitate their numerical treatment, maintaining the degree of accuracy, according to previous requirements.
- CE3: To determine if a model of a process is well made and well mathematically formulated from a physical standpoint.
- CE4: To be able to select a set of numerical techniques, languages and tools, appropriate to solve a mathematical model.
- CE5: To be able to validate and interpret the results, comparing them with visualizations, experimental measurements and functional requirements of the physical engineering system.
- CE6: To be able to extract, using different analytical techniques, qualitative as well as quantitative information of the models.
Lectures where the contents are developed and some examples and exercises are solved. Through this methodology the competencies CG1, CG4, CG5, CE2, CE3, CE4, CE5 and CE6 are developed.
The work in the classroom should be completed with student personal work in order to get a good understanding of the subject. Through this methodology the competencies CG1, CE4, CE5 and CE6 are developed.
The Optimization part and the Control part are evaluated separately and the average of both is done.
The evaluation of each of the parts will be carried out based on homework assigments proposed throughout the course. The proposed tasks will include problem solving, implementation of numerical methods and the use of specific software (CE2, CE3, CE4, CE5, CE6).
To complete the evaluation process, students will be called to a personal meeting.
For cases of fraudulent performance of exercises or tests, the provisions of the “Normativa de avaliación do rendemento académico dos estudantes e de revisión de cualificacións” may be applied.
- Lectures = 42 hours
- Personal work = 108 hours.
- Participatory attendance to class
- Daily study of the subject
- Realization of the exercises and proposed works.
Jeronimo Rodriguez Garcia
Coordinador/a- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813355
- jeronimo.rodriguez [at] usc.es
- Category
- Professor: Temporary PhD professor
| Wednesday | |||
|---|---|---|---|
| 09:00-10:00 | Grupo /CLE_01 | Spanish | Computer room 5 |
| Friday | |||
| 09:00-11:00 | Grupo /CLE_01 | Spanish | Computer room 5 |