Course on Control of PDEs under Uncertainty


From January 14th until January 16th, 2019
Turing Room – Faculty of Engineering 2. floor, University of Deusto

Jesús Martínez-Frutos and Francisco Periago

Politecnic University of Cartagena, Spain

Abstract:
This 10 hours course will offer a direct and comprehensive introduction to the basic theoretical and numerical concepts in the emergent field of optimal control of partial differential equations (PDEs) under uncertainty. The main objective of the course is to provide graduate students and researchers with a smooth transition from optimal control of deterministic PDEs to optimal control of random PDEs. Coverage includes uncertainty modelling in control problems, variational formulation of PDEs with random inputs, robust and risk averse formulations of optimal control problems, existence theory and numerical resolution methods. The exposition will be focused on running the whole path starting from uncertainty modelling and ending in the practical implementation of numerical schemes for the numerical approximation of the considered problems. To this end, a selected number of illustrative examples will be analysed in detail.

The course closely will follow the book BCAM SpringerBriefs in Mathematics, 2018. A preliminary version of the book as well as MatLab codes that will be used in the practical lessons can be downloaded from here . In addition, the final version of the book can be found here.

*Note – Practices with MatLab: Attendants must carry a laptop with MatLab installed in order to carry on with the practical seminars. The day and times of the those are stated in the table.

Timetable Monday 14th Tuesday 15th Wednesday 16th
9:30 – 11:00 F. Periago: Introduction. Mathematical Preliminaires. Numerical Approximation of random fields. J. Martínez: Numerical approximation of robust optimal control problems by using stochastic collocation methods(Part I).
Practice with MatLab*.
J. Martínez and F. Periago will be at students’ disposal for tutoring from 9:00 to 11:00.
11:00 – 11:45 J. Martínez: Numerical approximation of random fields(Part I).
Practice with MatLab*.
J. Martínez: Numerical approximation of robust optimal control problems by using stochastic collocation methods(Part II).
Practice with MatLab*.
11:45 – 12:15 Coffee Break Coffee Break
12:30 – 13:30 J. Martínez: Numerical approximation of random fields(Part II).
Practice with MatLab*.
F. Periago: Numerical approximation of risk averse optimal control problems by using stochastic expansion methods.
13:30 – 15:00 Lunch Break Lunch Break
15:00 – 16:00 F. Periago: Variational formulation of random PDEs. Existence of solutions for robust and risk averse control problems. F. Martínez: Numerics for risk averse.
Practice with MatLab*.
16:00 – 17:30 F. Periago: Numerical approximation of robust optimal control problems by using stochastic collocation methods.