Course 2022-2023

Functional approach to dynamical systems [SMATM122]

  • 6 credits
  • 30h+30h
  • 2nd quarter
Language of instruction: French / Français

Learning outcomes

This course objective is to help students to acquire the concepts and main results as well as the methods of the theory of infinite-dimensional dynamical systems (distributed parameter systems). The various aspects of studying such systems (modelling, analysis, design of stabilizing control laws, simulation) are discussed in lectures, tutorials and personal work.

Content

Study of linear differential equations where the state variable evolves in a Banach or Hilbert space of infinite dimension. Generalisation of the concept of matrix exponential. The homogeneous and controlled Cauchy problems. Study of the stability, the controllability and the observability of such systems. Design of stabilizing control laws (PI regulator, Linear-Quadratic (LQ) control laws, ...). Applications to partial differential equations (PDE), such as the heat equation, the vibrating string or reaction-convection-diffusion equations.


Co-requisites

Systèmes, contrôle et optimisation [SMATM101]

Teaching methods

Lectures, exercices, and personnal projects.

Evaluations

Report, seminars, and oral presentations.

Recommended readings

Curtain R. and Zwart H., Introduction to Infinite-Dimensional Systems Theory: A State-Space Approach, volume 71 of Texts in Applied Mathematics book series, Springer New York, United States, 2020.

Jacob B. and Zwart H., Linear port-Hamiltonian systems on infinite-dimensional spaces, Birkhäuser, Basel, 2012.

Lasota, A., & Mackey, M. C., Chaos, fractals, and noise: stochastic aspects of dynamics (Vol. 97). Springer Science & Business Media, 2013.

Bátkai, András, M. Kramar Fijavž, and Abdelaziz Rhandi. Positive operator semigroups. Birkhauser Verlag Ag, 2017.

 

Language of instruction

French / Français

Location for course

NAMUR

Organizer

Faculté des sciences
Rue de Bruxelles, 61
5000 NAMUR

Degree of Reference

Master's Degree