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.

Assessment method

Report, seminars, and oral presentations.

Sources, references and any support material

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

Anglais