Lecturer
Elarbi Achhab, Universite Chouaïb Doukkali, El Jadida, Morocco
Schedule and place
This 15-hour course will take place in 6 sessions over six days on October 9, 16, 23, 2018 and on November 6, 13, 20, 2018 at UCL, Bâtiment EULER, 4 Avenue Georges Lemaître, 1348 Louvain-la-Neuve (room A002, ground floor).
Schedule : 3 hours/day, from 09:30 to 12:45 (including a 15-minute coffee break) .
Travel instructions are available here.
Description
In many physical and economical phenomena, the evolution of some variables is modelled by partial differential equations or delay differential equations. These equations are mathematical models of systems called distributed parameter systems. Simple examples of these systems are the evolution of the temperature in a metal bar heated on its surface, the lateral displacement of a beam fixed in its ends, the concentrations in a tubular reactor, or the growth of a dynamic population. Partial differential equations and delay differential equations may be reformulated as differential equations on infinite dimensional spaces. These latter models are mathematically more interesting and more realistic in many applications, since they take into account the spatial aspect of the studied phenomena. The Systems analysis is based on concepts allowing a good comprehension of the behaviour of a system, and consequently a more efficient action or control. Among these concepts, controllability, observability, stability and stabilizability are certainly the most important. The aim of this course is to present a generalisation of such concepts and some results (linked to these concepts), including linear quadratic control, from classical linear systems theory to a large class of infinite dimensional systems. The state space considered approach is based on the strongly continuous semi-group theory. This useful mathematical tool allows a uniform, powerful and elegant treatment of the investigated questions. Some numerical issues of the approach will also be discussed.
List of topics :
- Strongly Continuous Semigroups
- The Cauchy problem in an infinite-dimensional Hilbert space
- Controllability and Observability analysis
- Stability, Stabilisability and Detectability
- Observers and Compensators
- Linear Quadratic Optimal Control problems
- Extensions to Nonlinear infinite-dimensional systems
- Applications to Tubular Chemical Reactors
Course material
To be determined
Evaluation
To be determined