Summer School of Automatic Control - Grenoble 2012

Modeling and Control of Distributed Parameter Systems

Context and motivations

Distributed parameter systems
are an area of research which appears in the 1960s. Their interests
appear naturally because they are found in many situations, for
example, in the modeling of traffic, plasma, chemical reactors, and in
fluid mechanics. In this school, we will focus more specifically to
issues of modeling and control of distributed parameter systems. Unlike
conventional systems, the most useful models are written in terms of Partial Differential Equations (PDE)
to reflect the distributed nature of the parameters. The issue of
modeling is already interesting and difficult, especially for physical
systems where the control and the sensors are only located at the edge
of the field.

Controllability and Observability are difficult concepts and relevant to this type of systems described mostly by a single PDE. The study of these questions involves mathematical techniques and sophisticated automatic control tools. Control of these systems allows the introduction of a loop (and hence coupling) which makes the study of the system even more complicated. There are already many mathematical tools to study and to formalize certain types of simple controls (even if there are open questions). The calculation of more sophisticated controls is difficult and remains a very current theory for distributed parameter systems.

In particular, the lectures of the school deal with Controllability and Observability are difficult concepts and relevant to this type of systems described mostly by a single PDE. The study of these questions involves mathematical techniques and sophisticated automatic control tools. Control of these systems allows the introduction of a loop (and hence coupling) which makes the study of the system even more complicated. There are already many mathematical tools to study and to formalize certain types of simple controls (even if there are open questions). The calculation of more sophisticated controls is difficult and remains a very current theory for distributed parameter systems.

- Partial Differential Equation,
- Port Hamiltonian System,
- System of Conservation laws,
- Nonlinear equation,
- Delay
- Fusion,
- Hyperbolic system, …