Infinite-dimensional port-Hamilton Systems
Modeling of dynamical systems with a spatial component leads to lumped parameter systems, when the spatial component may be denied, and to distributed parameter systems otherwise. The mathematical model of distributed parameter systems will be a partial differential equation. Examples of dynamical systems with a spatial component are, among others, temperature distribution of metal slabs or plates, and the vibration of aircraft wings.
In this talk we will study distributed parameter port-Hamiltonian systems. This class contains the above mentioned examples. The norm of such a system is given by the energy (Hamiltonian) of the system. This fact enables us to show relatively easy the existence and stability of solutions. Further, it is possible to determine which boundary variables are suitable as inputs and outputs, and how the system can be stabilized via the boundary.
Birgit Jacob, Universität Wuppertal, Germany