Modeling, simulation and control of multi-physical systems: A change of
Speaker: Prof. Dr. Volker Mehrmann
Affiliation: Technische Universität Berlin, Germany,
Zoom link: https://fau.zoom.us/j/64838854576?pwd=SnN5U2EvMDJUNXVaZERnSHN1Q1crdz09
Meeting ID: 648 3885 4576 Passcode: 672077
Abstract: Most real world dynamical systems consist of subsystems from
different physical domains, modeled by partial-differential equations, ordinary
differential equations, algebraic equations, combined with input and output
connections. To deal with such complex systems, in recent years the class of
dissipative port-Hamiltonian (pH) systems has emerged as a very efficient new
modeling methodology. The main reasons are that the network based
interconnection of pH systems is again pH, Galerkin projection in PDE
discretization and model reduction preserve the pH structure and the physical
properties are encoded in the geometric properties of the flow as well as the
algebraic properties of the equations. Furthermore, dissipative pH system form a
very robust representation under structured perturbations and directly indicate
Lyapunov functions for stability analysis.
We discuss dissipative pH systems and describe, how many classical models can be
formulated in this class. We illustrate some of the nice algebraic properties,
including local canonical forms, the formulation of an associated Dirac
structure, and the local invariance under space-time dependent diffeomorphisms.
The results are illustrated with some real world examples.