Speaker
Description
Infinite-dimensional Hamiltonian systems offer an energy-based approach to model complex physical phenomena, appearing e.g. in fluid dynamics or mechanics. They are defined via a formally skew-symmetric Hamiltonian operator and are associated with a non-quadratic Hamiltonian energy function. In various applications, however, the Hamiltonian function depends on spatial derivatives of the state. This characteristic prevents a direct description of the system dynamics using geometric structures, as in the framework of boundary port-Hamiltonian systems. The underlying reason is that the boundary port variables, which are necessary to derive an energy balance, are not straightforward to deduce due to the strong intertwinement of energy-storing components modeled by a Stokes-Lagrange structure, and energy-routing elements modeled by a Stokes-Dirac structure.
In this talk, we propose a method to reformulate infinite-dimensional Hamiltonian systems on one-dimensional spatial domains as boundary port-Hamiltonian systems by embedding the system into the (higher-dimensional) jet space, that is, augmenting the state variable with its spatial derivatives. This reformulation enables the application of the comprehensive theory of boundary port-Hamiltonian systems including control access.
