Port-representation of bi-Hamiltonian structure for infinite-dimensional symmetry

In this paper, the port-representation of conservation laws is extended to a wider class of symmetries, the infinite-dimensional symmetry expressed by the bi-Hamiltonian system. It is known from Noether´s theorem that a conservation law is associated with an invariant property called a symmetry. In certain cases, the symmetry appears in a system as a hidden infinite-dimensional structure. Such a structure can be defined by using a recursive operator consisting of a Hamiltonian pair and is called a bi-Hamiltonian structure. The bi-Hamiltonian structure induces a hierarchical set of conservation laws. This concept can be used for reducing a system possessing a bi-Hamiltonian structure to simpler port-representations of the conservation laws. Finally, a boundary observer for symmetry destruction is shown.