Abstract
This paper proposes a reduction of input/output variables used for boundary control and observation of energy in bi-Hamiltonian systems. The variables can be derived from a power balance equation defined by a Poisson bracket for infinite dimensional Hamiltonian systems. There is an infinite number of the balance equations of conserved quantities, i.e., Hamiltonians associated with infinite symmetry in bi-Hamiltonian systems. Hence, we can choose an appropriate input/output pair from the set of the balance equations.
