Symmetries and conservation laws for Hamiltonian systems with inputs and outputs: A generalization of Noether's theorem

Abstract

The definition of symmetries and conservation laws for autonomous (i.e. without external (cases) Hamiltonian systems are generalized to Hamiltonian systems with inputs and outputs. It is shown that a symmetry implies the existence of a conservation law and vice versa; thereby generalizing Noether's theorem for autonomous Hamiltonian systems.