Hamiltonian Realizations of Nonlinear Adjoint Operators

This paper addresses state-space realizations for nonlinear adjoint operators. In particular the relationship among nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are clarified. The characterization of controllability, observability and Hankel operators, and controllability and observability functions will be derived based on it. Furthermore a duality between the controllability and observability functions will be proven. The state-space realizations of such operators provide new insights to nonlinear control systems theory