Iterative learning control of Hamiltonian systems based on self-adjoint structure-I/O based optimal control

This paper reviews a novel iterative learning scheme to achieve optimal control for physical systems. It is shown that the variational systems of a class of Hamiltonian systems have self-adjoint state-space realizations, that is, the variational system and its adjoint have the same state-space realizations. This implies that the input-output mapping of the adjoint of the variational system of a given Hamiltonian system can be calculated by only using the input-output mapping of the original system. This property is applied to adjoint based iterative learning control with optimal control type cost functions. The proposed method is expected to be a basis for new I/O based optimal control.