Controlled invariance for hamiltonian systems

A notion of controlled invariance is developed which is suited to Hamiltonian control systems. This is done by replacing the controlled invariantdistribution, as used for general nonlinear control systems, by the controlled invariantfunction group. It is shown how Lagrangian or coisotropic controlled invariant function groups can be made invariant by static, respectively dynamic, Hamiltonian feedback. This constitutes a first step in the development of a geometric control theory for Hamiltonian systems that explicitly uses the given structure.