On Structure Preserving Transformations in Hamiltonian Control Systems

Abstract

Hamiltonian control systems with natural output in the sense of [12] are considered. We investigate state-dependent co-ordinate transformations in the space of controls $u$ and observables $y$ which preserve the Hamiltonian structure.These transformations can be characterized and constructed by canonical transformations in the ($y,u$)-pace.The results generalize known statements on Hamiltonian systems affine in the control and hold for general gradient-like control systems as well.