On structure preserving transformations in Hamiltonian control systems (Q1188362)

Summary: Hamiltonian control systems with natural output in the sense of \textit{A. J. van der Schaft} [System theoretic description of physical systems (1984; Zbl 0546.93001)] are considered. We investigate state-dependent coordinate 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 \((y,u)\)-space. The results generalize known statements on Hamiltonian systems affine in the control and hold for general gradient-like control systems as well.