Abstract
In this paper, we study the invariance of Hamiltonian structure for control systems under the feedback and the time scale transformations. The control systems that have such structure are called “Hamiltonian control systems” and many practical control systems (e.g, Power systems and mechanical systems) can be regarded as Hamiltonian control systems under some assumptions.
In general, Hamiltonian structure is not preserved by the feedback and the time scale transformations. We give the classes of these transformations that preserve the Hamiltonian structure. By means of symplectic geometry, it is shown that the conditions are characterized as the exactness of cirtain one form.
Conversely, some of non-Hamiltonian control systems can be turned inso Hamiltonian systems by feedback. We specify the properties of such systems and call the problem “non-dissipative control”. For some simple cases, several conditions are given.
