Abstract
In this paper, a normal form for nonlinear affine Hamiltonian control system is proposed. Its Hamiltonian is expressed as a polynomial of canonical momenta. Respondek proposed a similar normal form for usual affine nonlinear control system and gave a condition for the classification of nonlinear control systems by means of this normal form.
However, Hamiltonian control systems have several special structures and some attentions must be paid in appling above results to Hamiltonian control systems. We propose some normal forms corresponding to the dimension of the state space and the number of inputs. For each case, we give the conditions about state equivalence and weak feedback equivalence to the normal forms.
