ADJOINT AND HAMILTONIAN INPUT-OUTPUT DIFFERENTIAL-EQUATIONS

Based on recent developments in the theory of variational and Hamilton ian control systems by Crouch and van der Schaft, this paper answers t wo questions: given an input-output differential equation description of a nonlinear system, what is the adjoint variational system in input -output differential form and what are the conditions for the system t o be Hamiltonian, i.e., such that the variational and the adjoint vari ational systems coincide? This resulting set of conditions is then use d to generalize classical conditions such as the well-known Helmholtz conditions for the inverse problem in classical mechanics.