North-Holland Hamiltonian and self-adjoint control systems

Abstract: This paper outlines results recently obtained in the problem of determining when an input-output map has a Hamiltonian re~liT~tion. The results are obtained in terms of variations of the system trajectories, as in the solution of the Inverse Problem in Classical Mechanics. The variational and adjoint systems are introduced for any given nonlinear system, and self-adjointness defined. Under appropriate conditions self-adjoinmess characterizes Hamiltonian systems. A further characterization is given directly in terms of variations in the input and output rajectories, proving an earlier conjecture by the first author