Local dissipative Hamiltonian realization by feedback regulation

This paper considers the design of smooth feedback regulators for control affine nonlinear systems. The reference dynamics to track is generated by a dissipative Hamiltonian system. The objective of the paper is to show that damping assignment can be achieved by regulation, thus avoiding the solution of the matching equations when the expression of an energy function is unknown. The proposed approach consists in computing an expression for a local error potential and use it to construct a smooth feedback regulator. Conditions for the existence of a stabilizing regulator are given. Applications to predator-prey systems are presented to illustrate the construction.