Observer and Damping Feedback Construction Based on Approximate Hamiltonian Dissipative Realization

Abstract

AbstractThis paper considers observer and damping feedback design for control affine systems that admit an approximate dissipative Hamiltonian realization. The approach consists in constructing a locally-defined dissipative potential function by homotopy decomposition of a differential one-form associated to the system drift vector field. Under a condition on the obtained potential function convexity, a coordinate transformation is then defined such that the original system can be approximated by a dissipative Hamiltonian system with a constant structure. Using the approximate dissipative Hamiltonian realization, damping control and observer design are then carried, and the limitations associated to the approximation are discussed. Application to a predator-prey system is presented to illustrate the construction.