Observer-based adaptive output feedback stabilization of generalized Hamiltonian systems with unstructured component

This study considers the problem of adaptive feedback controller design for output stabilization of dissipative (generalized) Hamiltonian systems with unstructured dynamic. This class of models enable one to exploit the dissipative-conservative structure of generalized Hamiltonian systems for feedback control design while relaxing the burden of deriving an exact structured model representation. Assuming that the overall system is stabilizable and observable, and under mild assumptions on the unstructured part of the dynamics, a stabilizing adaptive control law is designed to stabilize systems to the desired output of the system. To fulfill the design procedure, a full order nonlinear Luenberger observer is designed for unknown states measurements. Stability of the closed-loop system is then demonstrated using Lyapunov stability arguments. A numerical illustration of the proposed approach is presented to demonstrate the potential of the design method.