Parameter identification of conservative Hamiltonian systems using first integrals

This paper presents a methodology for nonlinear parameter identification of conservative Hamiltonian systems. In the proposed approach, the system's Hamiltonian is used under the first integral concept. The time derivative of this first integral function is utilized to construct a signal termed surface variable, which depends on the system's parameters. Then, the parameter convergence is ensured by driving this surface variable towards zero, employing the parameter estimates as control inputs. This procedure is approached by treating the parameter identification problem as an optimization one. Hence, different cost functions are defined to obtain various parameter updating laws. Besides, an automatic tuning methodology based on a meta-heuristic algorithm is proposed for tuning the adaptation gains of the new parameter updating laws. The proposed scheme shows that, when the surface variable reaches zero, the parameter estimates converge to the real ones. Furthermore, better estimation results are obtained when applying the automatic tuning scheme. Numerous numerical simulations validate the proposed parameter identification methodology, including the cases where the unknown system variables are estimated through the dirty derivative and a sliding-mode differentiator.