Nonlinear parametric estimation of Hamiltonian systems: identification as stabilization

The paper presents two numerical procedures in the continuous time for the identification of parameters of a class of Hamiltonian systems. Employing the definition of First Integrals and their characteristics, the suggested approach permits to treat the parametric identification process as a stabilization of the derivative of the first integrals. It is realized by two proposed numerical procedures, supported by an super-twist differentiator to have online estimates of the derivatives of the generalized state coordinates and impulses. The convergence of these identification procedures and their implementation in a scalar and vector cases are presented. The numerical examples illustrate a good workability of the suggested method.