Tuning nonlinear identifiers: networks of coupled oscillators

Adaptive identification methods for nonlinear systems obtain parameter estimates by allowing them to evolve according to an identifier dynamical system. Lyapunov-based methods can establish asymptotic convergence of estimates to the correct values as long as the data used is persistently exciting. However, it may occur that the asymptotic convergence is too slow to render useful results if the identifier system exhibits dynamics on multiple time scales. This phenomenon is illustrated for a class of identifiers that occur in identification of coupling strength parameters in coupled oscillator networks. Additionally, the analysis shows how the parameters of the identification system can be chosen to avoid this difficulty