Invariant manifold approach for adaptive estimation of the time-varying parameters for a class of nonlinear systems

The parametric identification of models with uncertain time-varying parameters, especially for nonlinear systems, remains an open field of research. The desirable performance of the system depends, to some extent, on the accuracy of parameter estimation. In this research, the concept of invariant manifold is used to find an implicit mapping from known variables of the system to the unknown variables (the unknown time-varying parameters). This mapping provides a parameter estimation update law, which has been shown to converge to the unknown parameter values. This method is easy to implement with only one tuning parameter. The effectiveness of the proposed method is illustrated with a simulation example.