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Set-based Adaptive Parameter Estimation for a Class of Systems with Nonlinear Parametrization

In this paper, an alternative adaptive parameter estimation framework is developed for nonlinearly parametric systems. The proposed estimation approach is derived from the perspective of the set-based method, where the unknown constant parameters contains a fixed value and an unknown uncertainty. Based on this property, the mean-value theorem can be used to linearize the nonlinearly parameterized function with respect to the uncertainty. Inspired by this fact, the procedure of estimation method is that the nonlinearly parameterized function in the predictor error equation is first linearized by using the mean-value theorem. Subsequently, a low-pass filter is employed in the linearized function in order to derive parameter estimation errors and avoid using the predictor error derivative. Moreover, the estimator is designed based on the derived parameter estimation errors. Under the persistent excitation condition, the exponential convergence for the proposed estimator can be guaranteed. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed method.