We propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions—continuous or discrete time—and apply it for system identification and adaptive control. We restrict our attention to parameterizations that can be factorized as the product of two functions, a measurable one and a nonlinear function of the parameters to be estimated. Another feature of the proposed estimator is that parameter convergence is ensured without a persistency of excitation assumption. It is assumed that, after a coordinate change, some of the elements of the transformed function satisfy a monotonicity condition. The proposed estimators are applied to design identifiers and adaptive controllers for nonlinearly parameterized systems, which are traditionally tackled using overparameterization and assuming persistency of excitation.
