  In this paper 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.
Although in this case it is possible to define an extended vector of unknown
parameters to get a linear regression, it is well-known that
overparameterization suffers from some severe shortcomings. 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. In continuous-time
we consider a general class of nonlinear systems and those described by
Euler-Lagrange models, while in discrete-time we apply the method to the
challenging problems of direct and indirect adaptive pole-placement. The
effectiveness of our approach is illustrated with several classical examples,
which are traditionally tackled using overparameterization and assuming
persistency of excitation.
