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In this paper we propose a solution to the problem of parameter estimation ofnonlinearly parameterized regressions--continuous or discrete time--and applyit for system identification and adaptive control. We restrict our attention toparameterizations that can be factorized as the product of two functions, ameasurable one and a nonlinear function of the parameters to be estimated.Although in this case it is possible to define an extended vector of unknownparameters to get a linear regression, it is well-known thatoverparameterization suffers from some severe shortcomings. Another feature ofthe proposed estimator is that parameter convergence is ensured without apersistency of excitation assumption. It is assumed that, after a coordinatechange, some of the elements of the transformed function satisfy a monotonicitycondition. The proposed estimators are applied to design identifiers andadaptive controllers for nonlinearly parameterized systems. In continuous-timewe consider a general class of nonlinear systems and those described byEuler-Lagrange models, while in discrete-time we apply the method to thechallenging problems of direct and indirect adaptive pole-placement. Theeffectiveness of our approach is illustrated with several classical examples,which are traditionally tackled using overparameterization and assumingpersistency of excitation.

Parameter Estimation of Nonlinearly Parameterized Regressions without  Overparameterization nor Persistent Excitation: Application to System  Identification and Adaptive Control