Adaptation in the presence of a general nonlinear parameterization: an error model approach

Parametric uncertainties in adaptive estimation and control have been dealt with, by and large, in the context of linear parameterizations. Algorithms based on the gradient descent method either lead to instability or inaccurate performance when the unknown parameters occur nonlinearly. Complex dynamic models are bound to include nonlinear parameterizations which necessitate the need for new adaptation algorithms that behave in a stable and accurate manner. The authors introduce, in this paper, an error model approach to establish these algorithms and their global stability and convergence properties. A number of applications of this error model in adaptive estimation and control are included, in each of which the new algorithm is shown to result in global boundedness. Simulation results are presented which complement the authors' theoretical derivations.