Parameter convergence in systems with a general nonlinear parameterization using a hierarchical algorithm

In this paper, we address the problem of parameter convergence in systems with a general nonlinear parametrization. Using the stability framework for studying adaptive systems with nonlinear parametrization recently established, we consider parameter convergence in a class of systems with a general nonlinear parameterization. To accomplish this task, a hierarchical algorithm is proposed where the lower-level consists of a min-max algorithm as in earlier papers. To this, a higher-level component is added that updates the bounds on the parameter region within which the unknown parameter is known to lie. A necessary and sufficient condition is established for global parameter convergence using this algorithm for a class of nonlinear systems with a general nonlinear parameterization. An explanation of this condition, examples of the class of systems and simulation results are included to illustrate the behavior of the hierarchical algorithm.