Second level adaptation using multiple models

The concept of using multiple models to cope with transients which arise in adaptive systems with large parametric uncertainties was introduced in the 1990s. Both switching between multiple fixed models, and switching and tuning between fixed and adaptive models was proposed, and the stability of the resulting schemes was established. In all cases, the number of models needed is generally large, and the models used do not cooperate in any real sense. It was recently shown by the authors that if it is known a priori that the unknown plant parameter vector lies in the convex hull of a set of adaptive model parameter vectors at the initial time, it will remain in the convex hull of the parameters even as they evolve with time [1]. Later, a stability result was derived in [2] which decouples the stability and performance issues. In this paper, a new concept of second level adaptation is introduced to develop different stable strategies which improve the performance of the overall system. Simulation results are provided to illustrate the effectiveness of the proposed scheme in a rapidly time-varying environment, and are shown to be far superior to existing schemes.