A performance based model-set design strategy for Multiple Model Adaptive Estimation

This paper addresses the problem of Multiple Model Adaptive Estimator (MMAE) design for linear process models subjected to parameter uncertainty. MMAE algorithms rely on a finite number of representative models chosen from the original set of possibly infinite plant models. One of the standing issues that arise in the process of MMAE design is the selection of the model-set. Typical questions that arise at this phase are the following: i) what is gained by using a MMAE approach compared with a single model approach?, and ii) for a given required level of performance, what is the minimum number of models required and how should they be selected as a function of the parameter uncertainty region? For discrete-time, linear, time-invariant MIMO plants with parameter uncertainty, we propose a performance-based model-set design strategy. To this effect, we first introduce the concept of an Infinite Model Adaptive Estimation Performance (IMAEP) index that defines the best achievable performance of the MAAE, assuming an ideal MMAE with an infinite number of representative models. Then, based on a specified demanded performance relative to the ideal IMAEP (say, 85% of the IMAEP uniformly over the original parameter uncertainty set), we provide an algorithm that guarantees the demanded performance and yields the corresponding finite number of representative models. An example is described that illustrates the proposed strategy and the improvement in performance that is obtained when compared with other previously proposed design methodologies.