Model-set design: Uniformly distributed models

Abstract

Model-set design is one of the most important topics of the multiple-model approach, which is the state of the art for many estimation, control, and modeling problems. This paper proposes a method for model-set design in the parameter space based on a number theoretic approach to the design of statistical experiments. Here the uncertain system is characterized by uncertain parameters that parametrize the mode space. The model set is designed to approximate the mode based on the discretized values of each parameter by minimizing the distribution mismatch between the model set and the mode in each one-dimensional projection of the mode space. Two types of uniform model sets are proposed, where the models are uniformly distributed in the parameter space. Simulation examples are given to demonstrate the designs and their performance.