Improving Analysis of Uncertain Physical Systems

Model uncertainty leads to uncertainty in predicting system performance, which is the justification for a variety of robust control analysis and design methods. Analyzing the frequency response envelope (value set) of a model with parametric uncertainty is a precursor to using these methods, and is itself a challenging problem. Despite considerable progress in extending Kharitonov's theorem to analyzing models with a variety of uncertainty structures, most uncertain physical systems will not lead to a structure for which results are directly applicable. We have developed two distinct approaches to synthesizing value sets of uncertain models. The first uses projection, optimization, and an adaptive angular sweep algorithm to obtain a convex hull approximation of a value set. The second uses bond graphs to synthesize tree-structured transfer functions with disjoint parameters, which greatly simplify value set synthesis. In addition to facilitating the standard problem of value set synthesis, the tree-structured transfer functions have other applications, for example, model order reduction. The background, development, analysis, and application of uncertain physical system models will be discussed.