Probabilistic models for feedback systems.

Abstract

In previous work, we developed a Bayesian-based methodology to analyze the reliability of hierarchical systems. The output of the procedure is a statistical distribution of the reliability, thus allowing many questions to be answered. The principal advantage of the approach is that along with an estimate of the reliability, we also can provide statements of confidence in the results. The model is quite general in that it allows general representations of all of the distributions involved, it incorporates prior knowledge into the models, it allows errors in the 'engineered' nodes of a system to be determined by the data, and leads to the ability to determine optimal testing strategies. In this report, we provide the preliminary steps necessary to extend this approach to systems with feedback. Feedback is an essential component of 'complexity' and provides interesting challenges in modeling the time-dependent action of a feedback loop. We provide a mechanism for doing this and analyze a simple case. We then consider some extensions to more interesting examples with local control affecting the entire system. Finally, a discussion of the status of the research is also included.