Structural Controllability and Observability in Influence Diagrams

Influence diagram is a graphical representa­ tion of belief networks with uncertainty. This article studies the structural properties of a probabilistic model in an influence diagram. In particular, structural controllability the­ orems and structural observability theorems are developed and algorithms are formulated. Controllability and observability are funda­ mental concepts in dynamic systems (Luen­ berger 1979). Controllability corresponds to the ability to control a system \vhile observ­ ability analyzes the inferability of its vari­ ables. Both properties can be determined by the ranks of the system matrices. Structural controllability and observability, on the other hand, analyze the property of a system with its structure only, without the specific knowl­ edge of the values of its elements (Lin 1974, Shields and Pearson 1976). The structural analysis explores the connection between the structure of a model and the functional de­ pendence among its elements. It is useful in comprehending problem and formulating solution by challenging the underlying intu­ itions and detecting inconsistency in a model. This type of qualitative reasoning can some­ times provide insight even when there is in­ sufficient numerical information in a model.