Qualitative results for a hierarchical discrete event control paradigm applied to structures operating under nominal and fault conditions

This paper presents a mathematical discrete event state space model for plants and controllers that is amenable to classical state space control theory. The model is based upon industry-standard N-squared diagrams which are shown to readily translate into a state space matrix form. A hierarchical structure is defined that allows the design to scale in dimension and remain tractable. The motivation for using this state space model approach is to develop reachability, observability and stability results using approaches based upon existing control theory, and as well as to adapt certain control design paradigms. The state space model defined is based upon Boolean algebra, and so the desired theoretical results must be adapted accordingly. The model is described in the context of two examples, the first being a Bouc-Wen modified hysteresis model, and the second a general supervisory discrete-event servo controller.