Exploded time plants for observer and control synthesis of timed condition systems

Progress confusion refers to the situation where subsequent states of a discrete event system have identical observations, thus preventing identification of the state from just the observations. However, with a timed model, the timing information can be used to help identify periods where the state is known. In this paper, we introduce timing to condition systems models to allow the representation of this timing information. We also present a method of creating an exploded time plant model from the original plant model, and show how the trajectories of the original plant can be exhibited by this exploded time plant model. Although the exploded time plant is a deterministic system, it is able to represent state uncertainty in the original plant. The exploded time plant can then be used with observer and controller synthesis methods, to create observers and controllers that can be operated with the original plant.