Abstract
This paper presents that the structural controllability and observability can be used for a class of discrete event systems modeled by industry-standard N-squared diagrams. The main results of this paper provide analytical assessment of large scale industrial system properties before the software simulation and hardware demonstration; therefore it offers immense savings in verification time and cost. The dynamics of N-squared diagrams are represented by linear time-invariant systems over the Boolean algebra. Structural controllability and structural observability of discrete event systems are transformed to “standard” controllability and observability problems in traditional linear systems over real numbers. The rank of the controllability and observability matrices determine not only the structural controllability and observability, but also which discrete nodes cannot be reached by the initial states and which discrete states have no outgoing paths to the output nodes, respectively. This rank condition is extremely easy to be verified through computer software, such as MATLAB, it can be used in large scale industrial systems or communication networks.
Highlights
Discrete event systems are dynamic systems whose evolutions are driven by asynchronous discrete transitions triggered by physical events
This paper presents an alternative method to determine which nodes are reachable from the start nodes and which nodes can reach the final nodes for industrial discrete event systems modeled as N 2 diagrams, present state of the art relies upon expensive laboratory testing
Has no zero rows, the discrete event system modelled as an N 2 diagram is structurally controllable, where A is the transpose of the truth table of the N 2 diagram
Summary
Discrete event systems are dynamic systems whose evolutions are driven by asynchronous discrete transitions triggered by physical events. Major questions in discrete event systems include whether operational states can be reached from the initial states, or whether operational states can reach the final or exit states These questions can be formulated as structural controllability and structural observability ([5, 6, 7]) in event graphs. This paper continues this research and studies the structural controllability and observability for discrete event systems modeled as N 2 diagrams. Such a system is called structurally observable if, for any discrete state, there exists a path to at least one final node (or output node).
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