Reachability analysis for N-squared state charts over a Boolean semiring applied to a hysteretic discrete event structural control model

This paper presents reachability results for a class of discrete event systems modelled by industry-standard N-squared diagrams. These diagrams represent state transition charts using Boolean variables and functions, and form the basis for the design of hierarchical discrete event controllers used to operate, monitor and protect complex servomechanism systems. The presence of Boolean variables is addressed by means of dynamical systems modelled over semirings. Four distinct system descriptions capture the very subtle transformation from the physical problem to "standard" reachability constructions. The conditions are in a state space form and permit analytical assessment of plant and closed-loop system properties prior to coding in software, simulation and laboratory testing, thus offering immense savings in verification time and cost.