STP Approach to Model Controlled Automata with Application to Reachability Analysis of DEDS

Abstract

AbstractThis paper introduces semi‐tensor product of matrices (STP), a new matrix analysis tool, into the field of discrete event dynamic system (DEDS). Using STP, the dynamics of controlled automaton are modelled as an algebraic expression of the states, events and control specification. Based on this algebraic description, a sufficient and necessary condition is proposed to check whether any two states of a DEDS are reachable or not. The condition suggests an algorithm which can discover all the event strings by which a controlled automaton can move to one state from another one if they are reachable. All the results can be used to analyze corresponding problems of finite automata after simple modification. Finally, illustrative examples examine the correctness of the presented results/algorithm and demonstrate the modification after which the results are suitable for finite automata. The approach of this paper provides a new angle and means to understand and analyze the dynamics of DEDS.