State Estimation And Nonblockingness For Nondeterministic Discrete-event Systems

Discrete event systems(DESs)which characterize by discrete state and drive by discrete event are a kind of cyber physical system.It can be regarded as a model after discretizing the continuous part of cyber physical system,or a system model after ignoring physical process.The dynamic evolution mechanism of DESs is triggered by asynchronous discrete events,which means the state transition of system occurs at the moment the driving event is triggered,and according to the operating rules of the system,new discrete event will be triggered in other parts at the same time.DESs are widely used in engineering field,such as C3 I system,advanced vehicle or large building monitoring system,intelligent transportation system,distributed software system and queuing theory system,etc.DESs follow the intricate man-made rules rather than classical physical laws.Hence,DESs cannot be described by the conventional differential and difference equations,which used to analyze classical control system.Based on semi-tensor product technique,this paper investigates the problems of state estimation and nonblockingness in nondeterministic DESs respectively.Specifically,it mainly includes the following two aspects.(1)Regarding the problem of state estimation in nondeterministic DESs,using the semi-tensor product technique,we construct two kinds of matrix-based state estimators called a current-state estimator(C-estimator)and an initial-state estimator(I-estimator).By resorting to C-estimator and I-estimator,we compute three fundamental types of state estimates,namely current-state estimate,initial-state estimate,and delayed-state estimate.The notions of weak delayed detectability and weak delayed D-detectability are first proposed.Further,using the established C-estimator and I-estimator,we investigate the different types of detectability verification problems,namely weak(periodic)current-state detectability,weak initial-state detectability,weak delayed-state detectability,and weak delayed D-detectability.Accordingly,several necessary and sufficient criteria are derived for verifying the aforementioned different types of detectability.The detectability criteria obtained in this paper are all of the matrix-based characterization.Our approaches are completely different from the existing verification approaches in terms of technique.(2)Regarding the problem of verification and enforcement of state-based nonblockingness in nondeterministic DESs,under the framework of semi-tensor product of matrices,we express the dynamics of a controlled nondeterministic DES as an algebraic state-space representation.Based on this mathematical description,we propose a matrix-based criterion of verifying whether a given controlled nondeterministic DES is state-based nonblocking.Furthermore,we design a maximum admissible nonblocking supervisor for enforcing state-based nonblockingness.This optimal supervisor enforces the controlled closed-loop system satisfy state-based nonblockingness by restricting partial behavior of the original state-blocking system.