Matrix approach to reachability of parallel interconnected asynchronous sequential machines

This paper investigates fault tolerant control of parallel interconnected asynchronous sequential machines (ASMs) via matrix approach. This problem is challenging since each submachine can fall into an unauthorized transition caused by adversarial inputs. By using the semi-tensor product method, the dynamics of parallel interconnected ASMs are depicted as a discrete-time algebraic form. Under this framework, reachability and fault detectabillity of parallel interconnected ASMs are discussed. Then, several necessary and sufficient conditions for checking reachability and fault detectabillity are obtained. Finally, for better presentation, a system composed by three asynchronous error accumulators in parallel connection is provided to illustrate the feasibility of the proposed method.