State Estimation of Networked Finite State Machine With Communication Delays and Losses

Abstract

In this brief, state estimation problem of networked finite state machine (FSM) under partial observation is investigated. Based on the semi-tensor product (STP) of matrices, several algebraic expressions are defined to describe the communication losses (CL) and communication delays (CD). With the unobservable reach and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> -reach of state, one necessary and sufficient condition for detectability is obtained under CL. By constructing a state estimation set under CD, one criterion for detectability is established. Based on the composition of two mappings, one criterion for detectability under both CL and CD is obtained. Finally, a simple example is taken to illustrate the validity of the obtained theoretical results.