z-Reliable SE-Coprognosability of Discrete Event Systems and an Algebraic State Space Approach to Verification

This brief investigates the problem of fault prognosis in decentralized structure, where given systems are monitored by
$r$
local agents, and assumes that only
$z$
(
$1\leq z\leq r$
) local agents’ information can be obtained. In this case, under a state-estimate-based protocol, a notion called
$z$
-reliable SE-coprognosability is proposed. Compared with existing results,
$z$
-reliable SE-coprognosability is a more universal concept. Besides, with the help of semi-tensor product, an efficient algorithm for state estimation is presented, and based on which, the algorithm on verification of
$z$
-reliable SE-coprognosablity is also proposed. A dominating breakthrough is that the complexity of given algorithms is polynomial with respect to the number of agents.