Finite-Time Observability of Probabilistic Logical Control Systems

This study investigates finite-time observability of probabilistic logical control systems(PLCSs) under three definitions(i.e., finite-time observability with probability one, finite-time singleinput sequence observability with probability one, and finite-time arbitrary-input observability with probability one). The authors adopt a parallel extension technique to recast the finite-time observability problem of a PLCS as a finite-time set reachability problem. Then, the finite-time set reachability problem can be transferred to stabilization problem of a logic dynamical system by using the state transfer graph reconstruction method. Necessary and sufficient conditions for finite-time observability under the three definitions are derived respectively. Finally, the proposed methods are illustrated by numerical examples.