Asymptotical Feedback Controllability Of Continuous-Time Probabilistic Logic Control Networks

This paper investigates the controllability problem of continuous-time probabilistic logic control networks (CT-PLCNs) under sampled-data feedback controls. Firstly, we point out that it is nonsense to define finite-time controllability with probability one for CT-PLCNs. Then we introduce the concept of asymptotical controllability with probability one for CT-PLCNs. Secondly, based on the invariant subset theory, two necessary and sufficient conditions for the asymptotical controllability with probability one of CT-PLCNs are obtained. In addition, by resorting to the reachability matrix of network, an easy-to-verify necessary and sufficient condition is obtained, which is represented by the transition rate matrices. Finally, a numerical example is given to explain and validate the controllability criterion we proposed.