Asymptotical feedback controllability of probabilistic logic control networks

Abstract In this paper, we investigate the asymptotical feedback controllability (AFC) of probabilistic logic control networks (PLCNs). First, the concept of asymptotical feedback reachability (AFR) is proposed, allowing us to define AFC. Then, we prove that a state is asymptotically feedback reachable if and only if (iff) it is a control fixed point, and there is an admissible path to it from any other state. Based on this, we prove that a PLCN is asymptotically feedback controllable iff every state is asymptotically feedback stabilizable. Moreover, we express the criteria for the AFR and AFC of PLCNs in terms of the reachability matrix, which are easily checkable. The relations between the AFC and other definitions of controllability are also discussed. Finally, an illustrative example is provided to show the usage of the proposed results and to demonstrate the design of feedbacks achieving transitions between states.