On the maximum coverage area of wireless networked control systems under stability and cost-efficiency constraints

The integration of wireless communication and control systems revealed wireless networked control systems (WNCSs). One fundamental problem in WNCSs is to have a wide coverage area. For the first time in the literature, we address this problem and we obtain the maximum coverage area by solving an optimization problem. In this paper, we consider a WNCS where the output sensor measurements are transmitted over separate multi-hop wireless ad-hoc subnetworks. The system state is estimated using the Kalman filter. We present the critical arrival probability for a sensor measurement packet such that if the packet arrival probability is larger than the critical value, it is guaranteed that the expected state estimation error covariance is bounded, and hence the WNCS is stable. We find the optimum hop-diameter of a multi-hop wireless ad-hoc subnetwork under the constraints of both the stability of the WNCS and the cost-efficiency of the multi-hop wireless network. Furthermore, under these constraints, we derive the maximum total coverage area of the wireless subnetworks. The numerical analyses show that the maximum total coverage area can be increased by appropriately adjusting the number of sensors, the successful packet transmission probability between relay nodes, and the eigenvalues of the system matrix.