2024/12/03 by Biradar, Shivanagouda, Patil, Deepak U
#FOS: Electrical engineering #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2412.02315
A problem of reconstruction of the topology and the respective edge resistance values of an unknown circular planar passive resistive network using limitedly available resistance distance measurements is considered. We develop a multistage topology reconstruction method, assuming that the number of boundary and interior nodes, the maximum and minimum edge conductance, and the Kirchhoff index are known apriori. First, a maximal circular planar electrical network consisting of edges with resistors and switches is constructed; no interior nodes are considered. A sparse difference in convex program \mathbfΠ1 accompanied by round down algorithm is posed to determine the switch positions. The solution gives us a topology that is then utilized to develop a heuristic method to place the interior nodes. The heuristic method consists of reformulating \mathbfΠ1 as a difference of convex program \mathbfΠ2 with relaxed edge weight constraints and the quadratic cost. The interior node placement thus obtained may lead to a non-planar topology. We then use the modified Auslander, Parter, and Goldstein algorithm to obtain a set of planar network topologies and re-optimize the edge weights by solving \mathbfΠ3 for each topology. Optimization problems posed are difference of convex programming problem, as a consequence of constraints triangle inequality and the Kalmansons inequality. A numerical example is used to demonstrate the proposed method.