Synthesizing robust communication networks for UAVs

This article addresses the problem of synthesizing communication networks with maximum algebraic connectivity in the presence of constraints which limit the total number of communication links present in the network. This problem arises in Unmanned Aerial Vehicle (UAV) monitoring applications where some UAVs have to be deployed to relay and transmit time sensitive information between all the vehicles and the control stations. This network synthesis problem is a difficult optimization problem because of its non-linear objective coupled with the possibility that the number of feasible solutions increases rapidly with the size of the graph. The network synthesis problem is formulated as a mixed-integer, semi-definite program, and an algorithm to find the optimal solution is developed based on cutting plane and bisection methods. Some computational results are also presented to corroborate the performance of the proposed algorithm. Two other heuristics are presented along with numerical results corroborating their performance. Since these heuristics are based on evaluating the spectrum of the graph, they can be applied to large networks.