On the Use of Convex Optimization in Sensor Network Localization and Synchronization

In this paper we report some new results obtained in the field of multi-agent systems that are based on convex optimization. First, we provide review of a set of polynomial function optimization tools including sum of squares (SOS) and semidefinite programming (SDP). Then we present several applications of these tools in various multiagent system localization and synchronization tasks. As the first application, we propose a method based on SOS relaxation for agent localization using noisy measurements and describe the solution through SDP. Later, we apply this method to address the problems of cooperative target localization in the presence of noise and robot pose determination based on range measurements. Then we introduce the problem of anchor selection for minimizing the effect of noise in sensor networks via SDP. We use the same machinery to propose a method based on SDP to enhance synchronizability in networks. We do so by proposing a distributed algorithm for adding new edges to the network to enhance synchronizability. Finally, we present a method to identify the node in a network loss of which inflicts the most damage on the synchronizability of the network. Conclusions are presented in the last section.