Positivstellensatz Certificates for Non-Feasibility of Connectivity Graphs in Multi-agent Coordination
Abstract
In this paper, we discuss how to obtain certificates for thenon-feasibility of connectivity graphs arising from multi-agentformations. We summarize some previous work on connectivity graphsand their feasibility. Next, we introduce the Positivstellensatzto show how it can be used to better understand the space of allconnectivity graphs for a fixed number of vertices, which hadpreviously been understood as only a subspace of the space of allgraphs. We study one particular class of graphs and use ourmethodology to prove some more results in the feasibility ofconnectivity graphs.
