Graph-theoretic approach for connectivity maintenance in mobile networks in the presence of a jammer

In this work, we analyze the problem of maintaining connectivity in a network of mobile agents in the presence of a jammer. This is a variation of the standard connectivity maintenance problem in which the issue arises due to limitations in communications and sensing model for each agent. In our work, the limitations in communications are due to the presence of a jammer in the vicinity of the mobile agents. First, we present a differential game-theoretic formulation of the problem and provide the necessary conditions for optimal controls for each agent. Then we present a model that constructs a state-dependent graph based on the state-space of the agents. We use tools from algebraic-graph theory on the state-dependent graph in order to provide locally optimal control laws for the agents in the formation. Finally, we present some simulations to validate the proposed control scheme.