Port selection for optimal charging/discharging and external communication in single-integrator graphs networks

This paper studies optimal input port selection for simple undirected graphs with an objective to control the graph externally with least amount of supplied energy. Given a graph with n-nodes, we address the problem of selecting k out of these for external input with this minimization objective. We formulate a resistive-capacitive (RC) network analogy of such single integrator multiagent networks, allowing us to consider the given problem as that of optimal selection of the input ports w.r.t. the energy required for charging/discharging of the RC circuit. We set up a link between these optimal port locations and values in the Fiedler vector of the corresponding graph Laplacian matrix L and other eigenvectors of L. This paper contains new results involving passivity, Hamiltonian matrix and the Algebraic Riccati equation in the context of RC networks associated with such graphs. We link this formulation to optimal node(s) identification for optimal external communication with a multi-agent network of single integrator systems.