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Selecting Energy Efficient Inputs using Graph Structure

Selecting appropriate inputs for systems described by complex networks is an important but difficult problem that largely remains open in the field of control of networks. Recent work has proposed two methods for energy efficient input selection; a gradient based heuristic and a greedy approximation algorithm. We propose here an alternative method for input selection based on the analytic solution of the controllability Gramian of the `balloon graph', a special model graph that captures the role of both \emph{distance} and \emph{redundant paths} between a driver node and a target node. The method presented is especially applicable for large networks where one is interested in controlling only a small number of outputs, or target nodes, for which current methods may not be practical because they require computing a typically very ill-conditioned matrix, called the controllability Gramian. Our method produces comparable results to the previous methods while being more computational efficient.