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In this paper, we study the structural properties of optimal control of spatially distributed systems. Such systems consist of an infinite collection of possibly heterogeneous linear control systems that are spatially interconnected via certain distant-dependent coupling functions over arbitrary graphs. We study the structural properties of optimal control problems with infinite-horizon linear quadratic criteria, by analyzing the spatial structure of the solution to the corresponding operatordoi:10.1109/acc.2007.4282897 dblp:conf/acc/MoteeJ07 fatcat:gcwhctgdejchdlmyn4agmh6ufq