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This paper presents a novel optimal control problem formulation and new optimality conditions, referred to as distributed optimal control, for systems comprised of many dynamic agents that can each be described by the same ordinary differential equations (ODEs). The macroscopic system performance is represented by an integral cost function of a restriction operator comprised of the probability density function of the individual agents' state variables, and of their control laws. It is showndoi:10.1109/cdc.2010.5718021 dblp:conf/cdc/FoderaroF10 fatcat:ags7ptx6u5fmrnzbghj37ejdgq