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The authors consider the problem of finding an optimal feedback controller for a network of interconnected subsystems, each of which is a Markov decision process. Each subsystem is coupled to its neighbors via communication links by which signals are delayed but are otherwise transmit-ted noise-free. One of the subsystems receives input from a controller, and the controller receives delayed state-measurements from all of the subsystems. They show that an optimal controller requires only a finite amount of memory which does not grow with time, and obtain a bound on the amount of memory that a controller needs to have for each subsystem.
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