Information State for Markov Decision Processes with Network Delays

We consider a networked control system, where each subsystem evolves as a Markov decision process (MDP). Each subsystem is coupled to its neighbors via communication links over which the signals are delayed, but are otherwise transmitted noise-free. A centralized controller receives delayed state information from each subsystem. Such a distributed Markov decision process with delays can be represented as a partially observed Markov decision process (POMDP). We show that this POMDP has an information state that depends only on a finite history of measurements and control. Thus, the POMDP can be converted into an information state MDP, whose state does not grow with time. The optimal controller for distributed Markov decision processes can thus be computed using dynamic programming over a finite state space. This result generalizes the previous results on Markov decision processes with delayed state information.