  The impact of Vehicle-to-Everything (V2X) communications on platoon control
performance is investigated. Platoon control is essentially a sequential
stochastic decision problem (SSDP), which can be solved by Deep Reinforcement
Learning (DRL) to deal with both the control constraints and uncertainty in the
platoon leading vehicle's behavior. In this context, the value of V2X
communications for DRL-based platoon controllers is studied with an emphasis on
the tradeoff between the gain of including exogenous information in the system
state for reducing uncertainty and the performance erosion due to the
curse-of-dimensionality. Our objective is to find the specific set of
information that should be shared among the vehicles for the construction of
the most appropriate state space. SSDP models are conceived for platoon control
under different information topologies (IFT) by taking into account `just
sufficient' information. Furthermore, theorems are established for comparing
the performance of their optimal policies. In order to determine whether a
piece of information should or should not be transmitted for improving the
DRL-based control policy, we quantify its value by deriving the conditional KL
divergence of the transition models. More meritorious information is given
higher priority in transmission, since including it in the state space has a
higher probability in offsetting the negative effect of having higher state
dimensions. Finally, simulation results are provided to illustrate the
theoretical analysis.
