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We consider the control of dynamically decoupled subsystems whose state vectors are coupled in the cost function of a finite horizon optimal control problem. For a given cost structure, we generate distributed optimal control problems for each subsystem and establish that a distributed receding horizon implementation is asymptotically stabilizing. The communication requirements at each receding horizon update include the exchange of the previous optimal control trajectory between subsystems with coupling in the cost function. The key requirements for stability are that each distributed optimal control not deviate too far from the previous one, and that the receding horizon updates happen sufficiently fast. A simulation example of multi-vehicle formation stabilization is provided.