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A decentralized formulation is presented for model predictive control of systems with coupled constraints. The single large planning optimization is divided into small subproblems, each planning only for the states of a particular subsystem. Relevant plan data is exchanged between subsystems to ensure that all decisions are consistent with satisfaction of the coupled constraints. A typical application would be autonomous guidance of a fleet of UAVs, in which the systems are coupled by the need to avoid collisions, but each vehicle plans only its own path. The key property of the algorithm in this paper is that if an initial feasible plan can be found, then all subsequent optimizations are guaranteed to be feasible, and hence the constraints will be satisfied, despite the action of unknown but bounded disturbances. This is demonstrated in simulated examples, also showing the associated benefit in computation time.