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We consider a set of decoupled dynamical systems and an optimal control problem where cost function and constraints couple the dynamical behavior of the systems. The coupling is described through a connected graph where each system is a node, and cost and constraints of the optimization problem associated to each node are only function of its state and the states of its neighbors. For such scenario, we propose a framework for designing decentralized receding horizon control (RHC) control schemes. In these decentralized schemes, a centralized RHC controller is broken into distinct RHC controllers of smaller sizes. Each RHC controller is associated to a different node and computes the local control inputs based only on the states of the node and of its neighbors. The proposed decentralized control schemes are formulated in a rigorous mathematical framework. Moreover, we highlight the main issues involved in guaranteeing stability and constraint fulfillment for such schemes and the degree of conservativeness that the decentralized approach introduces.