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In this paper we introduce an iterative Jacobi algorithm for solvingdistributed model predictive control (DMPC) problems, with linear coupleddynamics and convex coupled constraints. The algorithm guarantees stability andpersistent feasibility, and we provide a localized procedure for constructingan initial feasible solution by constraint tightening. Moreover, we show thatthe solution of the iterative process converges to the centralized MPCsolution. The proposed iterative approach involves solving local optimizationproblems consisting of only few subsystems, depending on the choice of thedesigner and the sparsity of dynamical and constraint couplings. The gain inthe overall computational load compared to the centralized problem is balancedby the increased communication requirements. This makes our approach moreapplicable to situations where the number of subsystems is large, the couplingis sparse, and local communication is relatively fast and cheap. A numericalexample illustrates the effects of the local problem size, and the number ofiterations on convergence to the centralized solution.

A Jacobi algorithm for distributed model predictive control of dynamically coupled systems