  Recent advances in model predictive control (MPC) leverage local
communication constraints to produce localized MPC algorithms whose
complexities scale independently of total network size. However, no
characterization is available regarding global performance, i.e. whether
localized MPC (with communication constraints) performs just as well as global
MPC (no communication constraints). In this paper, we provide analysis and
guarantees on global performance of localized MPC -- in particular, we derive
sufficient conditions for optimal global performance in the presence of local
communication constraints. We also present an algorithm to determine the
communication structure for a given system that will preserve performance while
minimizing computational complexity. The effectiveness of the algorithm is
verified in simulations, and additional relationships between network
properties and performance-preserving communication constraints are
characterized. A striking finding is that in a network of 121 coupled pendula,
each node only needs to communicate with its immediate neighbors to preserve
optimal global performance. Overall, this work offers theoretical understanding
on the effect of local communication on global performance, and provides
practitioners with the tools necessary to deploy localized model predictive
control by establishing a rigorous method of selecting local communication
constraints. This work also demonstrates -- surprisingly -- that the inclusion
of severe communication constraints need not compromise global performance.
