Distributed MPC: Guaranteeing Global Stabilizability from Locally Designed Tubes

This paper studies a fundamental relation that exists between stabilizability assumptions usually employed in distributed model predictive control implementations, and the corresponding notions of invariance implicit in such controllers. The relation is made explicit in the form of a theorem that presents sufficient conditions for global stabilizability. It is shown that constraint admissibility of local robust controllers is sufficient for the global closed-loop system to be stable, and how these controllers are related to more complex forms of control such as tube-based distributed model predictive control implementations.