  In distributed model predictive control (MPC), the control input at each
sampling time is computed by solving a large-scale optimal control problem
(OCP) over a finite horizon using distributed algorithms. Typically, such
algorithms require several (virtually, infinite) communication rounds between
the subsystems to converge, which is a major drawback both computationally and
from an energetic perspective (for wireless systems). Motivated by these
challenges, we propose a suboptimal distributed MPC scheme in which the total
communication burden is distributed also in time, by maintaining a running
solution estimate for the large-scale OCP and updating it at each sampling
time. We demonstrate that, under some regularity conditions, the resulting
suboptimal MPC control law recovers the qualitative robust stability properties
of optimal MPC, if the communication budget at each sampling time is large
enough.
