  In this paper, we propose a distributed model predictive control (DMPC)
scheme for linear time-invariant constrained systems which admit a separable
structure. To exploit the merits of distributed computation algorithms, the
stabilizing terminal controller, value function and invariant terminal set of
the DMPC optimization problem need to respect the loosely coupled structure of
the system. Although existing methods in the literature address this task, they
typically decouple the synthesis of terminal controllers and value functions
from the one of terminal sets. In addition, these approaches do not explicitly
consider the effect of the current state of the system in the synthesis
process. These limitations can lead the resulting DMPC scheme to poor
performance since it may admit small or even empty terminal sets. Unlike other
approaches, this paper presents a unified framework to encapsulate the
synthesis of both the stabilizing terminal controller and invariant terminal
set into the DMPC formulation. Conditions for Lyapunov stability and invariance
are imposed in the synthesis problem in a way that allows the value function
and invariant terminal set to admit the desired distributed structure. We
illustrate the effectiveness of the proposed method on several examples
including a benchmark spring-mass-damper problem.
