  This paper presents a distributed learning model predictive control (DLMPC)
scheme for distributed linear time invariant systems with coupled dynamics and
state constraints. The proposed solution method is based on an online
distributed optimization scheme with nearest-neighbor communication. If the
control task is iterative and data from previous feasible iterations are
available, local data are exploited by the subsystems in order to construct the
local terminal set and terminal cost, which guarantee recursive feasibility and
asymptotic stability, as well as performance improvement over iterations. In
case a first feasible trajectory is difficult to obtain, or the task is
non-iterative, we further propose an algorithm that efficiently explores the
state-space and generates the data required for the construction of the
terminal cost and terminal constraint in the MPC problem in a safe and
distributed way. In contrast to other distributed MPC schemes which use
structured positive invariant sets, the proposed approach involves a control
invariant set as the terminal set, on which we do not impose any distributed
structure. The proposed iterative scheme converges to the global optimal
solution of the underlying infinite horizon optimal control problem under mild
conditions. Numerical experiments demonstrate the effectiveness of the proposed
DLMPC scheme.
