  This paper presents a novel approach for distributed model predictive control
(MPC) for piecewise affine (PWA) systems. Existing approaches rely on solving
mixed-integer optimization problems, requiring significant computation power or
time. We propose a distributed MPC scheme that requires solving only convex
optimization problems. The key contribution is a novel method, based on the
alternating direction method of multipliers, for solving the non-convex optimal
control problem that arises due to the PWA dynamics. We present a distributed
MPC scheme, leveraging this method, that explicitly accounts for the coupling
between subsystems by reaching agreement on the values of coupled states.
Stability and recursive feasibility are shown under additional assumptions on
the underlying system. Two numerical examples are provided, in which the
proposed controller is shown to significantly improve the CPU time and
closed-loop performance over existing state-of-the-art approaches.
