  Distributed optimization is often widely attempted and innovated as an
attractive and preferred methodology to solve large-scale problems effectively
in a localized and coordinated manner. Thus, it is noteworthy that the
methodology of distributed model predictive control (DMPC) has become a
promising approach to achieve effective outcomes, e.g., in decision-making
tasks for multi-agent systems. However, the typical deployment of such
distributed MPC frameworks would lead to the involvement of nonlinear processes
with a large number of nonconvex constraints. To address this important
problem, the development and innovation of a hierarchical three-block
alternating direction method of multipliers (ADMM) approach is presented in
this work to solve this nonconvex cooperative DMPC problem in multi-agent
systems. Here firstly, an additional slack variable is introduced to transform
the original large-scale nonconvex optimization problem. Then, a hierarchical
ADMM approach, which contains outer loop iteration by the augmented Lagrangian
method (ALM) and inner loop iteration by three-block semi-proximal ADMM, is
utilized to solve the resulting transformed nonconvex optimization problem.
Additionally, it is analytically shown and established that the requisite
desired stationary point exists for convergence in the algorithm. Finally, an
approximate optimization stage with a barrier method is then applied to further
significantly improve the computational efficiency, yielding the final improved
hierarchical ADMM. The effectiveness of the proposed method in terms of
attained performance and computational efficiency is demonstrated on a
cooperative DMPC problem of decision-making process for multiple unmanned
aerial vehicles (UAVs).
