Distributed optimization is widely used 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 ; and particularly in decision-making tasks for multi-agent systems. However, the typical deployment of such DMPC frameworks would lead to  involvement of nonlinear processes with a large number of nonconvex constraints. Noting all these attendant constraints and limitations , the development and innovation of a hierarchical three-block alternating direction method of multipliers (ADMM) approach is presented in the work here to solve the nonconvex optimization problem that arises for such a decision-making problem in multi-agent systems. Firstly thus , an additional slack variable is introduced to relax the original large-scale nonconvex optimization problem ; such that the intractable nonconvex coupling constraints are suitably related to the distributed agents . Then, the approach with a hierarchical ADMM that 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 relaxed nonconvex optimization problem. Additionally, it is shown that the appropriate desired stationary point exists for the procedures of the hierarchical stages for convergence in the algorithm. Next, the approximate optimization with a barrier method is then applied to accelerate the computational efficiency . Finally, a multi-agent system involving decision-making for multiple unmanned aerial vehicles (UAVs) is utilized to demonstrate the effectiveness of the proposed method in terms of attained performance and computational efficiency  .
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 along this line , 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 relax 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 relaxed nonconvex optimization problem. Additionally, it is analytically shown and established that the requisite desired stationary point exists for the procedures of the hierarchical stages 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) .
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