Decomposition Methods for Distributed Quadratic Programming with Application to Distributed Model Predictive Control

This paper studies different decomposition techniques for coupled quadratic programming problems arising in Distributed Model Predictive Control (DMPC). Here the resulting global problem is not directly separable due to the dynamical coupling between the agents in the networked system. In the last decade, the Alternating Direction Method of Multipliers (ADMM) has been generally adopted as the standard optimization algorithm in the DMPC literature due to its fast convergence and robustness with respect to other algorithms as the dual decomposition method. The goal of this paper is to introduce a novel decomposition technique which with respect to ADMM can reduce the number of iterations required for convergence. A benchmark model is used at the end of the paper to numerically show these results under different coupling factors and network topologies. The proposed method is closely related to the Diagonal Quadratic Approximation (DQA) and its successor, the Accelerated Distributed Augmented Lagrangian (ADAL) method. In these algorithms the coupling constraint is relaxed by introducing an augmented Lagrangian and the resulting non-separable quadratic penalty term is approximated through a sequence of separable quadratic functions. This paper proposes a different separable approximation for the penalty term which leads to several advantages as a flexible communication scheme and an overall better convergence when the coupling is not excessively high.