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首页> 外文会议>Annual Allerton Conference on Communication, Control, and Computing >Decomposition Methods for Distributed Quadratic Programming with Application to Distributed Model Predictive Control
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Decomposition Methods for Distributed Quadratic Programming with Application to Distributed Model Predictive Control

机译：分布式二次规划的分解方法及其在分布式模型预测控制中的应用

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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.
机译：本文针对分布式模型预测控制（DMPC）中出现的耦合二次规划问题研究了不同的分解技术。由于网络系统中代理之间的动态耦合，由此产生的全局问题无法直接分离。在最近的十年中，由于倍数的交替方向方法（ADMM）作为对偶分解方法相对于其他算法具有快速收敛性和鲁棒性，因此在DMPC文献中通常被用作标准优化算法。本文的目的是介绍一种新颖的分解技术，该技术相对于ADMM可以减少收敛所需的迭代次数。本文结尾处使用了基准模型，以数字方式显示了在不同耦合因子和网络拓扑下的这些结果。所提出的方法与对角二次逼近（DQA）及其后继者加速分布增强拉格朗日（ADAL）方法密切相关。在这些算法中，通过引入增强的拉格朗日法来放松耦合约束，并且通过一系列可分离的二次函数来近似所得的不可分离的二次惩罚项。本文针对惩罚项提出了一种不同的可分离的近似方法，当耦合度不太高时，它可以带来多种优势，例如灵活的通信方案和总体上更好的收敛性。

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