改进MPC的快速双上升-第一部分：分布式情况
Improving Fast Dual Ascent for MPC - Part I: The Distributed Case
摘要：
在对偶分解中，具有特定结构的最优化问题的对偶使用（子）梯度和最近的快速梯度法以分布式方式求解。传统的对偶分解存在两个主要的缺点。第一个是收敛通常很慢，尽管快速梯度法已经显著地改善了这种情况。第二个问题是最优步长的计算需要集中计算，这阻碍了算法的完全分布式实现。在本文中，第一个问题是通过提供一个更严格的双重功能比以前在文献中报道的特征。然后提出了一种分布式并行算法，在该算法中，所提供的对偶函数近似在每一步中被最小化。由于该近似比标准和快速对偶分解中使用的近似更精确，因此收敛性得到改善。对于第二个问题，我们扩展了最近的结果，允许一个完全分布的参数选择的算法。此外，我们展示了如何将所提出的算法的分布式模型预测控制（DMPC）中出现的最优化问题，并表明，所提出的分布式算法享有分布式重新配置，即插即用，在DMPC的上下文中。
英文摘要：
In dual decomposition, the dual to an optimization problem with a specific structure is solved in distributed fashion using (sub)gradient and recently also fast gradient methods. The traditional dual decomposition suffers from two main short-comings. The first is that the convergence is often slow, although fast gradient methods have significantly improved the situation. The second is that computation of the optimal step-size requires centralized computations, which hinders a fully distributed implementation of the algorithm. In this paper, the first issue is addressed by providing a tighter characterization of the dual function than what has previously been reported in the literature. Then a distributed and a parallel algorithm are presented in which the provided dual function approximation is minimized in each step. Since the approximation is more accurate than the approximation used in standard and fast dual decomposition, the convergence properties are improved. For the second issue, we extend a recent result to allow for a fully distributed parameter selection in the algorithm. Further, we show how to apply the proposed algorithms to optimization problems arising in distributed model predictive control (DMPC) and show that the proposed distributed algorithm enjoys distributed reconfiguration, i.e. plug-and-play, in the DMPC context.
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