On Fundamental Limitations of Dynamic Feedback Control in Regular Large-Scale Networks
On Fundamental Limitations of Dynamic Feedback Control in Regular Large-Scale Networks
复制标题
关于常规大规模网络中动态反馈控制的基本局限性
DOI：
10.1109/tac.2019.2909811
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发表时间：
2017
影响因子：
6.8
通讯作者：
Bassam Bamieh
中科院分区：
文献类型：
--
作者：
E. Tegling;P. Mitra;H. Sandberg;Bassam Bamieh
在本文中，我们研究了大规模网络动态系统的分布反馈控制的基本性能限制。具体来说，我们解决的问题，是否动态反馈控制器比静态（无记忆）的局部约束时，执行更好。我们考虑分布式线性共识和车辆编队控制问题建模复曲面格型网络。对于由此产生的空间不变的系统，我们研究了大规模的渐近（网络大小）的全球性能指标，量化网络的一致性水平。利用来自相对状态测量的静态反馈，已知这样的度量在低空间维度的网格中不利地缩放，从而防止例如一维车辆串像刚性物体一样移动。我们表明，同样的限制一般也适用于动态反馈控制，是本地的一阶。这意味着在控制器中加入一个局部状态可以得到与无记忆情形相似的渐近性能。除非控制器可以访问其相对于绝对参考系的局部状态的无噪声测量，否则这保持不变，在这种情况下，控制器存储器的添加可以从根本上提高性能。在模拟的排与20-200辆车，我们表明，我们得到的性能限制表现为不必要的手风琴状运动。类似的行为在任何可嵌入低维复曲面晶格的网络中都是可以预期的，并且同样的基本限制也适用。为了得到我们的结果，我们提出了一个通用的技术框架，在大型网络的限制空间不变系统的稳定性和性能的分析。
In this paper, we study fundamental performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of whether dynamic feedback controllers perform better than static (memoryless) ones when subject to locality constraints. We consider distributed linear consensus and vehicular formation control problems modeled over toric lattice networks. For the resulting spatially invariant systems, we study the large-scale asymptotics (in network size) of global performance metrics that quantify the level of network coherence. With static feedback from relative state measurements, such metrics are known to scale unfavorably in lattices of low spatial dimensions, preventing, for example, a one-dimensional string of vehicles to move like a rigid object. We show that the same limitations in general apply also to dynamic feedback control that is locally of first order. This means that the addition of one local state to the controller gives a similar asymptotic performance to the memoryless case. This holds unless the controller can access noiseless measurements of its local state with respect to an absolute reference frame, in which case the addition of controller memory may fundamentally improve performance. In simulations of platoons with 20–200 vehicles, we show that the performance limitations we derive manifest as unwanted accordionlike motions. Similar behaviors are to be expected in any network that is embeddable in a low-dimensional toric lattice, and the same fundamental limitations would apply. To derive our results, we present a general technical framework for the analysis of stability and performance of spatially invariant systems in the limit of large networks.