Communication Delay Co-Design in $\mathcal{ H}_{2}$-Distributed Control Using Atomic Norm Minimization
Communication Delay Co-Design in $\mathcal{ H}_{2}$-Distributed Control Using Atomic Norm Minimization
复制标题
$mathcal{ H}_{2}$-使用原子范数最小化的分布式控制中的通信延迟协同设计
DOI：
10.1109/tcns.2015.2497100
复制
发表时间：
2014
影响因子：
4.2
通讯作者：
N. Matni
中科院分区：
文献类型：
--
作者：
N. Matni
在为大型系统设计分布式控制器时，控制器的驱动、传感和通信架构不能再被视为给定的。特别是，使用密集架构实现的控制器通常优于使用较简单架构实现的控制器——然而，还希望最小化构建用于实现控制器的架构的成本。最近推出的正则化设计框架将控制器架构/控制律协同设计问题作为联合优化控制器架构成本和闭环性能的竞争指标之一，并表明该任务可以通过使用适当的原子范数惩罚增强最优控制问题的变分解来完成。尽管引入了对于驱动、感测和联合驱动/感测架构的设计有用的原子规范的显式构造，但是没有给出用于设计通信架构的原子规范的这样的构造。本文描述了一种可用于设计通信架构的原子范数，其中所得到的分布式最优控制器由凸程序的解指定。使用这个原子范数，我们证明在 $\mathcal{ H}_{2}$ 分布式最优控制的背景下，可以通过使用有限维二阶锥规划来执行通信架构/控制律协同设计任务。
When designing distributed controllers for large-scale systems, the actuation, sensing, and communication architectures of the controller can no longer be taken as given. In particular, controllers implemented using dense architectures typically outperform controllers implemented using simpler ones—however, it is also desirable to minimize the cost of building the architecture used to implement a controller. The recently introduced Regularization for Design framework poses the controller architecture/control law co-design problem as one of jointly optimizing the competing metrics of controller architecture cost and closed-loop performance, and shows that this task can be accomplished by augmenting the variational solution to an optimal control problem with a suitable atomic norm penalty. Although explicit constructions for atomic norms useful for the design of actuation, sensing and joint actuation/sensing architectures are introduced, no such construction is given for atomic norms used to design communication architectures. This paper describes an atomic norm that can be used to design communication architectures for which the resulting distributed optimal controller is specified by the solution to a convex program. Using this atomic norm, we then show that in the context of $\mathcal{ H}_{2}$-distributed optimal control, the communication architecture/control law co-design task can be performed through the use of finite-dimensional second-order cone programming.