Design of distributed controllers realizable over arbitrary directed networks
Design of distributed controllers realizable over arbitrary directed networks
复制标题
可通过任意有向网络实现的分布式控制器的设计
DOI：
--
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
N. Elia
中科院分区：
文献类型：
--
作者：
Satya Mohan Vamsi Andalam;N. Elia
研究了一组通过任意有向通信网络动态连接的子系统的稳定化分布式输出反馈控制器的设计问题，该控制器满足H2和H∞性能目标.对于一类特殊的离散线性定常互联系统，其特征在于其状态空间矩阵的结构性质，我们设计稳定的分布式控制器，可以使用可用的网络沿着的互联系统的子系统。这是通过输出反馈线性控制器的参数化来实现的，该参数化使闭环H2和H∞范数条件线性化，并提供等效的线性矩阵不等式（LMI）。使用这些线性矩阵不等式，我们制定的H2和H∞范数的最小化半定规划（SDP），可以有效地解决使用成熟的技术和工具。这些SDP的解决方案，使我们能够合成相应的控制器，可实现在给定的网络。即使我们只提供了充分条件的稳定分布式控制器的设计，仿真表明，我们得到的合成控制器提供了良好的性能，尽管次优相比，集中式控制器。从本质上讲，我们获得的优势，设计可实现的分布式控制器的代价是轻微的性能下降相比，集中式的解决方案。
We consider the problem of designing stabilizing distributed output-feedback controllers that achieve H2 and H∞ performance objectives for a group of sub-systems dynamically interconnected via an arbitrary directed communication network. For a particular class of discrete-time linear time-invariant interconnected systems that are characterized by a structural property of their state-space matrices, we design stabilizing distributed controllers which can use the available network along with the sub-systems of the interconnected system. This is achieved by means of a parameterization for the output-feedback linear controllers that linearizes the closed-loop H2 and H∞ norm conditions and provide equivalent linear matrix inequalities (LMIs). Using these LMIs, we formulate the minimization of H2 and H∞ norms as semi-definite programs (SDPs) that can be efficiently solved using well-established techniques and tools. The solutions of these SDPs allow us to synthesize the corresponding controllers that are realizable over the given network. Even though we provide only sufficiency conditions for the design of stabilizing distributed controllers, simulations show that the synthesized controllers we obtain provide good performance in spite of being suboptimal compared to the centralized controller. In essence, we gain the advantage of designing realizable distributed controllers at the expense of slight performance degradation compared to the centralized solutions.