论文标题
在结构化粘合环与结构化控制器的设计上：相对测量反馈的情况
On Structured-Closed-Loop versus Structured-Controller Design: the Case of Relative Measurement Feedback
论文作者
论文摘要
我们认为最佳分布式控制器设计问题受两个结构要求的约束：即可用的测量值和子控制器的交互，受图形结构的控制，相对反馈，即仅可用于控制器的测量差异。我们根据控制器的传输功能，状态空间实现或产生的闭环映射来形式化控制器局部性。我们证明，相对反馈要求可以写成对控制器的凸限制，并且（在特殊情况下）在所得的闭环上（在特殊情况下），我们表征了相对反馈控制器的允许结构。我们证明，即使在连续的时间IIR设置中，稀疏的闭环设计也是结构化控制器状态空间设计的凸松弛。这正式化并扩展了最近开发的系统水平合成框架的结果。我们通过构建一类示例（基于相对反馈要求）来量化与此凸松弛相关的性能差距的第一步，该示例的性能差异通过H2 Norm衡量，是无限的。提出的结果用于对比分布式控制设计中的几个结构性约束问题，这些问题仍然是开放问题。
We consider the optimal distributed controller design problem subject to two structural requirements: locality, i.e. available measurements and sub-controllers' interactions are governed by a graph structure, and relative feedback, i.e. only differences of measurements are available to the controller. We formalize controller locality in terms of the controller's transfer function, state-space realization, or resulting closed-loop mapping. We demonstrate that the relative feedback requirement can be written as a convex constraint on the controller and (in special cases) on the resulting closed-loop, and we characterize the allowable structures of relative feedback controllers. We prove that sparse closed-loop design is a convex relaxation of structured controller state-space design, even in the continuous time IIR setting. This formalizes and extends results of the recently developed System Level Synthesis framework. We take a first step toward quantifying the performance gap associated with this convex relaxation by constructing a class of examples (based on relative feedback requirements) for which the difference in performance, measured by an H2 norm, is infinite. The results presented are used to contrast several issues of structural constraints in distributed control design that remain as open problems.
