Distributed control of spatially invariant systems over Sobolev spaces
Distributed control of spatially invariant systems over Sobolev spaces
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Sobolev 空间上空间不变系统的分布式控制
DOI：
10.1109/ecc.2014.6862545
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Bassam Bamieh
中科院分区：
文献类型：
--
作者：
J. Epperlein;Bassam Bamieh
我们考虑空间不变系统的基础状态空间是一个内积Sobolev空间。这样的系统出现时，考虑某些状态空间表示的偏微分方程的更高的时间顺序。我们展示了如何标准的结果指数稳定性，稳定性和最优控制与二次准则可以推广到这些系统。这些推广需要一些簿记的空间频率加权函数相关的Sobolev内积，这样做的简单配方。最后给出了波方程和梁方程分布式控制的算例。
We consider spatially invariant systems where the underlying state space is an inner-product Sobolev space. Such systems arise when considering certain state-space representations of partial differential equations of higher temporal order. We show how standard results on exponential stability, stabilizability and optimal control with quadratic criteria can be generalized to those systems. These generalizations require some bookkeeping of spatial frequency weighting functions related to the Sobolev inner products, and simple recipes for doing so are given. The results are illustrated with examples of distributed control of wave and beam equations.