A Behavioral Approach to Control of Distributed Systems
A Behavioral Approach to Control of Distributed Systems
复制标题
分布式系统控制的行为方法
DOI：
10.1137/s0363012997321784
复制
发表时间：
1999
影响因子：
2.2
通讯作者：
S. Shankar
中科院分区：
文献类型：
--
作者：
H. Pillai;S. Shankar
本文发展了一种分布式系统的控制理论（即，由常系数偏微分算子系统定义的那些）通过Willems的行为方法。这里的研究是代数的，因为它将分布式系统的行为与多项式环上的自由模的子模联系起来。与集总情况一样，分布式阿尔马系统的行为可以归结为AR行为。本文首先根据Willems关于集中系统的定义，研究了AR能控分布系统的概念。它表明，在集总的情况下，类可控AR系统正是类MA系统。然后，它表明，可控的2-D分布系统必然是由自由子模块，而这不是情况下的n-D分布系统，$n \ge 3$。因此，这指出了这两种情况之间的一个重要区别。本文然后定义了两个概念的自治分布式系统，模仿集总自治系统的不同属性。
控制是将一个行为限制在一个特定的期望的自主子行为的过程。本文提出了一种稳定性概念，推广了集总系统的输入-输出有界稳定性，并定义了分布系统的极点配置问题。然后，本文解决了这个问题的一类分布式行为。
This paper develops a theory of control for distributed systems (i.e., those defined by systems of constant coefficient partial differential operators) via the behavioral approach of Willems. The study here is algebraic in the sense that it relates behaviors of distributed systems to submodules of free modules over the polynomial ring in several indeterminates. As in the lumped case, behaviors of distributed ARMA systems can be reduced to AR behaviors. This paper first studies the notion of AR controllable distributed systems following the corresponding definition for lumped systems due to Willems. It shows that, as in the lumped case, the class of controllable AR systems is precisely the class of MA systems. It then shows that controllable 2-D distributed systems are necessarily given by free submodules, whereas this is not the case for n-D distributed systems, $n \ge 3$. This therefore points out an important difference between these two cases. This paper then defines two notions of autonomous distributed systems which mimic different properties of lumped autonomous systems.
Control is the process of restricting a behavior to a specific desirable autonomous subbehavior. A notion of stability generalizing bounded input--bounded output stability of lumped systems is proposed and the pole placement problem is defined for distributed systems. This paper then solves this problem for a class of distributed behaviors.