The robustness of feedback systems with bounded complexity controllers
The robustness of feedback systems with bounded complexity controllers
复制标题
具有有限复杂度控制器的反馈系统的鲁棒性
DOI：
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发表时间：
1996
影响因子：
6.8
通讯作者：
G. Vinnicombe
中科院分区：
文献类型：
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作者：
G. Vinnicombe
用于分析和设计鲁棒反馈控制系统的 H/sub /spl infin// 方法有时因明显保守而受到批评。然而，最近的结果表明，在一组特定的假设下，它们可以提供尽可能保守的结果。例如，v 间隙度量中的球是最大的一组植物，可以通过已知仅满足特定闭环算子的诱导范数的界限的控制器来保证先验稳定。尽管如此，还是有一些不确定性的例子，虽然用 v 间隙度量测量时不确定性很大，但经验丰富的控制系统设计者会认为不确定性相对良性。本文探讨了这样一种可能性：在做出这种判断时，这样的设计者隐含地使用了这样的知识：他总是会选择完成工作所需的最简单的控制器。结果表明，给定控制器复杂度的适当界限，可以获得明显更强的先验鲁棒性结果。
H/sub /spl infin// methods for the analysis and design of robust feedback control systems have sometimes been criticized for an apparent conservatism. However, recent results have shown that they can provide the least conservative results possible under a particular set of assumptions. For example, a ball in the v-gap metric is the largest set of plants that can be guaranteed to be stabilized a priori by a controller known only to satisfy a bound on the induced norm of a particular closed-loop operator. Nevertheless, there are examples of uncertainty which, whilst large when measured by the v-gap metric, would be regarded as relatively benign by an experienced designer of control systems. The present paper examines the possibility that in arriving at this judgment, such a designer is implicitly using the knowledge that he will always choose the least complex controller necessary to do the job. It is shown that, given an appropriate bound on the complexity of the controller, significantly stronger a priori robustness results can be obtained.