Approximate reduction of dynamic systems
- 作者：Paulo Tabuada ; Aaron D. Ames ; Agung Julius ; George J. Pappas
- 关键词：Reduction ; Approximate reduction ; Dynamical systems ; Incremental input-to-state stability
- 刊名：Systems and Control Letters
- 出版年：2008
- 期刊代码：171_01676911
- 类别：et
- 出版时间：July 2008
- 卷：57
- 期：7
- 页码：538-545
- 文件大小：841 K
摘要
The reduction of dynamic systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an “exact” manner–as is the case with mechanical systems with symmetry–which, unfortunately, limits the type of systems to which it can be applied. The goal of this paper is to consider a more general form of reduction, termed approximate reduction, in order to extend the class of systems that can be reduced. Using notions related to incremental stability, we give conditions on when a dynamic system can be projected to a lower dimensional space while providing hard bounds on the induced errors, i.e. when it is behaviourally similar to a dynamic system on a lower dimensional space. These concepts are illustrated on a series of examples.