Pre-Lie algebra characterization of SISO feedback invariants
Pre-Lie algebra characterization of SISO feedback invariants
复制标题
SISO 反馈不变量的预李代数表征
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Luis A. Duffaut Espinosa
中科院分区：
文献类型：
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作者：
W. S. Gray;M. Thitsa;Luis A. Duffaut Espinosa
变换群自诞生以来就在系统理论中得到了广泛的应用。最近，作者描述了一个非线性输入输出系统的反馈变换群，其特征在于一个Chen-Fliess函数展开。特别地，给出了一类反馈不变序列的识别算法。他们的关系系列具有明确的相对程度也制定了。本文是这一工作的继续，但有三个创新。首先，新开发的代数工具，从该领域的前李代数的应用，使更多的洞察不变性理论。在本文中，相对度的作用是减少有利于系统与任意生成序列。最后，动态输出反馈，所描述的反馈产品，被认为是明确的。
Transformation groups have been used extensively in system theory since its inception. Recently, a feedback transformation group for a nonlinear input-output system characterized by a Chen-Fliess functional expansion was described by the authors. In particular, an algorithm was given to identify a class of feedback invariant series. Their relationship to series having well-defined relative degree was also developed. This paper is a continuation of that work, but with three innovations. First, newly developed algebraic tools from the field of pre-Lie algebras are applied to give more insight into the invariance theory. The role of relative degree in this paper is diminished in favor of systems with arbitrary generating series. Finally, dynamic output feedback, as described by the feedback product, is considered explicitly.