Observability of nonlinear systems - an algebraic approach
Observability of nonlinear systems - an algebraic approach
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非线性系统的可观测性 - 一种代数方法
DOI：
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发表时间：
2004
期刊：
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通讯作者：
B. Tibken
中科院分区：
文献类型：
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作者：
B. Tibken
本文研究了非线性系统的全局能观性。其主要思想是推导出一个判据，该判据允许根据系统的输出来决定是否可以区分系统的两个初始状态。这一众所周知的准则等价于一组无限的非线性方程。如果系统是全局可观测的，则这组方程有一个非常特殊的解集，它可以用代数来刻画。基于交换代数的结果，给出了描述解集的一些新的算法。这允许对多项式系统和某些特定类型的非线性系统进行全局可观测性分析。将新方法应用于文献中的一个算例。
In this contribution global observability of nonlinear systems is investigated. The main idea is to derive a criterion which allows to decide if two initial states of a system can be distinguished by the output of the system. This well known criterion is equivalent to an infinite set of nonlinear equations. If the system is globally observable this set of equations has a very special solution set which can be characterized algebraically. Based on results from commutative algebra some new algorithmic methods to describe the solution set are given. This allows a global observability analysis for polynomial systems and for some specific classes of nonlinear systems. The new method is applied to an example from the literature.