Symmetry-Preserving Observers
Symmetry-Preserving Observers
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DOI：
10.1109/tac.2008.2006929
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发表时间：
2008-12-01
影响因子：
6.8
通讯作者：
Rouchon, Pierre
中科院分区：
文献类型：
--
作者：
Bonnabel, Silvere;Martin, Philippe;Rouchon, Pierre
本文提出不变观测器的理论，即对称保持观测器。我们认为观测器由系统的副本和校正项组成，并提出了一种构造方法（基于Cartan移动帧法）来找到所有保持对称性的校正项。构造依赖于一个不变的框架（经典概念）和一个不变的输出错误（这里精确定义的一个不太标准的概念）。利用这一理论，我们为三个工程上感兴趣的例子建立了三个非线性观测器：一个非完整的汽车，一个化学反应堆和一个惯性导航系统。对于每个示例，设计都基于物理对称性，收敛分析依赖于使用不变状态误差，这是一种保持对称性的方法来定义估计误差。
This paper presents the theory of invariant observers, i.e, symmetry-preserving observers. We consider an observer to consist of a copy of the system and a correction term, and we propose a constructive method (based on the Cartan moving-frame method) to find all the symmetry-preserving correction terms. The construction relies on an invariant frame (a classical notion) and on an invariant output-error, a less standard notion precisely defined here. Using the theory we build three non-linear observers for three examples of engineering interest: a non-holonomic car, a chemical reactor, and an inertial navigation system. For each example, the design is based on physical symmetries and the convergence analysis relies on the use of invariant state-errors, a symmetry-preserving way to define the estimation error.