具有齐次观测的不变系统的观测器设计
Observer design for invariant systems with homogeneous observations
摘要：
本文考虑有限维连通李群上的不变系统的非线性观测器的设计问题，其测量值由相应的齐性空间上的传递群作用产生.我们考虑的情况下，群作用具有相反的不变性的系统不变性，并表明，组运动学项目的最小实现的系统可观察的动力学均匀的输出空间。观测器的设计问题是通过设计一个观测器的投影输出动态，然后提升到李群。一个结构分解定理的投影系统的观察员提供与表征相关的观察员误差动态的不变性。我们提出了一个观察器设计的基础上的梯度结构，导致强（几乎）整体收敛性能的规范误差动态齐次输出空间。观测器动态被提升到一个自然的方式和李群上的观测器的梯度误差动态几乎全局收敛到系统的不可观测子群，群作用的稳定器。
英文摘要：
This paper considers the design of nonlinear observers for invariant systems posed on finite-dimensional connected Lie groups with measurements generated by a transitive group action on an associated homogeneous space. We consider the case where the group action has the opposite invariance to the system invariance and show that the group kinematics project to a minimal realisation of the systems observable dynamics on the homogeneous output space. The observer design problem is approached by designing an observer for the projected output dynamics and then lifting to the Lie-group. A structural decomposition theorem for observers of the projected system is provided along with characterisation of the invariance properties of the associated observer error dynamics. We propose an observer design based on a gradient-like construction that leads to strong (almost) global convergence properties of canonical error dynamics on the homogeneous output space. The observer dynamics are lifted to the group in a natural manner and the resulting gradient-like error dynamics of the observer on the Lie-group converge almost globally to the unobservable subgroup of the system, the stabiliser of the group action.
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