测地流的简单内禀约化观测器
A simple intrinsic reduced-observer for geodesic flow
摘要：
Aghannan和Rouchon针对一类非线性力学系统：具有位形（位置）测量的Lagrange系统，提出了一种新的渐近观测器设计方法。该观测器是基于黎曼结构的配置流形赋予动能度量，是内在的。他们证明了局部收敛。当系统是保守的，我们提出了一个全局收敛的内在约化观测器的Jacobi度量的基础上。对于非保守系统，该观测器可作为Aghannan和Rouchon观测器的补充。更一般地，简化观测器提供了具有位置测量的测地流的速度估计。因此，在理想不可压缩流体的情况下，它可以（正式）用作流体流量软传感器。当曲率在所有平面上都为负时，测地流对初始条件敏感。令人惊讶的是，这种不稳定性产生了更快的收敛。
英文摘要：
Aghannan and Rouchon proposed a new design method of asymptotic observers for a class of nonlinear mechanical systems: Lagrangian systems with configuration (position) measurements. The observer is based on the Riemannian structure of the configuration manifold endowed with the kinetic energy metric and is intrinsic. They proved local convergence. When the system is conservative, we propose a globally convergent intrinsic reduced-observer based on the Jacobi metric. For non-conservative systems the observer can be used as a complement to the one of Aghannan and Rouchon. More generally the reduced-observer provides velocity estimation for geodesic flow with position measurements. Thus it can be (formally) used as a fluid flow soft sensor in the case of a perfect incompressible fluid. When the curvature is negative in all planes the geodesic flow is sensitive to initial conditions. Surprisingly this instability yields faster convergence.
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