Letellier Christophe, Aguirre Luis A
Analyse Topologique et de Modélisation de Systèmes Dynamiques, Université de Rouen-CORIA, BP 12, F-76801 Saint-Etienne du Rouvray Cedex, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jun;79(6 Pt 2):066210. doi: 10.1103/PhysRevE.79.066210. Epub 2009 Jun 22.
In practical problems, the observability of a system not only depends on the choice of observable(s) but also on the space which is reconstructed. In fact starting from a given set of observables, the reconstructed space is not unique, since the dimension can be varied and, in the case of multivariate measurement functions, there are various ways to combine the measured observables. Using a graphical approach recently introduced, we analytically compute symbolic observability coefficients which allow to choose from the system equations the best observable, in the case of scalar reconstructions, and the best way to combine the observables in the case of multivariate reconstructions. It is shown how the proposed coefficients are also helpful for analysis in higher dimension.
在实际问题中，系统的可观测性不仅取决于可观测变量的选择，还取决于重建的空间。事实上，从给定的一组可观测变量出发，重建空间并非唯一，因为维度可以变化，而且在多变量测量函数的情况下，有多种方式来组合测量得到的可观测变量。利用最近引入的一种图形方法，我们通过解析计算符号可观测性系数，在标量重建的情况下，该系数能从系统方程中选出最佳可观测变量；在多变量重建的情况下，能确定组合可观测变量的最佳方式。文中展示了所提出的系数在高维分析中也很有帮助。
