Towards a multiresolution approach to linear control
Towards a multiresolution approach to linear control
复制标题
迈向线性控制的多分辨率方法
DOI：
10.1109/tac.2006.878717
复制
发表时间：
2006
影响因子：
6.8
通讯作者：
A. Girard
中科院分区：
文献类型：
--
作者：
A. Girard
我们开发了用于线性控制的多分辨率近似框架。我们构建了线性系统输入函数集的多分辨率分析。输入 u 在尺度 j 上的近似值被定义为最小能量的输入 uj，使得与 u 和 uj 相关的系统轨迹在步长为 2-j 的网格上重合。我们提出了一组生成这种多分辨率分析的小波函数。这些函数称为控制理论小波，满足表示线性系统控制输入的有用属性。作为我们的多分辨率近似框架的应用示例，我们提出了一种根据多个标准对控制输入进行有效编码的方法
We develop a multiresolution approximation framework for linear control. We construct a multiresolution analysis of the set of input functions of a linear system. The approximation of an input u at a scale j is defined as the input uj of minimal energy such that the trajectories of the system associated with u and uj coincide on a grid of step length 2-j. We propose a set of wavelet functions which generate this multiresolution analysis. These functions, called control theoretic wavelets, satisfy useful properties for the representation of control inputs of a linear system. As an example of application of our multiresolution approximation framework, we propose a method for efficient encoding of control inputs with regard to several criteria