Optimal Mode Decomposition for control. More...

Classes
class	DataStore
	interface to internal representation of OMDc data More...

class	LineSearchFunctor
	Functor for linesearch along geodesic. More...

Detailed Description

Optimal Mode Decomposition for control.

The original identification problem is

$\min_{L,M,P} \Vert Y - LML^\top X - LPU \Vert_F^2 \qquad X = [s_0 \cdots s_{m-2}], \,\, Y = [s_1 \cdots s_{m-1}]$

where the low-rank model

$L\in\mathbb{R}^{n\times r}, \,\, M\in\mathbb{R}^{r\times r} \,\, P\in\mathbb{R}^{r\times p}$

shall approximate the given data set $S\in\mathbb{R}^{n\times m}$ for inputs $U\in\mathbb{R}^{p\times (m-1)}$ . The original problem can be transformed into

$\min_L \Vert (I-LL^\top)Y +LL^\top \hat{Y} \big( I - \hat{X}^\top L ( L^\top \hat{X}\hat{X}^\top L )^{-1} L\top \hat{X} \big) \Vert_F^2 \quad \mathrm{s.t.} \,\,L^\top L = I$

where

$\hat{X} = X \big(I - U^\top (U U^\top)^{-1} U\big) \qquad \hat{Y} = Y \big(I - U^\top (U U^\top)^{-1} U\big)$

Classes

Detailed Description