New Identification Approach for PWA Model

Overview

PWA (Piecewise affine) model is natural and powerful extension of commonly used linear models. But, its identification from noisy data set has been extremely challenging problem so far, and our group have been developing the new method for this problem.

In our method, the model is also represented by a set of data and constructed by compressing the noisy data set obtained from the real world. And, we developed compression strategy which removes undesired noise from the data set while preserving essential property of the target system. The compression is performed via l1 optimization, which can enjoy the benefits of rapidly growing computation technology, and can be performed for the problems with practical size.

Now, our interest is to develop the strategy for more larger scale / higher dimensional problems and to search for stimulating applications.

Publications

Code

Identification via Data Compression

In our approach, a noisy data set (left) is simplified by compressing the data set while preserving PWA structure. The obtained data set (right) represents the model suitable for analysis.

Compression power and PWA map

This movie shows how the obtained PWA map changes according to the power of compression.

Continuous-time System Identification

Continuous-time model is powerful tool for describing practical systems because the most of natural laws can be described by continuous-time differential equations. However, the most of the researches on system identification method are focused on discrete-time models.

Comparison between discrete-time and continuous-time models