HIT Toolbox

HIT logo
The Hybrid Identification Toolbox (HIT) is a free MatLab toolbox for regression with Piece-Wise Affine (PWA) maps and identification of Piece-Wise AutoRegressive Exogenous (PWARX) models. HIT implements the clustering-based algorithms documented in some of my papers (see  Bibliography.txt in the root directory of HIT).
Its development has been supported by the EU projects HYGEIA and HYCON.

Download

16 Jan.2006: HIT 1.00 - .zip package. Required software: MatLab >= 6.5.

Installation and first steps

HIT uses the Multi Parametric Toolbox (MPT) developed at ETH (Zurich, Switzerland) for handling polytopes and solving LP/QP problems.
From 06/12/2005, HIT is shipped as part of MPT, thus it is automatically installed if you download  MPT >= 2.5.

For a stand-alone installation of HIT, unzip it and add its path (and the path of the subdirectories as well) to the matlabpath.
Then, try out the examples in the /examples directory. The code of the examples is well commented and you won't have any difficulty in adapting them for solving your problems.
In the /doc directory there is the html documentation of HIT and a manual (in pdf).


Main features of HIT

  • Clustering algorithms: weighted K-means and single-linkage
  • Pattern recognition algorithms:
    • Linear Support Vector Classifiers (SVC)
    • Multicategory Robust Linear Programmng (MRLP)
    • Proximal Support Vector Classifiers (PSVC)
  • Continuous and discontinuous PWA/PWARX models
  • Post-processing: optional re-classification of outliers

Problems solved by HIT

  • Regression problem: reconstruct a PWA map from noisy samples. In this case, one is not dealing with a dynamical system (with inputs and outputs) but just with a static map that is sampled. HIT returns a data-based PWA approximation of the map (see the examples ex_approx_1d.m and ex_cake1.m. - the second example shows how to approximate discontinuous PWA maps). The approximation has idmodes.s modes (in HITs jargon, a "mode" is an affine hyperplane + the region where it is valid).
  • Identification problem: reconstruct a PWARX hybrid system from noisy inputs and outputs (see for instance ex_pwarx_2d_3modes.m). PWARX systems are multi-input/single-output descriptions of hybrid systems. Thus no state appears. But they can be re-written as PWA system pretty much the same way ARX models can be re-written as linear systems in the state-space form.

    The PWARX systems used in the HIT toolbox are in the form

    y(k)=idmodes.par{i}* [x(k)' 1]' if x(k) \in \idmodes.regions(i)

    where x(k)=[y(k-1) ... y(k-na) u'(k-1) ... u'(k-nb)] is the vector of regressors and the integers na and nb are the system order. If you want to write a PWARX model in the PWA form you have to interpret x(k) as a state, y(k) as an output and find the matrices A_i, b_i, f_i, C_i, D_i, g_i that given a sequence u(k) produce the same output of the PWARX model.

Citation info

BibTeX entry:

@MISC{HIT,
author = {G. Ferrari-Trecate},
title = {{Hybrid Identification Toolbox (HIT)}},
year = {2005},
}

Acknowledgments

See the file Acknowledgments.txt in the root directory of HIT.