Introduction

The PieceWise Affine system IDentification toolbox (PWAID), a free Matlab toolbox for identification of piecewise affine models, has been developed by Simone Paoletti and Jacob Roll in the framework of the EU Project HYCON (Milestone M3.3.3: Implementation of at least one identification tool).

The toolbox implements two identification algorithms. The Mixed-Integer Programming (MIP) algorithm, presented in [2], is an algorithm for optimal identification of Hinging-Hyperplane ARX (HHARX) models. It formulates the identification problem as a mixed-integer linear or quadratic program that can be solved for the global optimum. The bounded-error algorithm, presented in [1], allows the user to impose a bound on the prediction error, and estimates a PieceWise affine ARX (PWARX) model which satisfies the bounded-error condition for all the samples in the estimation data set.

PWAID has been designed as a stand-alone toolbox. A minimum requirement is the availability of at least one solver for (mixed-integer) linear and quadratic programs. Given the input-output data, the user is only asked to select the model structure, choose the identification algorithm, and set the parameters of the selected algorithm, if any. The identified model is then automatically returned. The Data Interchange Format developed within the project HYCON is supported to facilitate the data exchange with other tools (e.g., tools for analysis, verification and control of hybrid systems). Interfaces to several LP/QP/MILP/MIQP solvers, and functions for conversion of the results, are provided. The software is also compatible for joint use with the Hybrid Toolbox, the Multi-Parametric Toolbox, and the Hybrid Identification Toolbox. Some functionalities of the mentioned toolboxes can be accessed directly from PWAID.

Download

The toolbox can be downloaded here.

License

The PWAID toolbox is distributed under the GNU Public License.

Version history

The toolbox is still under development, and bug reports, suggestions and other comments are very welcome!

2007-04-04: POLYCHECK.M updated to better handle numerically problematic cases.

2007-03-30: First release.

Contact information

Bug reports, comments etc. can be sent to any of the following email addresses:

Bibliography

[1] Alberto Bemporad, Andrea Garulli, Simone Paoletti, and Antonio Vicino. A bounded-error approach to piecewise affine system identification. IEEE Transactions on Automatic Control, 50(10):1567-1580, October 2005.

[2] Jacob Roll, Alberto Bemporad, and Lennart Ljung. Identification of piecewise affine systems via mixed-integer programming. Automatica, 40(1):37-50, January 2004.