Efficient and reliable algorithms and associated software for system identification and control are highly desirable both in industry and academia. New tools have been developed and are integrated into the SLICOT Library (freely available in the directory /pub/WGS/SLICOT/, and its subdirectories, of the ftp site ftp://wgs.esat.kuleuven.ac.be), the most important outcome of the Numerics in Control Network NICONET. To increase the user-friendliness, Matlab and Scilab interfaces have been made available for many computational routines. The main algorithmic and software developments during the year 2000 are related to system analysis and synthesis, including model and controller reduction calculations (in cooperation with Dr. Andras Varga, German Aerospace Center, Institute of Robotics and Mechatronics, Oberpfaffenhofen, D-82234 Wessling, Germany), linear system identification based on subspace techniques, the solution of discrete-time Sylvester equations, and the factorization and/or solution of symmetric positive definite block Toeplitz matrices or systems of equations, respectively (in cooperation with Prof. Paul van Dooren, CESAME, Universite Catholique de Louvain, Louvain-la-Neuve, Belgium, and Daniel Kressner, Technical University Chemnitz, Chemnitz, Germany). Structure exploiting algorithms and specialized linear algebra algorithms, performing all the processing steps of the commonly used subspace-based identification approaches, MOESP and N4SID, have been thoroughly investigated. These algorithms start by building a block-Hankel-block matrix H, using the available input-output data, and finding an upper triangular factor R from a QR (or RQ) factorization of H. Either standard or fast QR factorization of H, as well as Cholesky factorization of the matrix product H'H, fastly built exploiting the block-Hankel structure, are used for data compression. When a fast factorization algorithm fails, the QR factorization is automatically called. Usually, the fast algorithms enabled to obtain the factor R by more than 50 times faster than with the standard procedure. An option to process the input-output data either in a single, or in multiple data batches is included, which is important from a practical point of view. Moreover, the calculations are organized so that much flexibility is achieved. The techniques are implemented in the new system identification toolbox for the SLICOT Library. Two Matlab demonstration packages, for the newly developed SLICOT toolboxes for structured matrix decompositions and linear system identification, have been recently posted on the SLICOT ftp site. The results obtained so far show that the SLICOT-based calculations could significantly outperform Matlab calculations in terms of speed, while retaining the accuracy.
Co-ordinator(s): Sabine
Van Huffel
Researcher(s): Nicola
Mastronardi, Vasile
Sima
Research Homepage:
http://www.win.tue.nl/wgs/niconet.html