Pertinent choice of parameters for discrete Kautz approximation

• Published in: IEEE transactions on automatic control Vol. 47; no. 5; pp. 783 - 787
• Main Authors: Tanguy, N., Morvan, R., Vilbe, P., Calvez, L.-C.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2002; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Approximation; Automatic control; Computer aided manufacturing; Computer Science; Computer science; control theory; systems; Control systems; Control theory. Systems; Cost function; Engineering Sciences; Exact sciences and technology; Flexible manufacturing systems; Flow production systems; Manufacturing systems; Mathematical analysis; Mathematical models; Micro and nanotechnologies; Microelectronics; Minimization; Modeling and Simulation; Modelling and identification; Optimization; Production control; Production systems; Truncation errors; Uncertainty; Upper bounds; Approximation; Modeling; Orthogonal polynomial; Kautz approximation; Kautz functions; orthonormal approximation; modeling
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2002.1000273

Kautz functions have received much attention in the recent mathematical modeling and identification literature. These functions which involve free parameters can approximate efficiently signals with strong oscillatory behavior. We consider here the choice of the free parameters in discrete (two-parameter) Kautz approximation. Using a key relationship between Kautz and Laguerre expansions we derive an upper bound for the quadratic truncation error. Minimization of this upper bound yields pertinent parameters, whose computation then requires reduced knowledge of the function to be modeled.