Name
Title | ||
|---|---|---|
Bi-Orthonormal Polynomial Basis Function Framework With Applications in System Identification. |
Abstract | ||
|---|---|---|
Numerical aspects are of central importance in identification and control. Many computations in these fields involve approximations using polynomial or rational functions that are obtained using orthogonal or oblique projections. The aim of this paper is to develop a new and general theoretical framework to solve a large class of relevant problems. The proposed method is built on the introduction of bi-orthonormal polynomials with respect to a data-dependent bi-linear form. This bi-linear form generalises the conventional inner product and allows for asymmetric and indefinite problems. The proposed approach is shown to lead to optimal numerical conditioning ( = 1) in a recent frequency-domain instrumental variable system identification algorithm. In comparison, it is shown that these recent algorithms exhibit extremely poor numerical properties when solved using traditional approaches. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1109/TAC.2015.2509451 | IEEE Trans. Automat. Contr. |
Keywords | Field | DocType |
Approximation methods,Approximation algorithms,Frequency-domain analysis,Mathematical model,Control systems,Instruments,Linear systems | Polynomial basis,Approximation algorithm,Mathematical optimization,Linear system,Polynomial,Control theory,Orthonormal basis,Rational function,System identification,Mathematics,Computation | Journal |
Volume | Issue | ISSN |
61 | 11 | 0018-9286 |
Citations | PageRank | References |
1 | 0.36 | 12 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Robbert van Herpen | 1 | 27 | 4.27 |
| Okko H. Bosgra | 2 | 109 | 16.28 |
| Tom Oomen | 3 | 61 | 9.63 |