Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
On global identifiability for arbitrary model parametrizations
Automatica (Journal of IFAC)
An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems
Automatica (Journal of IFAC)
A theoretical basis for the reduction of polynomials to canonical forms
ACM SIGSAM Bulletin
| Hi-index | 22.14 |
The framework of differential algebra, especially Ritt's algorithm, has turned out to be a useful tool when analyzing the identifiability of certain nonlinear continuous-time model structures. This framework provides conceptually interesting means to analyze complex nonlinear model structures via the much simpler linear regression models. One difficulty when working with continuous-time signals is dealing with white noise in nonlinear systems. In this paper, difference algebraic techniques, which mimic the differential-algebraic techniques, are presented. Besides making it possible to analyze discrete-time model structures, this opens up the possibility of dealing with noise. Unfortunately, the corresponding discrete-time identifiability results are not as conclusive as in continuous time. In addition, an alternative elimination scheme to Ritt's algorithm will be formalized and the resulting algorithm is analyzed when applied to a special form of the nfir model structure.