Publications
Data-driven simulation for NARX systems KU Leuven
Decoupling multivariate functions using second-order information and tensors KU Leuven Vrije Universiteit Brussel
© Springer International Publishing AG, part of Springer Nature 2018. The power of multivariate functions is their ability to model a wide variety of phenomena, but have the disadvantages that they lack an intuitive or interpretable representation, and often require a (very) large number of parameters. We study decoupled representations of multivariate vector functions, which are linear combinations of univariate functions in linear combinations ...
Decoupling Static Nonlinearities in a Parallel Wiener-Hammerstein System: A First-order Approach KU Leuven Vrije Universiteit Brussel
© 2015 IEEE. We present a method to decompose a static MIMO (multiple-input-multiple-output) nonlinearity into a set of SISO (single-input-single-output) polynomials acting on internal variables that are related to the inputs and outputs of the MIMO nonlinearity by linear transformations. The method is inspired on the small-signal analysis of nonlinear circuits and proceeds by collecting first-order information of the MIMO function into a set of ...
Recovering Wiener-Hammerstein nonlinear state-space models using linear algebra KU Leuven Vrije Universiteit Brussel
© 2015 This paper considers Wiener-Hammerstein systems consisting of a cascade of a linear dynamical system, a static nonlinearity and another linear dynamical system. We start from a black-box nonlinear state-space description of the system and develop a method to reconstruct the parameters of the underlying Wiener-Hammerstein block structure by means of linear algebra operations. First, the static nonlinearity is retrieved by decoupling the ...
Block-Decoupling Multivariate Polynomials Using the Tensor Block-Term Decomposition KU Leuven Vrije Universiteit Brussel
© Springer International Publishing Switzerland 2015. We present a tensor-based method to decompose a given set of multivariate functions into linear combinations of a set of multivariate functions of linear forms of the input variables. The method proceeds by forming a three-way array (tensor) by stacking Jacobian matrix evaluations of the function behind each other. It is shown that a blockterm decomposition of this tensor provides the ...
A fast iterative orthogonalization scheme for the Macaulay matrix KU Leuven
In this article we present a fast recursive orthogonalization scheme for two important subspaces of the Macaulay matrix: its row space and null space. It requires a graded monomial ordering and exploits the resulting structure of the Macaulay matrix induced by this graded ordering. The resulting orthogonal basis for the row space will retain a similar structure as the Macaulay matrix and is as a consequence sparse. The computed orthogonal basis ...
The canonical decomposition of Cnd and numerical Gröbner and border bases KU Leuven
© 2014 Society for Industrial and Applied Mathematics. This article introduces the canonical decomposition of the vector space of multivariate polynomials for a given monomial ordering. Its importance lies in solving multivariate polynomial systems, computing Gröbner bases, and solving the ideal membership problem. An SVD-based algorithm is presented that numerically computes the canonical decomposition. It is then shown how, by introducing the ...