In this paper we develop a general and very simple construction for complete orthonormal bases for system identiication. This construction provides a unifying formulation of all known orthonormal bases since the common FIR and recently popular Laguerre and Kautz model structures are restrictive special cases of our construction as is another construction method based on balanced realisations of...

The stable spline (SS) kernel and the diagonal correlated (DC) kernel are two kernels that have been applied and studied extensively for kernel-based regularized LTI system identification. In this note, we show that similar to the derivation of the SS kernel, the continuous-time DC kernel can be derived by applying the same “stable” coordinate change to a “generalized” first-order spline kernel...

Miller et al. (1994) describe a model for representing spatial objects with no obvious landmarks. Each object is represented by a global translation and a normal deformation of a sphere. The normal deformation is defined via the orthonormal spherical-harmonic basis. In this paper we analyse the spherical deformation model in detail and describe how it may be used to summarize the shape of star-...

SUMMARY A state space compression method based on multivariate analysis was developed and applied to reinforcement learning for high-dimensional continuous state spaces. First, useful components in the state variables of an environment are extracted and meaningless ones are removed by using multiple regression analysis. Next, the state space of the environment is compressed by using principal c...

Driven by the current economical needs, developments in process design and control point out that deliberate operation of chemical process requires better models and control designs than what is offered by the traditional Linear Time-Invariant (LTI) framework. In this paper an identification approach based on Linear Parameter-Varying (LPV) models is introduced for process systems which enables ...

New orthonormal basis of eigenfunctions for the Vladimirov operator of p–adic fractional derivation is constructed. The map of p–adic numbers onto real numbers (p–adic change of variable) is considered. p–Adic change of variable (for p = 2) provides an equivalence between the constructed basis of eigenfunctions of the Vladimirov operator and the wavelet basis in L 2 (R +) generated from the Haa...

We propose a new method for simulating a Gaussian process, whose spectrum diverges at one or multiple frequencies in 0; 1 2 ] (not necessarily at zero). The method utilizes a generalization of the discrete wavelet transform, the discrete wavelet packet transform (DWPT), and only requires explicit knowledge of the spectral density function of the process { not its autocovariance sequence. An ort...

A simple construction of an orthonormal basis starting with a so called mother wavelet, together with an efficient implementation gained the wavelet decomposition easy acceptance and generated a great research interest in its applications. An orthonormal basis may not, however, always be a suitable representation of a signal, particularly when time (or space) invariance is a required property. ...

Superconvergence of the gradient for the linear simplicial nite element method applied to elliptic equations is a well-known feature in one, two, and three space dimensions. In this paper we show that, in fact, there exists an elegant proof of this feature independent of the space dimension. As a result, superconvergence for dimensions four and up is proved simultaneously. The key ingredient wi...

2-D denominator-separable digital filters represent an important subclass of 2-D recursive W t a l filters. Various implementations have been suggested. In this paper, to derive new realizations the fact is used that, different from the case of a general 2-D digital filter, a denominator-separable filter can be developed as an orthonormal expansion. The orthonormal basis has been chosen such th...