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In this paper, a data-driven update or design method of desirable state feedback gains is presented. By utilizing the “canonical controller” developed in the behavioral framework, we derive a fundamental kernel representation of the canonical controller which yields a desirable state feedback gain and is also compatible with the trajectory of the system. We also show that such a kernel representation...
It is shown that for the case of minimum phase stable plants there exists, among the set of stabilizers controllers, a solution, simultaneously decoupling the outputs and at-tenuating the perturbations of the system. At the same time, the dynamics is assigned to stable positions. The at-tenuation is given by an approximation of the controllers rejecting the perturbations, which are singulars. These...
In this paper, we make use of the behavioural approach to extend the optimal LQ-control problem to multidimensional (N-D) systems. We use the theory of Quadratic Differential Forms (QDFs) to define cost functional on N-D systems and derive conditions that have to be satisfied by these QDFs to allow an optimal behaviour. We show how the optimal behaviour is dependent only on the QDF and derive conditions...
In this paper, we analyze the classification performance of a likelihood-frequency-time (LiFT) analysis designed for partial tracking and automatic transcription of music using support vector machines. The LiFT analysis is based on constant-Q filtering of signals with a filter-bank designed to filter 24 quarter-tone frequencies of an octave. Using the LiFT information, features are extracted from...
Repetitive processes are a distinct class of 2D systems (i.e. information propagation occurs in two independent directions) of both systems theoretic and applications interest. The feature which makes them distinct from other classes of 2D systems is that information propagation in one of the two independent directions only occurs over a finite duration. Discrete linear repetitive processes are a...
This paper aims at providing some new insights into the linear quadratic optimization problem in the behavioral approach. A new problem statement is given and some comparisons with the standard LQ problem in the state space approach are provided. The problem solution is analyzed in detailed terms so that all optimal trajectories can be easily computed from the initial data. Noteworthy, the set of...
In this paper the blind identification problem of a finite extent quadratic system driven by a sequence of independent and identically distributed random variables is considered. Output cumulants up to the fourth-order are used and solutions are obtained for special cases of quadratic systems.
Topological signal processing, especially persistent homology, is a growing field of study for analyzing sets of data points that has been heretofore applied to unlabeled data. In this work, we consider the case of labeled data and examine the topology of the decision boundary separating different labeled classes. Specifically, we propose a novel approach to construct simplicial complexes of decision...
Many state-of-the-art i-vector based voice biometric systems use linear discriminant analysis (LDA) as a post-processing stage to increase the computational efficiency in the back-end via dimensionality reduction, as well as annihilate the undesired (noisy) directions in the total variability subspace. The traditional approach for computing the LDA transform uses parametric representations for both...
We propose a sampling scheme that can perfectly reconstruct a collection of spikes on the sphere from samples of their lowpass-filtered observations. The proposed algorithm can reconstruct K spikes from (K + √K)2 spatial samples, thus improving over previously known FRI sampling schemes on the sphere by a factor of up to four. Further, we show how multiple sound source localization (SSL) by a spherical...
We study the problem of learning constitutive features for the effective representation of graph signals, which can be considered as observations collected on different graph topologies. We propose to learn graph atoms and build graph dictionaries that provide sparse representations for classes of signals, which share common spectral characteristics but reside on the vertices of different graphs....
We present new methods for pointwise spatially-adaptive filtering of anisotropic multivariable signals. It is assumed that the observations are given by a broad class of models with a signal-dependent variance. The proposed methods are based on the local quasi-likelihood, incorporating the directional-windowed local polynomial approximations (LPA) of the signal. The intersection of confidence intervals...
Finite-dimensional autonomous behaviors [2,6] are the sets of solutions of certain two-dimensional (2D) difference equations, endowed with the property of constituting finite-dimensional vector spaces. For this class of behaviors, there are two possible representations: kernel descriptions (corresponding to right factor prime polynomial matrix operators) or 2D state-space descriptions (associated...
Linear Parameter-Varying (LPV) systems are usually described in either state-space or input-output form. When analyzing system equivalence between different models it appears that time-shifted versions of the scheduling signal (dynamic dependence) need to be taken into account. In order to construct a parametrization-free description of LPV systems a behavioral approach is introduced that serves as...
The problem addressed in this paper is the computation of the solution set for systems of polynomial equations, a key issue in several system analysis and control problems. A new approach is presented, which represents a possible alternative to well-known techniques, based on algebraic geometry and homotopy methods. The basic idea is to characterize the solution set in terms of the kernel of a symmetric...
We show that a delay-differential system, i.e. a dynamical system that is defined by a set of equations involving differentiation and both punctual and distributed delays, can be written in a pseudo-state space form, called also first- order representation, which generalizes the state space form for purely differential systems and employs only first-order derivatives and punctual delays.
Various optimal control strategies exist in the literature. Prominent approaches are Robust Control and Linear Quadratic Regulators, the first one being related to the H∞ norm of a system, the second one to the H2 norm. In 1994, F. De Bruyne et al [1] showed that assuming knowledge of the poles of a transfer function one can derive upper bounds on the H∞ norm as a constant multiple of its H2 norm...
The central object of interest of this paper are systems of linear constant coefficient ordinary differential equations of arbitrary order of the form s(d/dt)w = M(d/dt)f with G and M given, but otherwise arbitrary, polynomial matrices. In these equations w and f are vector-valued functions of which f is assumed to be given, while w is the solution to (1) that we are looking for. Alongside (1) we...
Given a nominal plant, together with a fixed neighborhood of this plant, the problem of robust stabilization is to find a controller that stabilizes all plants in that neighborhood (in an appropriate sense). If a controller achieves this design objective, we say that it robustly stabilizes the nominal plant. In this paper we formulate the robust stabilization problem in a behavioral framework, with...
The diagnosis of the arythema disease is a real difficulty in dermatology. It causes redness induced in the lower level of the skin by hyperemia of the capillaries. It can harm several skin damages, inflammations. In this paper, we have put our efforts to design a diagnostic approach based on Support Vector Machine (SVM) with linear kernel by classifying the erythemato-squamous disease. SVM being...
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