Vincent Wertz

Université Catholique de Louvain - UCLouvain | UCLouvain · Department of Mathematical Engineering

Cet article décrit un nouveau dispositif d’évaluation des acquis d’apprentissage basé sur des cartes conceptuelles « à trous » (CCàT) permettant également l’apprentissage par les pairs en grands auditoires durant les tests et une correction automatisée par des formulaires QCM.L’intérêt du dispositif est de garantir une évaluation qualitative (à hau...

This paper presents a new methodology for enhancing Generalized Predictive Control (GPC) in order to robustify the closed loop system in the face of neglected dynamics. This methodology occurs in two distinct steps. In the first step a nominal controller is obtained by minimizing the GPC tracking performance index, in the second step a systematic p...

We present an open loop control design allowing to steer in a minimum time a wheeled robot along a prespecified smooth geometric path, between arbitrary given postures, while satisfying a set of dynamical constraints, such as actuator saturation or maximum admissible accelerations. Using the concept of 'differential flatness' the problem is shown t...

The aim of this paper is to propose an improvement of a classical change of variables useful to solve multi‐objective control design problems that can be formulated with LMIs. For multi‐objective problems, the only approach guaranteed to converge to global optima is to use an iterative approach where the order of the design parameter grows (until n...

A semi-linear reduced-order state estimator is presented to reconstruct approximately the state variable initially unknown of a class of nonlinear tubular reactors models, namely the exothermal plug-flow tubular reactor involving sequential reactions for which the kinetics depends on both the temperature and the reactant concentration. Our concepti...

The feedback stabilization problem in the presence of nonsymmetrical constraints on both control and its rate is addressed for a class of distributed parameter systems.Necessary and sufficient conditions are established, under which the constraints are satisfied for autonomous infinitedimensional systems. The approach is developed using the semigro...

In this note we aim at putting more emphasis on the fact that trying to solve non-convex optimization problems with coordinate-descent iterative linear matrix inequality algorithms leads to suboptimal solutions, and put forward other optimization methods better equipped to deal with such problems (having theoretical convergence guarantees and/or be...

One the earliest challenges a practitioner is faced with when using distance-based tools lies in the choice of the distance, for which there often is very few information to rely on. This chapter proposes to find a compromise between an a priori unoptimized choice (e.g. the Euclidean distance) and a fully-optimized, but computationally expensive, c...

The motivation of this work is to illustrate the efficiency of some often overlooked alternatives to deal with optimization problems in systems and control. In particular, we will consider a problem for which an iterative linear matrix inequality algorithm (ILMI) has been proposed recently. As it often happens, this algorithm does not have guarante...

The main goal of this paper is to give a short tutorial on the positivity and the positive stabilization of infinite dimensional linear systems together with some new points of view and perspectives. Algebraic conditions of positivity for dynamical systems defined on an ordered Banach space whose positive cone has an empty interior are derived. The...

This paper proposes the design of an advanced control technique to improve the control performances of industrial plants. Indeed, classical industrial solutions are typically based on SISO loops including classical PID controllers. This control strategy can clearly be improved. The solution proposed here is not to remove the industrial solution but...

Dimensionality reduction techniques aim at representing high-dimensional data in low-dimensional spaces. To be faithful and reliable, the representation is usually required to preserve proximity relationships. In practice, methods like multidimensional scaling try to fulfill this requirement by preserving pairwise distances in the low-dimensional r...

During the first year at university, a remarkably small number of students stay in school and succeed. To explain that phenomenon, we first take into account the students’ socio-demographic characteristics and school backgrounds. For thirty years, other elements have also been studied based on different theoretical trends. On the one hand education...

During the first year at university, a remarkably small number of students stay in school and succeed. To explain that phenomenon, we first take into account the students' socio-demographic characteristics and school backgrounds. For thirty years, other elements have also been studied based on different theoretical trends. On the one hand education...

This paper presents an LMI (linear matrix inequality) approach to obtain an optimal controller, for a coal-fired power plant. This is an alternative and an extension of the results obtained. The objective considered is a fast tracking of load step changes while keeping the pressure variations constrained. Also a constraint on the control inputs, in...

The stabilization by a finite-dimensional compensator for a class of infinite-dimensional linear systems with control inequality constraints is investigated. The main result shows that the corresponding state feedback results cannot be directly extended to the composite system including a full-state observer. However, we get conditions of asymptoti...

This paper presents a framework for nonlinear dimensionality reduction methods aimed at projecting data on a non-Euclidean manifold, when their structure is too complex to be embedded in an Euclidean space. The methodology proposes an optimization procedure on manifolds to minimize a pairwise distance criterion that implements a control of the trad...

This work presents an application of linear and nonlinear robust predictive control onto a three tanks system. The design of the linear solution is based on Single-Input Single-Output Controlled Auto Regressive Integrated Moving Average (CARIMA) model and the nonlinear controller considers Nonlinear Auto Regressive with eXogenous output (NARX) mode...

This paper provides an application of linear and nonlinear multivariable robust predictive control to a three tanks system. The design of the nonlinear solution is based on a Multi-Input Multi-Output Nonlinear Auto Regressive with eXogenous outputs (MIMO-NARX) model and the linear controller considers a MIMO Controlled Auto Regressive Integrated Mo...

This note addresses the stabilization problem for linear infinite-dimensional systems, partially observed, in the presence of inequality constraints on both control and its rate. We propose a stabilizing state feedback on the estimated state, reconstructed from a full state observer. So, we give the necessary and sufficient conditions under which t...

This paper presents results on performance limitations for direct fired coal power plants. A specific feature of this system is the existence of a very large input delay between one of the inputs, namely coal flow, and the two outputs, load and vapour pressure. This problem motivates the main theoretical question addressed in this paper: To examine...

This paper presents a nonlinear method aimed to project data on a non-Euclidean manifold, when their structure is too complex to be embedded in an Euclidean space. The method optimizes a pairwise dis- tance criterion that implements a control between trustworthiness and continuity that respectively represent the risks of attening and tearing the pr...

This paper present sufficient conditions to construct an exponential state estimator for a class of infinite dimensional non-linear systems driven in a real Hilbert state description. The theory is applied to a nonisothermal plug flow tubular reactor, governed by hyperbolic first order partial differential equations. For this application performanc...

This paper presents results on performance limitations for direct fired coal power plants. A specific feature of this system is the existence of a very large input delay between one of the inputs, namely coal flow, and the two outputs, load and vapour pressure. This problem motivates the main theoretical question addressed in this paper: To examine...

Predicting time series necessitates choosing adequate re- gressors. For this purpose, prior knowledge of the data is required. By projecting the series on a low-dimensional space, the visualization of the regressors helps to extract relevant information. However, when the series includes some periodicity, the structure of the time series is better...

Combining the mutual information criterion with a forward feature selection strategy offers a good trade-off between optimality of the selected feature subset and computation time. However, it requires to set the parameter(s) of the mutual information estimator and to determine when to halt the forward procedure. These two choices are difficult to...

The large number of spectral variables in most data sets encountered in spectral chemometrics often renders the prediction of a dependent variable uneasy. The number of variables hopefully can be reduced, by using either projection techniques or selection methods; the latter allow for the interpretation of the selected variables. Since the optimal...

Data from spectrophotometers form vectors of a large number of exploitable variables. Building quantitative models using these variables most often requires using a smaller set of variables than the initial one. Indeed, a too large number of input variables to a model results in a too large number of parameters, leading to overfitting and poor gene...

Nearest neighbor search and many other numerical data analysis tools most often rely on the use of the euclidean distance. When data are high dimensional, however, the euclidean distances seem to concentrate; all distances between pairs of data elements seem to be very similar. Therefore, the relevance of the euclidean distance has been questioned...

For decades, success in postsecondary education has preoccupied psychological and educational researchers. In this respect, Tinto's student integration model (1982, 1997) is one of the most frequently cited models. Tinto proposed that students' background characteristics, initial intentions and aspirations towards college influence their academic a...

In spectrometric problems, objects are characterized by high-resolution spectra that correspond to hundreds to thousands of variables. In this context, even fast variable selection methods lead to high computational load. However, spectra are generally smooth and can therefore be accurately approximated by splines. In this paper, we propose to use...

Selecting relevant features in mass spectra analysis is important both for classification and search for causality. In this paper, it is shown how using mutual information can help answering to both objectives, in a model-free nonlinear way. A combination of ranking and forward selection makes it possible to select several feature groups that may l...

A key question in stochastic adaptive control theory is whether or not it is possible to stabilize a linear system which is perturbed by unmeasured random disturbances and whose model is only partially known. Use of the Certainty-Equivalence principle divides the problem into two parts: using a gradient type estimation algorithm to estimate the mod...

The estimation of mutual information for feature selection is often subject to inaccuracies due to noise, small sample size, bad choice of parameter for the estimator, etc. The choice of a threshold above which a feature will be considered useful is thus difficult to make. Therefore, the use of the permutation test to assess the reliability of the...

This paper describes a method for predicting the presence or absence of ice on the road. The method is based on a Least Squares Support Vector Machine applied to data from the road in Wallonia (Belgium). It is shown that including a prediction of the air temperature given by a meteorological center in the model helps having better accuracy. In this...

Nonlinear time-series prediction offers potential performance increases compared to linear models. Nevertheless, the enhanced complexity and computation time often prohibits an efficient use of nonlinear tools. In this paper, we present a simple nonlinear procedure for time-series forecasting, based on the use of vector quantization techniques; the...

Using resampling methods like cross-validation and bootstrap is a necessity in neural network design, for solving the problem of model structure selection. The bootstrap is a powerful method offering a low variance of the model generalization error estimate. Unfortunately, its computational load may be excessive when used to select among neural net...

In the context of classification, the dissimilarity between data elements is often measured by a metric defined on the data space. Often, the choice of the metric is often disregarded and the Euclidean distance is used without further inquiries. This paper illustrates the fact that when other noise schemes than the white Gaussian noise are encounte...

Gaussian kernels are widely used in many data analysis tools such as Radial-Basis Function networks, Support Vector Machines and many others. Gaus-sian kernels are most often deemed to provide a local measure of similarity between vectors. In this paper, we show that Gaussian kernels are adequate measures of similarity when the representation dimen...

Time series forecasting is usually limited to one-step ahead prediction. This goal is extended here to longer-term prediction, obtained using the least-square support vector machines model. The influence of the model parameters is observed when the time horizon of the prediction is increased and for various prediction methods. The model selection t...

This paper deals with the application of model identification and control to an industrial polymerisation process. The final control objective in the present process is to obtain a polymer of a viscosity as homogeneous as possible. The process has two inputs : the catalyst feed rate and the air flow rate in the reactor. The first input is the contr...

The bootstrap resampling method may be efficiently used to estimate the generalization error of a family of nonlinear regression models, as artificial neural networks. The main difficulty associated with the bootstrap in real-world applications is the high computation load. In this paper we propose a simple procedure based on empirical evidence, to...

A business plan is a document presenting in a concise form the key elements (management, finance, marketing, ...) describing a percieved business opportunity. It is used among others as a tool for evaluating the feasibility and profitability of a project from the entrepreneur' or investor's point of view.

This paper compares several model selection methods, based on experimental estimates of their generalization errors. Experiments in the context of nonlinear time series prediction by Radial-Basis Function Networks show the superiority of the bootstrap methodology over classical cross-validations and leave-one-out.

Modern data analysis often faces high-dimensional data.

We propose a method of function approximation by radial basis function networks. We will demonstrate that this approximation method can be improved by a pre-treatment of data based on a linear model. This approximation method will be applied to option pricing. This choice justifies itself through the known nonlinear nature of the behavior of option...

Classical nonlinear models for time series prediction exhibit improved capabilities compared to linear ones. Nonlinear regression has however drawbacks, such as overfitting and local minima problems, user-adjusted parameters, higher computation times, etc. There is thus a need for simple nonlinear models with a restricted number of learning paramet...

In line with the work of Delmar and Davidsson, (1998) which examines the types of distinct growth patterns that high-growth firms exhibit and how these growth patterns and corresponding firms differ from each other in terms of their demographic affiliation, this paper discusses the existence of different growth trajectories of start-ups. Using fina...

The Bootstrap resampling method may be efficiently used to estimate the generalization error of nonlinear regression models, as artificial neural networks and especially Least-square Support Vector Machines. Nevertheless, the use of the Bootstrap implies a high computational load. In this paper we present a simple procedure to obtain a fast approxi...

Fuzzy Logic , which has recently drawn a great deal of attention, possesses conceptually the quality of the simplicity. However, its early application relied on trial and error in selecting either the fuzzy membership functions or the fuzzy rules. This made it heavily dependent on expert knowledge, which may not always available. Hence, an adaptive...

The predictive control has become currently a precious tool for control in various domains. It is largely studied and well known in the case of linear systems. The extension of this technique for the control of nonlinear systems has recently been the subject of many researches, and several algorithms were proposed, particularly those using fuzzy lo...

In this paper, a multiobjective decision-making process is modeled by a multiobjective fuzzy linear programming problem with fuzzy coefficients for the objectives and the constraints. Moreover, the decision variables are linked together because they have to sum up to a constant. Most of the time, the solutions of a multiobjective fuzzy linear progr...

this paper we propose an effective procedure to reduce the computation time of a bootstrap approximation of the generalization error in a family of nonlinear regression models. The bootstrap [1] is based on the general plug-in principle which permits to obtain an estimator of a statistic according to an empirical distribution. In our context we use...

Modern data analysis often faces high-dimensional data. Nevertheless, most neural network data analysis tools are not adapted to high- dimensional spaces, because of the use of conventional concepts (as the Euclidean distance) that scale poorly with dimension. This paper shows some limitations of such concepts and suggests some research directions...

Classical nonlinear models for time series prediction exhibit im- proved capabilities compared to linear ones. Nonlinear regression has however drawbacks, such as overfitting and local minima problems, user-adjusted pa- rameters, higher computation times, etc. There is thus a need for simple nonlin- ear models with a restricted number of learning p...

We propose a method of function approximation by radial basis function networks. We will demonstrate that this approximation method can be improved by a pre-treatment of data based on a linear model. This approximation method will be applied to option pricing. This choice justifies itself through the known nonlinear nature of the behaviour of optio...

Fuzzy models, especially Takagi-Sugeno (T-S) fuzzy models, have received particular attention in the area of nonlinear modeling due to their capability to approximate any nonlinear behavior. Based only on measured data without any prior knowledge, there is no systematic way to obtain a T-S fuzzy model with a simple structure and sufficient accuracy...

We developed in this paper a method to predict time series with non-linear tools. The specificity of the method is to use as much information as possible as input to the model (many past values of the series, many exogenous variables), to compress this information (by a non-linear method) in order to obtain a state vector of limited size, facilitat...

A general-purpose useful parameter in time series forecasting is the regressor size, corresponding to the minimum number of variables necessary to forecast the future values of the time series. If the models are nonlinear, the choice of this regressor becomes very difficult. We present a quasi-automatic method using a nonlinear projection named cur...

The problem of electrical load forecasting presents some particularities, compared to the generic problem of time-series prediction. One of these particularities is that several values (corresponding to one day of consumption) are usually expected as the result of the prediction. In this paper, we propose an original method dividing the problem int...

Plugging is well known to be a major cause of instability in industrial cement mills. A simple nonlinear model able to simulate the plugging phenomenon is presented. It is shown how a nonlinear robust controller can be designed in order to fully prevent the mill from plugging