Volume 23 (2013): Edizione 4 (December 2013)

We study the exact boundary controllability of two coupled one dimensional wave equations with a control acting only in one equation. The problem is transformed into a moment problem. This framework has been used in control theory of distributed parameter systems since the classical works of A.G. Butkovsky, H.O. Fattorini and D.L. Russell in the late 1960s to the early 1970s. We use recent results on the Riesz basis property of exponential divided differences.

This paper is concerned with observer design for nonlinear systems that are modeled by T-S fuzzy systems containing parametric and nonparametric uncertainties. Unlike most Sugeno models, the proposed method contains nonlinear functions in the consequent part of the fuzzy IF-THEN rules. This will allow modeling a wider class of systems with smaller modeling errors. The consequent part of each rule contains a linear part plus a nonlinear term, which has an incremental quadratic constraint. This constraint relaxes the conservativeness introduced by other regular constraints for nonlinearities such as the Lipschitz conditions. To further reduce the conservativeness, a nonlinear injection term is added to the observer dynamics. Simulation examples show the effectiveness of the proposed method compared with the existing techniques reported in well-established journals.

The minimum energy control problem for positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of a solution to the problem are established. A procedure for solving the problem is proposed and illustrated with a numerical example.

In many applications, there is a need to choose mathematical models that depend on non-smooth functions. The task of simulation becomes especially difficult if such functions appear on the right-hand side of an initial value problem. Moreover, solution processes from usual numerics are sensitive to roundoff errors so that verified analysis might be more useful if a guarantee of correctness is required or if the system model is influenced by uncertainty. In this paper, we provide a short overview of possibilities to formulate non-smooth problems and point out connections between the traditional non-smooth theory and interval analysis. Moreover, we summarize already existing verified methods for solving initial value problems with non-smooth (in fact, even not absolutely continuous) right-hand sides and propose a way of handling a certain practically relevant subclass of such systems. We implement the approach for the solver VALENCIA-IVP by introducing into it a specialized template for enclosing the first-order derivatives of non-smooth functions. We demonstrate the applicability of our technique using a mechanical system model with friction and hysteresis. We conclude the paper by giving a perspective on future research directions in this area.

A hybrid method combining an evolutionary search strategy, interval mathematics and pole assignment-based closed-loop control synthesis is proposed to design a robust TSK fuzzy controller. The design objective is to minimize the number of linear controllers associated with rule conclusions and tune the triangular-shaped membership function parameters of a fuzzy controller to satisfy stability and desired dynamic performances in the presence of system parameter variation. The robust performance objective function is derived based on an interval Diophantine equation. Thus, the objective of a fuzzy logic-based control scheme is to place all the closed-loop control system characteristic polynomial coefficients within desired intervals. The reproduction process in the proposed Evolutionary Algorithm (EA) is based on the arithmetical crossover, uniform and non-uniform mutation along with gene deletion/insertion mutation ensuring a diversity of genomes sizes, as well as a diversity in the parameter space of membership functions. The proposed algorithm was implemented to design a fuzzy logic-based anti-sway crane control system taking into consideration the rope length and the mass of a payload variation. The results of experiments conducted using the EA for different conditions assumed for system parameter intervals and desired closed-loop system performances are compared with results achieved using the iterative procedure which is also described in the paper.

In this paper, we present a vaccination model with multiple transmission ways and derive the control reproduction number. The stability analysis of both the disease-free and endemic equilibria is carried out, and bifurcation theory is applied to explore a variety of dynamics of this model. In addition, we present numerical simulations to verify the model predictions. Mathematical results suggest that vaccination is helpful for disease control by decreasing the control reproduction number below unity.

Traditional traffic control systems based on traffic light have achieved a great success in reducing the average delay of vehicles or in improving the traffic capacity. The main idea of these systems is based on the optimization of the cycle time, the phase sequence, and the phase duration. The right-of-ways are assigned to vehicles of one or several movements for a specific time. With the emergence of cooperative driving, an innovative traffic control concept, Autonomous Intersection Management (AIM), has emerged. In the framework of AIM, the right-of-way is customized on the measurement of the vehicle state and the traffic control turns to determine the passing sequence of vehicles. Since each vehicle is considered individually, AIM faces a combinatorial optimization problem. This paper proposes a dynamic programming algorithm to find its optimal solution in polynomial time. Experimental results obtained by simulation show that the proper arrangement of the vehicle passing sequence can greatly improve traffic efficiency at intersections.

Naive Bayes is among the simplest probabilistic classifiers. It often performs surprisingly well in many real world applications, despite the strong assumption that all features are conditionally independent given the class. In the learning process of this classifier with the known structure, class probabilities and conditional probabilities are calculated using training data, and then values of these probabilities are used to classify new observations. In this paper, we introduce three novel optimization models for the naive Bayes classifier where both class probabilities and conditional probabilities are considered as variables. The values of these variables are found by solving the corresponding optimization problems. Numerical experiments are conducted on several real world binary classification data sets, where continuous features are discretized by applying three different methods. The performances of these models are compared with the naive Bayes classifier, tree augmented naive Bayes, the SVM, C4.5 and the nearest neighbor classifier. The obtained results demonstrate that the proposed models can significantly improve the performance of the naive Bayes classifier, yet at the same time maintain its simple structure.

This paper describes a study of emotion recognition based on speech analysis. The introduction to the theory contains a review of emotion inventories used in various studies of emotion recognition as well as the speech corpora applied, methods of speech parametrization, and the most commonly employed classification algorithms. In the current study the EMO-DB speech corpus and three selected classifiers, the k-Nearest Neighbor (k-NN), the Artificial Neural Network (ANN) and Support Vector Machines (SVMs), were used in experiments. SVMs turned out to provide the best classification accuracy of 75.44% in the speaker dependent mode, that is, when speech samples from the same speaker were included in the training corpus. Various speaker dependent and speaker independent configurations were analyzed and compared. Emotion recognition in speaker dependent conditions usually yielded higher accuracy results than a similar but speaker independent configuration. The improvement was especially well observed if the base recognition ratio of a given speaker was low. Happiness and anger, as well as boredom and neutrality, proved to be the pairs of emotions most often confused.

We propose an adaptation of the partitioning method for determination of theMoore-Penrose inverse of a matrix augmented by a block-column matrix. A simplified implementation of the partitioning method on specific Toeplitz matrices is obtained. The idea for observing this type of Toeplitz matrices lies in the fact that they appear in the linear motion blur models in which blurring matrices (representing the convolution kernels) are known in advance. The advantage of the introduced method is a significant reduction in the computational time required to calculate the Moore-Penrose inverse of specific Toeplitz matrices of an arbitrary size. The method is implemented in MATLAB, and illustrative examples are presented.

In web search engines, such as Google, the ranking of a particular keyword is determined by mathematical tools, e.g., Pagerank or Hits. However, as the size of the network increases, it becomes increasingly difficult to use keyword ranking to quickly find the information required by an individual user. One reason for this phenomenon is the interference of superfluous information with the link structure. The WorldWideWeb can be expressed as an enormous directed graph. The purpose of the present study is to provide tools for studying the web as a directed graph in order to find clues to the solution of the problem of interference from superfluous information, and to reform the directed graph to clarify the relationships between the nodes.

The paper presents a system of Composite Graph Grammars (CGGs)modelling adaptive two dimensional hp Finite Element Method (hp-FEM) algorithms with rectangular finite elements. A computational mesh is represented by a composite graph. The operations performed over the mesh are defined by the graph grammar rules. The CGG system contains different graph grammars defining different kinds of rules of mesh transformations. These grammars allow one to generate the initial mesh, assign values to element nodes and perform h- and p-adaptations. The CGG system is illustrated with an example from the domain of geophysics.

A novel method is presented for mining fuzzy association rules that have a temporal pattern. Our proposed method contributes towards discovering temporal patterns that could otherwise be lost from defining the membership functions before the mining process. The novelty of this research lies in exploring the composition of fuzzy and temporal association rules, and using a multi-objective evolutionary algorithm combined with iterative rule learning to mine many rules. Temporal patterns are augmented into a dataset to analyse the method’s ability in a controlled experiment. It is shown that the method is capable of discovering temporal patterns, and the effect of Boolean itemset support on the efficacy of discovering temporal fuzzy association rules is presented.

The Probability Density Function (PDF) is a key concept in statistics. Constructing the most adequate PDF from the observed data is still an important and interesting scientific problem, especially for large datasets. PDFs are often estimated using nonparametric data-driven methods. One of the most popular nonparametric method is the Kernel Density Estimator (KDE). However, a very serious drawback of using KDEs is the large number of calculations required to compute them, especially to find the optimal bandwidth parameter. In this paper we investigate the possibility of utilizing Graphics Processing Units (GPUs) to accelerate the finding of the bandwidth. The contribution of this paper is threefold: (a) we propose algorithmic optimization to one of bandwidth finding algorithms, (b) we propose efficient GPU versions of three bandwidth finding algorithms and (c) we experimentally compare three of our GPU implementations with the ones which utilize only CPUs. Our experiments show orders of magnitude improvements over CPU implementations of classical algorithms.

A novel method for feature extraction and recognition called Kernel Fuzzy Discriminant Analysis (KFDA) is proposed in this paper to deal with recognition problems, e.g., for images. The KFDA method is obtained by combining the advantages of fuzzy methods and a kernel trick. Based on the orthogonal-triangular decomposition of a matrix and Singular Value Decomposition (SVD), two different variants, KFDA/QR and KFDA/SVD, of KFDA are obtained. In the proposed method, the membership degree is incorporated into the definition of between-class and within-class scatter matrices to get fuzzy between-class and within-class scatter matrices. The membership degree is obtained by combining the measures of features of samples data. In addition, the effects of employing different measures is investigated from a pure mathematical point of view, and the t-test statistical method is used for comparing the robustness of the learning algorithm. Experimental results on ORL and FERET face databases show that KFDA/QR and KFDA/SVD are more effective and feasible than Fuzzy Discriminant Analysis (FDA) and Kernel Discriminant Analysis (KDA) in terms of the mean correct recognition rate.

In this addendum we address some unintentional omission in the description of the swimming model in our recent paper (Khapalov, 2013)