Numerical calculation of the left and right fractional derivatives

The calculation of fractional derivatives is an important topic in scientific research. While formal definitions are clear from the mathematical point of view, they pose limitations in applied sciences that have not been yet tackled. This paper addresses the problem of obtaining left and right side derivatives when adopting numerical approximations. The results reveal the relationship between the resulting distinct values for different fractional orders and types of signals.

An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index

The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.

Allocation of Parallel Real-Time Tasks in Distributed Multi-core Architectures supported by an FTT-SE Network

Distributed real-time systems such as automotive applications are becoming larger and more complex, thus, requiring the use of more powerful hardware and software architectures. Furthermore, those distributed applications commonly have stringent real-time constraints. This implies that such applications would gain in flexibility if they were parallelized and distributed over the system. In this paper, we consider the problem of allocating fixed-priority fork-join Parallel/Distributed real-time tasks onto distributed multi-core nodes connected through a Flexible Time Triggered Switched Ethernet network. We analyze the system requirements and present a set of formulations based on a constraint programming approach. Constraint programming allows us to express the relations between variables in the form of constraints. Our approach is guaranteed to find a feasible solution, if one exists, in contrast to other approaches based on heuristics. Furthermore, approaches based on constraint programming have shown to obtain solutions for these type of formulations in reasonable time.

Generalized Extraction of Real-Time Parameters for Homogeneous Synchronous Dataflow Graphs

23rd Euromicro International Conference on Parallel, Distributed, and Network-Based Processing (PDP 2015). 4 to 6, Mar, 2015. Turku, Finland.

A framework for using real data with distributed low cost sensors

Currently, due to the widespread use of computers and the internet, students are trading libraries for the World Wide Web and laboratories with simulation programs. In most courses, simulators are made available to students and can be used to proof theoretical results or to test a developing hardware/product. Although this is an interesting solution: low cost, easy and fast way to perform some courses work, it has indeed major disadvantages. As everything is currently being done with/in a computer, the students are loosing the “feel” of the real values of the magnitudes. For instance in engineering studies, and mainly in the first years, students need to learn electronics, algorithmic, mathematics and physics. All of these areas can use numerical analysis software, simulation software or spreadsheets and in the majority of the cases data used is either simulated or random numbers, but real data could be used instead. For example, if a course uses numerical analysis software and needs a dataset, the students can learn to manipulate arrays. Also, when using the spreadsheets to build graphics, instead of using a random table, students could use a real dataset based, for instance, in the room temperature and its variation across the day. In this work we present a framework which uses a simple interface allowing it to be used by different courses where the computers are the teaching/learning process in order to give a more realistic feeling to students by using real data. A framework is proposed based on a set of low cost sensors for different physical magnitudes, e.g. temperature, light, wind speed, which are connected to a central server, that the students have access with an Ethernet protocol or are connected directly to the student computer/laptop. These sensors use the communication ports available such as: serial ports, parallel ports, Ethernet or Universal Serial Bus (USB). Since a central server is used, the students are encouraged to use sensor values results in their different courses and consequently in different types of software such as: numerical analysis tools, spreadsheets or simply inside any programming language when a dataset is needed. In order to do this, small pieces of hardware were developed containing at least one sensor using different types of computer communication. As long as the sensors are attached in a server connected to the internet, these tools can also be shared between different schools. This allows sensors that aren't available in a determined school to be used by getting the values from other places that are sharing them. Another remark is that students in the more advanced years and (theoretically) more know how, can use the courses that have some affinities with electronic development to build new sensor pieces and expand the framework further. The final solution provided is very interesting, low cost, simple to develop, allowing flexibility of resources by using the same materials in several courses bringing real world data into the students computer works.

P-SOCRATES: A parallel software framework for time-critical many-core systems

Article in Press, Corrected Proof

Introducing numerical analysis tools in engineering: a Scilab user case in electronics course

Software tools in education became popular since the widespread of personal computers. Engineering courses lead the way in this development and these tools became almost a standard. Engineering graduates are familiar with numerical analysis tools but also with simulators (e.g. electronic circuits), computer assisted design tools and others, depending on the degree. One of the main problems with these tools is when and how to start use them so that they can be beneficial to students and not mere substitutes for potentially difficult calculations or design. In this paper a software tool to be used by first year students in electronics/electricity courses is presented. The growing acknowledgement and acceptance of open source software lead to the choice of an open source software tool – Scilab, which is a numerical analysis tool – to develop a toolbox. The toolbox was developed to be used as standalone or integrated in an e-learning platform. The e-learning platform used was Moodle. The first approach was to assess the mathematical skills necessary to solve all the problems related to electronics and electricity courses. Analysing the existing circuit simulators software tools, it is clear that even though they are very helpful by showing the end result they are not so effective in the process of the students studying and self learning since they show results but not intermediate steps which are crucial in problems that involve derivatives or integrals. Also, they are not very effective in obtaining graphical results that could be used to elaborate reports and for an overall better comprehension of the results. The developed tool was based on the numerical analysis software Scilab and is a toolbox that gives their users the opportunity to obtain the end results of a circuit analysis but also the expressions obtained when derivative and integrals calculations, plot signals, obtain vector diagrams, etc. The toolbox runs entirely in the Moodle web platform and provides the same results as the standalone application. The students can use the toolbox through the web platform (in computers where they don't have installation privileges) or in their personal computers by installing both the Scilab software and the toolbox. This approach was designed for first year students from all engineering degrees that have electronics/electricity courses in their curricula.

New Concepts Towards the Synthesis of Digital Circuits Through Genetic Algorithms

This paper analyses the performance of a Genetic Algorithm using two new concepts, namely a static fitness function including a discontinuity measure and a fractional-order dynamic fitness function, for the synthesis of combinational logic circuits. In both cases, experiments reveal superior results in terms of speed and convergence to achieve a solution.

Improved Numerical Simulation for a Novel Adaptive Control Using Fractional Order Derivatives

A novel control technique is investigated in the adaptive control of a typical paradigm, an approximately and partially modeled cart plus double pendulum system. In contrast to the traditional approaches that try to build up ”complete” and ”permanent” system models it develops ”temporal” and ”partial” ones that are valid only in the actual dynamic environment of the system, that is only within some ”spatio-temporal vicinity” of the actual observations. This technique was investigated for various physical systems via ”preliminary” simulations integrating by the simplest 1st order finite element approach for the time domain. In 2004 INRIA issued its SCILAB 3.0 and its improved numerical simulation tool ”Scicos” making it possible to generate ”professional”, ”convenient”, and accurate simulations. The basic principles of the adaptive control, the typical tools available in Scicos, and others developed by the authors, as well as the improved simulation results and conclusions are presented in the contribution.

System Modeling and Control Through Fractional-Order Algorithms

The theory of fractional calculus goes back to the beginning of thr throry of differential calculus but its inherent complexity postponed the applications of the associated concepts. In the last decade the progress in the areas of chaos and fractals revealed subtle relationships with the fractional calculus leading to an increasing interest in the development of the new paradigm. In the area of automaticcontrol preliminary work has already been carried out but the proposed algorithms are restricted to the frequency domain. The paper discusses the design of fractional-order discrete-time controllers. The algorithms studied adopt the time domein, which makes them suited for z-transform analusis and discrete-time implementation. The performance of discrete-time fractional-order controllers with linear and non-linear systems is also investigated.

Towards the Combination of Work-Stealing and Semi-Partitioned Scheduling for Parallel Tasks

Paper/Poster presented in Work in Progress Session, 28th GI/ITG International Conference on Architecture of Computing Systems (ARCS 2015). 24 to 26, Mar, 2015. Porto, Portugal.

Towards the Combination of Work-Stealing and Semi-Partitioned Scheduling for Parallel Tasks

Poster presented in Work in Progress Session, 28th GI/ITG International Conference on Architecture of Computing Systems (ARCS 2015). 24 to 26, Mar, 2015. Porto, Portugal.

Aquisição e Processamento de Imagens de Microscopia em Balística Forense

As novas tecnologias aplicadas ao processamento de imagem e reconhecimento de padrões têm sido alvo de um grande progresso nas últimas décadas. A sua aplicação é transversal a diversas áreas da ciência, nomeadamente a área da balística forense. O estudo de evidências (invólucros e projeteis) encontradas numa cena de crime, recorrendo a técnicas de processamento e análise de imagem, é pertinente pelo facto de, aquando do disparo, as armas de fogo imprimirem marcas únicas nos invólucros e projéteis deflagrados, permitindo relacionar evidências deflagradas pela mesma arma. A comparação manual de evidências encontradas numa cena de crime com evidências presentes numa base de dados, em termos de parâmetros visuais, constitui uma abordagem demorada. No âmbito deste trabalho pretendeu-se desenvolver técnicas automáticas de processamento e análise de imagens de evidências, obtidas através do microscópio ótico de comparação, tendo por base algoritmos computacionais. Estes foram desenvolvidos com recurso a pacotes de bibliotecas e a ferramentas open-source. Para a aquisição das imagens de evidências balísticas foram definidas quatro modalidades de aquisição: modalidade Planar, Multifocus, Microscan e Multiscan. As imagens obtidas foram aplicados algoritmos de processamento especialmente desenvolvidos para o efeito. A aplicação dos algoritmos de processamento permite a segmentação de imagem, a extração de características e o alinhamento de imagem. Este último tem como finalidade correlacionar as evidências e obter um valor quantitativo (métrica), indicando o quão similar essas evidências são. Com base no trabalho desenvolvido e nos resultados obtidos, foram definidos protocolos de aquisição de imagens de microscopia, que possibilitam a aquisição de imagens das regiões passiveis de serem estudadas, assim como algoritmos que permitem automatizar o posterior processo de alinhamento de imagens de evidências, constituindo uma vantagem em relação ao processo de comparação manual.

Real-time Parallel Applications on Many-core Architectures

Presented at INForum - Simpósio de Informática (INFORUM 2015). 7 to 8, Sep, 2015. Portugal.

Testing Nelder-Mead Based Repulsion Algorithms for Multiple Roots of Nonlinear Systems via a Two-Level Factorial Design of Experiments

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.