Fractional order calculus: basic concepts and engineering applications

The fractional order calculus (FOC) is as old as the integer one although up to recently its application was exclusively in mathematics. Many real systems are better described with FOC differential equations as it is a well-suited tool to analyze problems of fractal dimension, with long-term “memory” and chaotic behavior. Those characteristics have attracted the engineers' interest in the latter years, and now it is a tool used in almost every area of science. This paper introduces the fundamentals of the FOC and some applications in systems' identification, control, mechatronics, and robotics, where it is a promissory research field.

Foraging at the Edge of Chaos: Internal Clock versus External Forcing

Activity rhythms in animal groups arise both from external changes in the environment, as well as from internal group dynamics. These cycles are reminiscent of physical and chemical systems with quasiperiodic and even chaotic behavior resulting from “autocatalytic” mechanisms. We use nonlinear differential equations to model how the coupling between the self-excitatory interactions of individuals and external forcing can produce four different types of activity rhythms: quasiperiodic, chaotic, phase locked, and displaying over or under shooting. At the transition between quasiperiodic and chaotic regimes, activity cycles are asymmetrical, with rapid activity increases and slower decreases and a phase shift between external forcing and activity. We find similar activity patterns in ant colonies in response to varying temperature during the day. Thus foraging ants operate in a region of quasiperiodicity close to a cascade of transitions leading to chaos. The model suggests that a wide range of temporal structures and irregularities seen in the activity of animal and human groups might be accounted for by the coupling between collectively generated internal clocks and external forcings.

Exciting dynamical behavior in a network of two coupled rings of Chen oscillators

We study exotic patterns appearing in a network of coupled Chen oscillators. Namely, we consider a network of two rings coupled through a “buffer” cell, with Z3×Z5 symmetry group. Numerical simulations of the network reveal steady states, rotating waves in one ring and quasiperiodic behavior in the other, and chaotic states in the two rings, to name a few. The different patterns seem to arise through a sequence of Hopf bifurcations, period-doubling, and halving-period bifurcations. The network architecture seems to explain certain observed features, such as equilibria and the rotating waves, whereas the properties of the chaotic oscillator may explain others, such as the quasiperiodic and chaotic states. We use XPPAUT and MATLAB to compute numerically the relevant states.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Cooperative scheduling system with emergent swarm based behavior

This paper presents a Swarm based Cooperation Mechanism for scheduling optimization. We intend to conceptualize real manufacturing systems as interacting autonomous entities in order to support decision making in agile manufacturing environments. Agents coordinate their actions automatically without human supervision considering a common objective – global scheduling solution taking advantages from collective behavior of species through implicit and explicit cooperation. The performance of the cooperation mechanism will be evaluated consider implicit cooperation at first stage through ACS, PSO and ABC algorithms and explicit through cooperation mechanism application.

Intelligent behavior in a Cyber-Ambient training system for control center operators

This paper deals with the application of an intelligent tutoring approach to delivery training in diagnosis procedures of a Power System. In particular, the mechanisms implemented by the training tool to support the trainees are detailed. This tool is part of an architecture conceived to integrate Power Systems tools in a Power System Control Centre, based on an Ambient Intelligent paradigm. The present work is integrated in the CITOPSY project which main goal is to achieve a better integration between operators and control room applications, considering the needs of people, customizing requirements and forecasting behaviors.

Seller, buyer and VPP agents behavior on a simulated electricity market

Competitive electricity markets are complex environments, involving a large number of different entities, playing in a dynamic scene to obtain the best advantages and profits. MASCEM is an electricity market simulator able to model market players and simulate their operation in the market. As market players are complex entities, having their characteristics and objectives, making their decisions and interacting with other players, a multi-agent architecture is used and proved to be adequate. MASCEM players have learning capabilities and different risk preferences. They are able to refine their strategies according to their past experience (both real and simulated) and considering other agents’ behavior. Agents’ behavior is also subject to its risk preferences.

Case-based reasoning for self-optimizing behavior

In this paper we present a Self-Optimizing module, inspired on Autonomic Computing, acquiring a scheduling system with the ability to automatically select a Meta-heuristic to use in the optimization process, so as its parameterization. Case-based Reasoning was used so the system may be able of learning from the acquired experience, in the resolution of similar problems. From the obtained results we conclude about the benefit of its use.

Leis de potência em sistemas naturais e artificiais

A Lei de Potência é uma particularidade de um sistema não linear, revelando um sistema complexo próximo da auto-organização. Algumas características de sistemas naturais e artificiais, tais como dimensão populacional das cidades, valor dos rendimentos pessoais, frequência de ocorrência de palavras em textos e magnitude de sismos, seguem distribuições do tipo Lei de Potência. Estas distribuições indicam que pequenas ocorrências são muito comuns e grandes ocorrências são raras, podendo porém verificar-se com razoável probabilidade. A finalidade deste trabalho visa a identificação de fenómenos associados às Leis de Potência. Mostra-se o comportamento típico destes fenómenos, com os dados retirados dos vários casos de estudo e com a ajuda de uma meta-análise. As Leis de Potência em sistemas naturais e artificiais apresentam uma proximidade a um padrão, quando os valores são normalizados (frequências relativas) para dar origem a um meta-gráfico.

Static and hydrodynamic monitoring of citalopram based on its electro-oxidation behavior at a glassy-carbon surface

The electrooxidative behavior of citalopram (CTL) in aqueous media was studied by cyclic voltammetry (CV) and square-wave voltammetry (SWV) at a glassy-carbon electrode. The electrochemical behaviour of CTL involves two electrons and two protons in the irreversible and diffusion controlled oxidation of the tertiary amine group. The maximum analytical signal was obtained in a phosphate buffer (pH ¼ 8.2). For analytical purposes, an SWV method and a flow-injection analysis (FIA) system with amperometric detection were developed. The optimised SWV method showed a linear range between 1.10 10 5–1.20 10 4 molL 1, with a limit of detection (LOD) of 9.5 10 6 molL 1. Using the FIA method, a linear range between 2.00 10 6–9.00 10 5 molL 1 and an LODof 1.9 10 6 molL 1 were obtained. The validation of both methods revealed good performance characteristics confirming applicability for the quantification of CTL in several pharmaceutical products.

Adsorption behavior of α-cypermethrin on cork and activated carbon

Studies were undertaken to determine the adsorption behavior of α-cypermethrin [R)-α-cyano-3-phenoxybenzyl(1S)-cis- 3-(2,2-dichlorovinyl)-2,2-dimethylcyclopropanecarboxylate, and (S)-α-cyano-3-phenoxybenzyl (1R)-cis-3-(2,2-dichlorovinyl)-2,2- dimethylcyclopropanecarboxylate] in solutions on granules of cork and activated carbon (GAC). The adsorption studies were carried out using a batch equilibrium technique. A gas chromatograph with an electron capture detector (GC-ECD) was used to analyze α-cypermethrin after solid phase extraction with C18 disks. Physical properties including real density, pore volume, surface area and pore diameter of cork were evaluated by mercury porosimetry. Characterization of cork particles showed variations thereby indicating the highly heterogeneous structure of the material. The average surface area of cork particles was lower than that of GAC. Kinetics adsorption studies allowed the determination of the equilibrium time—24 hours for both cork (1–2 mm and 3–4 mm) and GAC. For the studied α-cypermethrin concentration range, GAC revealed to be a better sorbent. However, adsorption parameters for equilibrium concentrations, obtained through the Langmuir and Freundlich models, showed that granulated cork 1–2 mm have the maximum amount of adsorbed α-cypermethrin (qm) (303 μg/g); followed by GAC (186 μg/g) and cork 3-4 mm (136 μg/g). The standard deviation (SD) values, demonstrate that Freundlich model better describes the α-cypermethrin adsorption phenomena on GAC, while α-cypermethrin adsorption on cork (1-2 mm and 3-4 mm) is better described by the Langmuir. In view of the adsorption results obtained in this study it appears that granulated cork may be a better and a cheaper alternative to GAC for removing α-cypermethrin from water.

Competitive dynamics for behavior coordination in a joint transportation task

We address the problem of coordinating two non-holonomic mobile robots that move in formation while transporting a long payload. A competitive dynamics is introduced that gradually controls the activation and deactivation of individual behaviors. This process introduces (asymmetrical) hysteresis during behavioral switching. As a result behavioral oscillations, due to noisy information, are eliminated. Results in indoor environments show that if parameter values are chosen within reasonable ranges then, in spite of noise in the robots communi- cation and sensors, the overall robotic system works quite well even in cluttered environments. The robots overt behavior is stable and smooth.

Fractional dynamics in the trajectory control of redundant manipulators

Under the pseudoinverse control, robots with kinematical redundancy exhibit an undesirable chaotic joint motion which leads to an erratic behavior. This paper studies the complexity of fractional dynamics of the chaotic response. Fourier and wavelet analysis provides a deeper insight, helpful to know better the lack of repeatability problem of redundant manipulators. This perspective for the study of the chaotic phenomena will permit the development of superior trajectory control algorithms.

Power Law Behavior and Self-similarity in Modern Industrial Accidents

Advances in technology have produced more and more intricate industrial systems, such as nuclear power plants, chemical centers and petroleum platforms. Such complex plants exhibit multiple interactions among smaller units and human operators, rising potentially disastrous failure, which can propagate across subsystem boundaries. This paper analyzes industrial accident data-series in the perspective of statistical physics and dynamical systems. Global data is collected from the Emergency Events Database (EM-DAT) during the time period from year 1903 up to 2012. The statistical distributions of the number of fatalities caused by industrial accidents reveal Power Law (PL) behavior. We analyze the evolution of the PL parameters over time and observe a remarkable increment in the PL exponent during the last years. PL behavior allows prediction by extrapolation over a wide range of scales. In a complementary line of thought, we compare the data using appropriate indices and use different visualization techniques to correlate and to extract relationships among industrial accident events. This study contributes to better understand the complexity of modern industrial accidents and their ruling principles.

Students’ reading behavior: digital vs. print preferences in portuguese context

The aim of this paper is to present the main Portuguese results from a multi-national study on reading format preferences and behaviors from undergraduate students from Polytechnic Institute of Porto (Portugal). For this purpose we apply an adaptation of the Academic Reading Questionnaire previously created by Mizrachi (2014). This survey instrument has 14 Likert-style statements regarding the format influence in the students reading behavior, including aspects such as ability to remember, feelings about access convenience, active engagement with the text by highlighting and annotating, and ability to review and concentrate on the text. The importance of the language and dimension of the text to determine the preference format is also inquired. Students are also asked about the electronic device they use to read digital documents. Finally, some demographic and academic data were gathered. The analysis of the results will be contextualized on a review of the literature concerning youngsters reading format preferences. The format (digital or print) in which a text is displayed and read can impact comprehension, which is an important information literacy skill. This is a quite relevant issue for class readings in academic context because it impacts learning. On the other hand, students preferences on reading formats will influence the use of library services. However, literature is not unanimous on this subject. Woody, Daniel and Baker (2010) concluded that the experience of reading is not the same in electronic or print context and that students prefer print books than e-books. This thesis is reinforced by Ji, Michaels and Waterman (2014) which report that among 101 undergraduates the large majority self-reported to read and learn more when they use printed format despite the fact that they prefer electronically supplied readings instead of those supplied in printed form. On the other side, Rockinson-Szapkiw, et al (2013) conducted a study were they demonstrate that e-textbook is as effective for learning as the traditional textbook and that students who choose e-textbook had significantly higher perceived learning than students who chose to use print textbooks.