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.

Inteligência artificial aplicada na previsão de mercados financeiros

Neste documento, são investigados vários métodos usados na inteligência artificial, com o objetivo de obter previsões precisas da evolução dos mercados financeiros. O uso de ferramentas lineares como os modelos AR, MA, ARMA e GARCH têm muitas limitações, pois torna-se muito difícil adaptá-los às não linearidades dos fenómenos que ocorrem nos mercados. Pelas razões anteriormente referidas, os algoritmos como as redes neuronais dinâmicas (TDNN, NARX e ESN), mostram uma maior capacidade de adaptação a estas não linearidades, pois não fazem qualquer pressuposto sobre as distribuições de probabilidade que caracterizam estes mercados. O facto destas redes neuronais serem dinâmicas, faz com que estas exibam um desempenho superior em relação às redes neuronais estáticas, ou outros algoritmos que não possuem qualquer tipo de memória. Apesar das vantagens reveladas pelas redes neuronais, estas são um sistema do tipo black box, o que torna muito difícil extrair informação dos pesos da rede. Isto significa que estes algoritmos devem ser usados com precaução, pois podem tornar-se instáveis.

Optimal operation of multiproduct batch plants

Multiproduct plants, Dynamic Optimization, Mixed Integer Linear/Non-Linear Programming, Scheduling

Modelització i control d'un reactor de producció d'hidrogen per a l'alimentació de piles de combustible

Les piles de combustible permeten la transformació eficient de l’energia química de certs combustibles a energia elèctrica a través d’un procés electroquímic. De les diferents tecnologies de piles de combustible, les piles de combustible de tipus PEM són les més competitives i tenen una gran varietat d’aplicacions. No obstant, han de ser alimentades únicament per hidrogen. Per altra banda, l’etanol, un combustible interessant en el marc dels combustibles renovables, és una possible font d’hidrogen. Aquest treball estudia la reformació d’etanol per a l’obtenció d’hidrogen per a alimentar piles de combustible PEM. Només existeixen algunes publicacions que tractin l’obtenció d’hidrogen a partir d’etanol, i aquestes no inclouen l’estudi dinàmic del sistema. Els objectius del treball són el modelat i l’estudi dinàmic de reformadors d’etanol de baixa temperatura. Concretament, proposa un model dinàmic d’un reformador catalític d’etanol amb vapor basat en un catalitzador de cobalt. Aquesta reformació permet obtenir valors alts d’eficiència i valors òptims de monòxid de carboni que evitaran l’enverinament d’una la pila de combustible de tipus PEM. El model, no lineal, es basa en la cinètica obtinguda de diferents assaigs de laboratori. El reformador modelat opera en tres etapes: deshidrogenació d’etanol a acetaldehid i hidrogen, reformat amb vapor d’acetaldehid, i la reacció WGS (Water Gas Shift). El treball també estudia la sensibilitat i controlabilitat del sistema, caracteritzant així el sistema que caldrà controlar. L’anàlisi de controlabilitat es realitza sobre la resposta de dinàmica ràpida obtinguda del balanç de massa del reformador. El model no lineal és linealitzat amb la finalitat d’aplicar eines d’anàlisi com RGA, CN i MRI. El treball ofereix la informació necessària per a avaluar la possible implementació en un laboratori de piles de combustibles PEM alimentades per hidrogen provinent d’un reformador d’etanol.

Dynamic changes in brain functional connectivity during concurrent dual-task performance.

This study investigated the spatial, spectral, temporal and functional proprieties of functional brain connections involved in the concurrent execution of unrelated visual perception and working memory tasks. Electroencephalography data was analysed using a novel data-driven approach assessing source coherence at the whole-brain level. Three connections in the beta-band (18-24 Hz) and one in the gamma-band (30-40 Hz) were modulated by dual-task performance. Beta-coherence increased within two dorsofrontal-occipital connections in dual-task conditions compared to the single-task condition, with the highest coherence seen during low working memory load trials. In contrast, beta-coherence in a prefrontal-occipital functional connection and gamma-coherence in an inferior frontal-occipitoparietal connection was not affected by the addition of the second task and only showed elevated coherence under high working memory load. Analysis of coherence as a function of time suggested that the dorsofrontal-occipital beta-connections were relevant to working memory maintenance, while the prefrontal-occipital beta-connection and the inferior frontal-occipitoparietal gamma-connection were involved in top-down control of concurrent visual processing. The fact that increased coherence in the gamma-connection, from low to high working memory load, was negatively correlated with faster reaction time on the perception task supports this interpretation. Together, these results demonstrate that dual-task demands trigger non-linear changes in functional interactions between frontal-executive and occipitoparietal-perceptual cortices.

SAT Modulo Linear Arithmetic for Solving Polynomial

Polynomial constraint solving plays a prominent role in several areas of hardware and software analysis and verification, e.g., termination proving, program invariant generation and hybrid system verification, to name a few. In this paper we propose a new method for solving non-linear constraints based on encoding the problem into an SMT problem considering only linear arithmetic. Unlike other existing methods, our method focuses on proving satisfiability of the constraints rather than on proving unsatisfiability, which is more relevant in several applications as we illustrate with several examples. Nevertheless, we also present new techniques based on the analysis of unsatisfiable cores that allow one to efficiently prove unsatisfiability too for a broad class of problems. The power of our approach is demonstrated by means of extensive experiments comparing our prototype with state-of-the-art tools on benchmarks taken both from the academic and the industrial world.

Blind Inversion of Wiener Systems

A system in which a linear dynamic part is followed by a non linear memoryless distortion a Wiener system is blindly inverted This kind of systems can be modelised as a postnonlinear mixture and using some results about these mixtures an e cient algorithm is proposed Results in a hard situation are presented and illustrate the e ciency of this algorithm

Dynamic models of energy allocation and investment

In dynamic models of energy allocation, assimilated energy is allocated to reproduction, somatic growth, maintenance or storage, and the allocation pattern can change with age. The expected evolutionary outcome is an optimal allocation pattern, but this depends on the environment experienced during the evolutionary process and on the fitness costs and benefits incurred by allocating resources in different ways. Here we review existing treatments which encompass some of the possibilities as regards constant or variable environments and their predictability or unpredictability, and the ways in which production rates and mortality rates depend on body size and composition and age and on the pattern of energy allocation. The optimal policy is to allocate resources where selection pressures are highest, and simultaneous allocation to several body subsystems and reproduction can be optimal if these pressures are equal. This may explain balanced growth commonly observed during ontogeny. Growth ceases at maturity in many models; factors favouring growth after maturity include non-linear trade-offs, variable season length, and production and mortality rates both increasing (or decreasing) functions of body size. We cannot yet say whether these are sufficient to account for the many known cases of growth after maturity and not all reasonable models have yet been explored. Factors favouring storage are also reviewed.

Update on the non-prewhitening model observer in computed tomography for the assessment of the adaptive statistical and model-based iterative reconstruction algorithms.

The state of the art to describe image quality in medical imaging is to assess the performance of an observer conducting a task of clinical interest. This can be done by using a model observer leading to a figure of merit such as the signal-to-noise ratio (SNR). Using the non-prewhitening (NPW) model observer, we objectively characterised the evolution of its figure of merit in various acquisition conditions. The NPW model observer usually requires the use of the modulation transfer function (MTF) as well as noise power spectra. However, although the computation of the MTF poses no problem when dealing with the traditional filtered back-projection (FBP) algorithm, this is not the case when using iterative reconstruction (IR) algorithms, such as adaptive statistical iterative reconstruction (ASIR) or model-based iterative reconstruction (MBIR). Given that the target transfer function (TTF) had already shown it could accurately express the system resolution even with non-linear algorithms, we decided to tune the NPW model observer, replacing the standard MTF by the TTF. It was estimated using a custom-made phantom containing cylindrical inserts surrounded by water. The contrast differences between the inserts and water were plotted for each acquisition condition. Then, mathematical transformations were performed leading to the TTF. As expected, the first results showed a dependency of the image contrast and noise levels on the TTF for both ASIR and MBIR. Moreover, FBP also proved to be dependent of the contrast and noise when using the lung kernel. Those results were then introduced in the NPW model observer. We observed an enhancement of SNR every time we switched from FBP to ASIR to MBIR. IR algorithms greatly improve image quality, especially in low-dose conditions. Based on our results, the use of MBIR could lead to further dose reduction in several clinical applications.

Integrability of a linear center perturbed by a fourth degree homogeneous polynomial

In this work we study the integrability of a two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fourth degree. We give sufficient conditions for integrability in polar coordinates. Finally we establish a conjecture about the independence of the two classes of parameters which appear in the system; if this conjecture is true the integrable cases found will be the only possible ones.

Integrability of a linear center perturbed by a fifth degree homogeneous polynomial

In this work we study the integrability of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fifth degree. We give a simple characterisation for the integrable cases in polar coordinates. Finally we formulate a conjecture about the independence of the two classes of parameters which appear on the system; if this conjecture is true the integrable cases found will be the only possible ones.

Three-dimensional hydrodynamic numerical modelling of fold nappe formation, basement-cover deformation and slab detachment with applications to the helvetic nappe system (W Switzerland)

Many three-dimensional (3-D) structures in rock, which formed during the deformation of the Earth's crust and lithosphere, are controlled by a difference in mechanical strength between rock units and are often the result of a geometrical instability. Such structures are, for example, folds, pinch-and-swell structures (due to necking) or cuspate-lobate structures (mullions). These struc-tures occur from the centimeter to the kilometer scale and the related deformation processes con-trol the formation of, for example, fold-and-thrust belts and extensional sedimentary basins or the deformation of the basement-cover interface. The 2-D deformation processes causing these structures are relatively well studied, however, several processes during large-strain 3-D defor-mation are still incompletely understood. One of these 3-D processes is the lateral propagation of these structures, such as fold and cusp propagation in a direction orthogonal to the shortening direction or neck propagation in direction orthogonal to the extension direction. Especially, we are interested in fold nappes which are recumbent folds with amplitudes usually exceeding 10 km and they have been presumably formed by ductile shearing. They often exhibit a constant sense of shearing and a non-linear increase of shear strain towards their overturned limb. The fold axes of the Morcles fold nappe in western Switzerland plunges to the ENE whereas the fold axes in the more eastern Doldenhorn nappe plunges to the WSW. These opposite plunge direc-tions characterize the Rawil depression (Wildstrubel depression). The Morcles nappe is mainly the result of layer parallel contraction and shearing. During the compression the massive lime-stones were more competent than the surrounding marls and shales, which led to the buckling characteristics of the Morcles nappe, especially in the north-dipping normal limb. The Dolden-horn nappe exhibits only a minor overturned fold limb. There are still no 3-D numerical studies which investigate the fundamental dynamics of the formation of the large-scale 3-D structure including the Morcles and Doldenhorn nappes and the related Rawil depression. We study the 3-D evolution of geometrical instabilities and fold nappe formation with numerical simulations based on the finite element method (FEM). Simulating geometrical instabilities caused by sharp variations of mechanical strength between rock units requires a numerical algorithm that can accurately resolve material interfaces for large differences in material properties (e.g. between limestone and shale) and for large deformations. Therefore, our FE algorithm combines a nu-merical contour-line technique and a deformable Lagrangian mesh with re-meshing. With this combined method it is possible to accurately follow the initial material contours with the FE mesh and to accurately resolve the geometrical instabilities. The algorithm can simulate 3-D de-formation for a visco-elastic rheology. The viscous rheology is described by a power-law flow law. The code is used to study the 3-D fold nappe formation, the lateral propagation of folding and also the lateral propagation of cusps due to initial half graben geometry. Thereby, the small initial geometrical perturbations for folding and necking are exactly followed by the FE mesh, whereas the initial large perturbation describing a half graben is defined by a contour line inter-secting the finite elements. Further, the 3-D algorithm is applied to 3-D viscous nacking during slab detachment. The results from various simulations are compared with 2-D resulats and a 1-D analytical solution. -- On retrouve beaucoup de structures en 3 dimensions (3-D) dans les roches qui ont pour origines une déformation de la lithosphère terrestre. Ces structures sont par exemple des plis, des boudins (pinch-and-swell) ou des mullions (cuspate-lobate) et sont présentés de l'échelle centimétrique à kilométrique. Mécaniquement, ces structures peuvent être expliquées par une différence de résistance entre les différentes unités de roches et sont généralement le fruit d'une instabilité géométrique. Ces différences mécaniques entre les unités contrôlent non seulement les types de structures rencontrées, mais également le type de déformation (thick skin, thin skin) et le style tectonique (bassin d'avant pays, chaîne d'avant pays). Les processus de la déformation en deux dimensions (2-D) formant ces structures sont relativement bien compris. Cependant, lorsque l'on ajoute la troisiéme dimension, plusieurs processus ne sont pas complètement compris lors de la déformation à large échelle. L'un de ces processus est la propagation latérale des structures, par exemple la propagation de plis ou de mullions dans la direction perpendiculaire à l'axe de com-pression, ou la propagation des zones d'amincissement des boudins perpendiculairement à la direction d'extension. Nous sommes particulièrement intéressés les nappes de plis qui sont des nappes de charriage en forme de plis couché d'une amplitude plurikilométrique et étant formées par cisaillement ductile. La plupart du temps, elles exposent un sens de cisaillement constant et une augmentation non linéaire de la déformation vers la base du flanc inverse. Un exemple connu de nappes de plis est le domaine Helvétique dans les Alpes de l'ouest. Une de ces nap-pes est la Nappe de Morcles dont l'axe de pli plonge E-NE tandis que de l'autre côté de la dépression du Rawil (ou dépression du Wildstrubel), la nappe du Doldenhorn (équivalent de la nappe de Morcles) possède un axe de pli plongeant O-SO. La forme particulière de ces nappes est due à l'alternance de couches calcaires mécaniquement résistantes et de couches mécanique-ment faibles constituées de schistes et de marnes. Ces différences mécaniques dans les couches permettent d'expliquer les plissements internes à la nappe, particulièrement dans le flanc inver-se de la nappe de Morcles. Il faut également noter que le développement du flanc inverse des nappes n'est pas le même des deux côtés de la dépression de Rawil. Ainsi la nappe de Morcles possède un important flanc inverse alors que la nappe du Doldenhorn en est presque dépour-vue. A l'heure actuelle, aucune étude numérique en 3-D n'a été menée afin de comprendre la dynamique fondamentale de la formation des nappes de Morcles et du Doldenhorn ainsi que la formation de la dépression de Rawil. Ce travail propose la première analyse de l'évolution 3-D des instabilités géométriques et de la formation des nappes de plis en utilisant des simulations numériques. Notre modèle est basé sur la méthode des éléments finis (FEM) qui permet de ré-soudre avec précision les interfaces entre deux matériaux ayant des propriétés mécaniques très différentes (par exemple entre les couches calcaires et les couches marneuses). De plus nous utilisons un maillage lagrangien déformable avec une fonction de re-meshing (production d'un nouveau maillage). Grâce à cette méthode combinée il nous est possible de suivre avec précisi-on les interfaces matérielles et de résoudre avec précision les instabilités géométriques lors de la déformation de matériaux visco-élastiques décrit par une rhéologie non linéaire (n>1). Nous uti-lisons cet algorithme afin de comprendre la formation des nappes de plis, la propagation latérale du plissement ainsi que la propagation latérale des structures de type mullions causé par une va-riation latérale de la géométrie (p.ex graben). De plus l'algorithme est utilisé pour comprendre la dynamique 3-D de l'amincissement visqueux et de la rupture de la plaque descendante en zone de subduction. Les résultats obtenus sont comparés à des modèles 2-D et à la solution analytique 1-D. -- Viele drei dimensionale (3-D) Strukturen, die in Gesteinen vorkommen und durch die Verfor-mung der Erdkruste und Litosphäre entstanden sind werden von den unterschiedlichen mechani-schen Eigenschaften der Gesteinseinheiten kontrolliert und sind häufig das Resulat von geome-trischen Istabilitäten. Zu diesen strukturen zählen zum Beispiel Falten, Pich-and-swell Struktu-ren oder sogenannte Cusbate-Lobate Strukturen (auch Mullions). Diese Strukturen kommen in verschiedenen Grössenordungen vor und können Masse von einigen Zentimeter bis zu einigen Kilometer aufweisen. Die mit der Entstehung dieser Strukturen verbundenen Prozesse kontrol-lieren die Entstehung von Gerbirgen und Sediment-Becken sowie die Verformung des Kontaktes zwischen Grundgebirge und Stedimenten. Die zwei dimensionalen (2-D) Verformungs-Prozesse die zu den genannten Strukturen führen sind bereits sehr gut untersucht. Einige Prozesse wäh-rend starker 3-D Verformung sind hingegen noch unvollständig verstanden. Einer dieser 3-D Prozesse ist die seitliche Fortpflanzung der beschriebenen Strukturen, so wie die seitliche Fort-pflanzung von Falten und Cusbate-Lobate Strukturen senkrecht zur Verkürzungsrichtung und die seitliche Fortpflanzung von Pinch-and-Swell Strukturen othogonal zur Streckungsrichtung. Insbesondere interessieren wir uns für Faltendecken, liegende Falten mit Amplituden von mehr als 10 km. Faltendecken entstehen vermutlich durch duktile Verscherung. Sie zeigen oft einen konstanten Scherungssinn und eine nicht-lineare zunahme der Scherverformung am überkipp-ten Schenkel. Die Faltenachsen der Morcles Decke in der Westschweiz fallen Richtung ONO während die Faltenachsen der östicher gelegenen Doldenhorn Decke gegen WSW einfallen. Diese entgegengesetzten Einfallrichtungen charakterisieren die Rawil Depression (Wildstrubel Depression). Die Morcles Decke ist überwiegend das Resultat von Verkürzung und Scherung parallel zu den Sedimentlagen. Während der Verkürzung verhielt sich der massive Kalkstein kompetenter als der Umliegende Mergel und Schiefer, was zur Verfaltetung Morcles Decke führ-te, vorallem in gegen Norden eifallenden überkippten Schenkel. Die Doldenhorn Decke weist dagegen einen viel kleineren überkippten Schenkel und eine stärkere Lokalisierung der Verfor-mung auf. Bis heute gibt es keine 3-D numerischen Studien, die die fundamentale Dynamik der Entstehung von grossen stark verformten 3-D Strukturen wie den Morcles und Doldenhorn Decken sowie der damit verbudenen Rawil Depression untersuchen. Wir betrachten die 3-D Ent-wicklung von geometrischen Instabilitäten sowie die Entstehung fon Faltendecken mit Hilfe von numerischen Simulationen basiert auf der Finite Elemente Methode (FEM). Die Simulation von geometrischen Instabilitäten, die aufgrund von Änderungen der Materialeigenschaften zwischen verschiedenen Gesteinseinheiten entstehen, erfortert einen numerischen Algorithmus, der in der Lage ist die Materialgrenzen mit starkem Kontrast der Materialeigenschaften (zum Beispiel zwi-schen Kalksteineinheiten und Mergel) für starke Verfomung genau aufzulösen. Um dem gerecht zu werden kombiniert unser FE Algorithmus eine numerische Contour-Linien-Technik und ein deformierbares Lagranges Netz mit Re-meshing. Mit dieser kombinierten Methode ist es mög-lich den anfänglichen Materialgrenzen mit dem FE Netz genau zu folgen und die geometrischen Instabilitäten genügend aufzulösen. Der Algorithmus ist in der Lage visko-elastische 3-D Ver-formung zu rechnen, wobei die viskose Rheologie mit Hilfe eines power-law Fliessgesetzes beschrieben wird. Mit dem numerischen Algorithmus untersuchen wir die Entstehung von 3-D Faltendecken, die seitliche Fortpflanzung der Faltung sowie der Cusbate-Lobate Strukturen die sich durch die Verkürzung eines mit Sediment gefüllten Halbgraben bilden. Dabei werden die anfänglichen geometrischen Instabilitäten der Faltung exakt mit dem FE Netz aufgelöst wäh-rend die Materialgranzen des Halbgrabens die Finiten Elemente durchschneidet. Desweiteren wird der 3-D Algorithmus auf die Einschnürung während der 3-D viskosen Plattenablösung und Subduktion angewandt. Die 3-D Resultate werden mit 2-D Ergebnissen und einer 1-D analyti-schen Lösung verglichen.

Study of the optical properties of TeO2-PbO-TiO2 glass system

We describe the preparation and some optical properties of high refractive index TeO2-PbO-TiO2 glass system. Highly homogeneous glasses were obtained by agitating the mixture during the melting process in an alumina crucible. The characterization was done by X-ray diffraction, Raman scattering, light absorption and linear refractive index measurements. The results show a change in the glass structure as the PbO content increases: the TeO4 trigonal bipyramids characteristics of TeO2 glasses transform into TeO3 trigonal pyramids. However, the measured refractive indices are almost independent of the glass composition. We show that third-order nonlinear optical susceptibilities calculated from the measured refractive indices using Lines' theoretical model are also independent of the glass composition.

Learning Robot Motions from Visual Sensing

Learning from demonstration becomes increasingly popular as an efficient way of robot programming. Not only a scientific interest acts as an inspiration in this case but also the possibility of producing the machines that would find application in different areas of life: robots helping with daily routine at home, high performance automata in industries or friendly toys for children. One way to teach a robot to fulfill complex tasks is to start with simple training exercises, combining them to form more difficult behavior. The objective of the Master’s thesis work was to study robot programming with visual input. Dynamic movement primitives (DMPs) were chosen as a tool for motion learning and generation. Assuming a movement to be a spring system influenced by an external force, making this system move, DMPs represent the motion as a set of non-linear differential equations. During the experiments the properties of DMP, such as temporal and spacial invariance, were examined. The effect of the DMP parameters, including spring coefficient, damping factor, temporal scaling, on the trajectory generated were studied.

Application of a Pid+fuzzy controller on the motion control system in machine tools

This work deals with an hybrid PID+fuzzy logic controller applied to control the machine tool biaxial table motions. The non-linear model includes backlash and the axis elasticity. Two PID controllers do the primary table control. A third PID+fuzzy controller has a cross coupled structure whose function is to minimise the trajectory contour errors. Once with the three PID controllers tuned, the system is simulated with and without the third controller. The responses results are plotted and compared to analyse the effectiveness of this hybrid controller over the system. They show that the proposed methodology reduces the contour error in a proportion of 70:1.