On the fractional order control of heat systems

The differentiation of non-integer order has its origin in the seventeenth century, but only in the last two decades appeared the first applications in the area of control theory. In this paper we consider the study of a heat diffusion system based on the application of the fractional calculus concepts. In this perspective, several control methodologies are investigated namely the fractional PID and the Smith predictor. Extensive simulations are presented assessing the performance of the proposed fractional-order algorithms.

Tuning and application of integer and fractional order PID controllers

Fractional calculus (FC) is widely used in most areas of science and engineering, being recognized its ability to yield a superior modeling and control in many dynamical systems. In this perspective, this article illustrates two applications of FC in the area of control systems. Firstly, is presented a methodology of tuning PID controllers that gives closed-loop systems robust to gain variations. After, a fractional-order PID controller is proposed for the control of an hexapod robot with three dof legs. In both cases, it is demonstrated the system's superior performance by using the FC concepts.

Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.

On moduli of smoothness of fractional order

In this paper we consider the properties of moduli of smoothness of fractional order. The main result of the paper describes the equivalence of the modulus of smoothness and a function from some class.

The third order Melnikov function of a quadratic center under quadratic perturbation

We study quadratic perturbations of the integrable system (1+x)dH; where H =(x²+y²)=2: We prove that the first three Melnikov functions associated to the perturbed system give rise at most to three limit cycles.

The adaptive function of melanin-based coloration in the tawny owl (Strix aluco) ; the proximate role of the melanocortin system

Colour polymorphism is common in wild population. One of the main questioning of evolutionary biologists is to understand how different colour variants could have evolved and be maintained in fluctuating environments, a selective process that forces individuals to constantly adapt their strategies in order to survive. This issue is particularly true for traits that are genetically inherited. Natural selection erodes genotypes with lowest fitness (less adapted), reducing in turn global genetic variation within population. In this context, the study of the evolution and maintenance of melanin- based coloration is relevant since inter-individual variation in the deposition of these pigments is common in animal and plant kingdoms and is under strong genetic control. In this thesis, I focus on the specific case of the tawny owl (Strix aluco), a species displaying continuous variation in reddish pheomelanin-based coloration. Interestingly, empirical studies highlighted covariations between melanin-based coloration and important behavioural, physiological and life history traits. Recently, a genetic model pointed out the melanocortin system and their pleiotropic effects as a potential regulator of these covariations. Accordingly, this PhD thesis further investigates colour-specific behavioural, physiological, or life history strategies, while examining the proximate mechanisms underlying these reaction norms. We found that differently coloured tawny owls differently resolve fundamental trade-off between offspring number and quality (Chapter 1), light melanic individuals producing many low- quality offspring and dark, melanic ones producing few high-quality offspring. These reproductive strategies are likely to induce alternative physiological constraints. Indeed, we demonstrated that light melanic individuals produced higher levels of reactive oxygen species (ROS, Chapter 2), but also expressed higher levels of antioxidant (GSH, Chapters 2 & 3). Interestingly, we showed that light melanic breeding females could modulate their POMC prohormone levels according to the environmental conditions, while dark reddish ones produced constant levels of this prohormone {Chapter 4). Finally, we highlighted colour-specific patterns of prohormone convertase 1 (PCI) gene expression (Chapter 5), an enzyme responsible for POMC prohormone processing to ACTH and a- MSH, for instance. Altogether, these results provide strong evidence of colour-specific strategies, light and melanic tawny owls better coping with stressful and relaxed environments, respectively. Variation in melanin-based coloration is likely to be maintained by the heterogeneity of our study area and strong environmental stochasticity within and between years, these process favouring differently coloured tawny owls at different periods of time. From a proximate point of view, this PhD thesis supports the hypothesis that covariations between phenotypic traits and melanin-based coloration stems from the melanocortin system, especially the fundamental role of POMC gene expression and its processing to melanocortin peptides. - Le polymorphisme de couleur est une variation phénotypique très fréquente dans la nature. En biologie évolutive, une des problématiques clés est donc de comprendre comment différent morphes de couleur peuvent être apparus et maintenus au cours du temps dans des environnements aussi variables que les nôtres, surtout que ces fluctuations forcent ces morphes à s'adapter constamment pour assurer leur survie. Cette thématique est particulièrement réelle lorsque les variations phénotypiques sont héréditaires et donc sous forte influence génétique. La sélection naturelle a en effet le pouvoir d'éroder rapidement la variation génétique en éliminant les génotypes mal adaptés. Dans ce sens, l'étude de l'évolution, et de la maintenance de la coloration mélanique est donc tout à fait pertinente car la variation de coloration entre individus est très répandue à travers les règnes animal et végétal et sous forte influence génétique. Dans cette thèse, je me suis concentré sur le cas spécifique de la chouette hulotte (Strix aluco), une espèce présentant une variation continue dans la déposition de pigments pheomélaniques roux. De précédentes études ont déjà montré que cette variation de coloration était associée avec des variations de traits comportementaux, physiologiques ou d'histoire de vie. Récemment, une étude a souligné l'importance du système des mélanocortines et de leurs effets pléiotropes dans la régulation de ces covariations. En conséquence, cette thèse de doctoral a pour but d'étudier un peu plus les stratégies comportementales, physiologiques ou d'histoire de vie spécifiques à chaque morphe de couleur, tout en examinant un peu plus les mécanismes proximaux potentiellement à la base de ces normes de réactions. Nous constatons tout d'abord que les morphes de couleurs étaient associés à différentes stratégies dans la résolution de compromis telle que la production de beaucoup de jeunes ou des jeunes de qualité (Chapitre 1). Les morphes gris (dit peu mélaniques) ont tendance à produire beaucoup de jeunes mains de moindre qualité, alors que les morphes roux (dit fortement mélaniques) produisent moins de jeunes mais de meilleure qualité. Ces stratégies sont susceptibles alors d'induire certaines contraintes physiologiques. Par exemple, nous montrons que les morphes gris produisent plus de dérivés réactifs de l'oxygène (ROS, Chapitre 2), mais aussi plus d'antioxydants (GSH, Chapitres 2 & 3). Nous montrons ensuite que les femelles grises ont une plus grande capacité à moduler leur niveau de POMC prohormone dans le sang en fonction des conditions environnementales, alors que les femelles rousses gardent un niveau constant (Chapitre 4). Finalement, nous démontrons que les patterns d'expression du gène codant pour la prohormone convertase 1 varient chez des jeunes issus de parents gris ou roux (Chapitre 5). Ceci est particulièrement intéressant car cette enzyme permet de scinder la POMC prohormone en plusieurs peptides importants tels que l'ACTH ou l'a-MSH. En conclusion, ces résultats démontrent qu'il y a bel et bien des stratégies évolutives différentes entre les morphes de couleurs, les chouettes hulottes grises et rousses étant respectivement plus adaptés à des environnements stressants ou favorables. L'hétérogénéité de notre zone d'étude et la stochasticité environnementale qui caractérise ses habitats pourraient donc agir comme une source de sélection temporelle, laquelle favoriserait les différents morphes de couleurs à diverses périodes. D'un point de vue plus proximale maintenant, cette thèse de doctorat soutient l'hypothèse que les covariations observées entre la coloration mélanique et des traits phénotypiques importants sont modulées par les effets pléiotropes du système des mélanocortines, et met en avant le rôle prépondérant que pourrait jouer l'expression du gène POMC et sa post traduction en mélanocortines.

Emergence of order in visual system development.

Neural connections in the adult central nervous system are highly precise. In the visual system, retinal ganglion cells send their axons to target neurons in the lateral geniculate nucleus (LGN) in such a way that axons originating from the two eyes terminate in adjacent but nonoverlapping eye-specific layers. During development, however, inputs from the two eyes are intermixed, and the adult pattern emerges gradually as axons from the two eyes sort out to form the layers. Experiments indicate that the sorting-out process, even though it occurs in utero in higher mammals and always before vision, requires retinal ganglion cell signaling; blocking retinal ganglion cell action potentials with tetrodotoxin prevents the formation of the layers. These action potentials are endogenously generated by the ganglion cells, which fire spontaneously and synchronously with each other, generating "waves" of activity that travel across the retina. Calcium imaging of the retina shows that the ganglion cells undergo correlated calcium bursting to generate the waves and that amacrine cells also participate in the correlated activity patterns. Physiological recordings from LGN neurons in vitro indicate that the quasiperiodic activity generated by the retinal ganglion cells is transmitted across the synapse between ganglion cells to drive target LGN neurons. These observations suggest that (i) a neural circuit within the immature retina is responsible for generating specific spatiotemporal patterns of neural activity; (ii) spontaneous activity generated in the retina is propagated across central synapses; and (iii) even before the photoreceptors are present, nerve cell function is essential for correct wiring of the visual system during early development. Since spontaneously generated activity is known to be present elsewhere in the developing CNS, this process of activity-dependent wiring could be used throughout the nervous system to help refine early sets of neural connections into their highly precise adult patterns.

Observation of generalized synchronization of chaos in a driven chaotic system

We report on the experimental observation of the generalized synchronization of chaos in a real physical system. We show that under a nonlinear resonant interaction, the chaotic dynamics of a single mode laser can become functionally related to that of a chaotic driving signal and furthermore as the coupling strength is further increased, the chaotic dynamics of the laser approaches that of the driving signal.

Analysis of the mouse transcriptome for genes involved in the function of the nervous system

We analyzed the mouse Representative Transcript and Protein Set for molecules involved in brain function. We found full-length cDNAs of many known brain genes and discovered new members of known brain gene families, including Family 3 G-protein coupled receptors, voltage-gated channels, and connexins. We also identified previously unknown candidates for secreted neuroactive molecules. The existence of a large number of unique brain ESTs suggests an additional molecular complexity that remains to be explored. A list of genes containing CAG stretches in the coding region represents a first step in the potential identification of candidates for hereditary neurological disorders.

Root-locus practical sketching rules for fractional-order system

For integer-order systems, there are well-known practical rules for RL sketching. Nevertheless, these rules cannot be directly applied to fractional-order (FO) systems. Besides, the existing literature on this topic is scarce and exclusively focused on commensurate systems, usually expressed as the ratio of two noninteger polynomials. The practical rules derived for those do not apply to other symbolic expressions, namely, to transfer functions expressed as the ratio of FO zeros and poles. However, this is an important case as it is an extension of the classical integer-order problem usually addressed by control engineers. Extending the RL practical sketching rules to such FO systems will contribute to decrease the lack of intuition about the corresponding system dynamics. This paper generalises several RL practical sketching rules to transfer functions specified as the ratio of FO zeros and poles. The subject is presented in a didactic perspective, being the rules applied to several examples.

Stability of fractional order systems

The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, from the mathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled.

Fractional order modelling of zero length column desorption response for adsorbents with variable particle sizes

This manuscript analyses the data generated by a Zero Length Column (ZLC) diffusion experimental set-up, for 1,3 Di-isopropyl benzene in a 100% alumina matrix with variable particle size. The time evolution of the phenomena resembles those of fractional order systems, namely those with a fast initial transient followed by long and slow tails. The experimental measurements are best fitted with the Harris model revealing a power law behavior.

Fractional order models of leaves

Leaves are mainly responsible for food production in vascular plants. Studying individual leaves can reveal important characteristics of the whole plant, namely its health condition, nutrient status, the presence of viruses and rooting ability. One technique that has been used for this purpose is Electrical Impedance Spectroscopy, which consists of determining the electrical impedance spectrum of the leaf. In this paper we use EIS and apply the tools of Fractional Calculus to model and characterize six species. Two modeling approaches are proposed: firstly, Resistance, Inductance, Capacitance electrical networks are used to approximate the leaves’ impedance spectra; afterwards, fractional-order transfer functions are considered. In both cases the model parameters can be correlated with physical characteristics of the leaves.

Application of fractional order concepts in the study of electrical potential

The Maxwell equations, expressing the fundamental laws of electricity and magnetism, only involve the integer-order calculus. However, several effects present in electromagnetism, motivated recently an analysis under the fractional calculus (FC) perspective. In fact, this mathematical concept allows a deeper insight into many phenomena that classical models overlook. On the other hand, genetic algorithms (GA) are an important tool to solve optimization problems that occur in engineering. In this work we use FC and GA to implement the electrical potential of fractional order. The performance of the GA scheme and the convergence of the resulting approximations are analyzed.

Application of genetic algorithms in the design of an electrical potential of fractional order

Fractional calculus (FC) is currently being applied in many areas of science and technology. In fact, this mathematical concept helps the researches to have a deeper insight about several phenomena that integer order models overlook. Genetic algorithms (GA) are an important tool to solve optimization problems that occur in engineering. This methodology applies the concepts that describe biological evolution to obtain optimal solution in many different applications. In this line of thought, in this work we use the FC and the GA concepts to implement the electrical fractional order potential. The performance of the GA scheme, and the convergence of the resulting approximation, are analyzed. The results are analyzed for different number of charges and several fractional orders.