Minimizing the Homogeneous L2\mathcal{L}_2-Gain of Homogeneous Differentiators

The differentiation of noisy signals using the family of homogeneous differentiators is considered. It includes the high-gain (linear) as well as robust exact (discontinuous) differentiator. To characterize the effect of noise and disturbance on the differentiation estimation error, the generalized, homogeneous $\mathcal{L}_2$-gain is utilized. Analog to the classical $\mathcal{L}_p$-gain, it is not defined for the discontinuous case w.r.t. disturbances acting on the last channel. Thus, only continuous differentiators are addressed. The gain is estimated using a differential dissipation inequality, where a scaled Lyapunov function acts as storage function for the homogeneous $\mathcal{L}_2$ supply rate. The fixed differentiator gains are scaled with a gain-scaling parameter similar to the high-gain differentiator. This paper shows the existence of an optimal scaling which (locally) minimizes the homogeneous $\mathcal{L}_2$-gain estimate and provides a procedure to obtain it. Differentiators of dimension two are considered and the results are illustrated via numerical evaluation and a simulation example

Centennial-scale vegetation and North Atlantic Oscillation changes during the Late Holocene in the southern Iberia

High-reso CE to lution pollen analysis, charcoal, non-pollen palynomorphs and magnetic susceptibility have been analyzed in the sediment record of a peat bog in Sierra Nevada in southern Iberia. The study of these proxies provided the reconstruction of vegetation, climate, fire and human activity of the last ∼4500 cal yr BP. A progressive trend towards aridification during the late Holocene is observed in this record. This trend is interrupted by millennial- and centennial-scale variability of relatively more humid and arid periods. Arid conditions are recorded between ∼4000 and 3100 cal yr BP, being characterized by a decline in arboreal pollen and with a spike in magnetic susceptibility. This is followed by a relatively humid period from ∼3100 to 1600 cal yr BP, coinciding partially with the Iberian-Roman Humid Period, and is indicated by the increase of Pinus and the decrease in xerophytic taxa. The last 1500 cal yr BP are characterized by several centennial-scale climatic oscillations. Generally arid conditions from ∼450 to 1300 CE, depicted by a decrease in Pinus and an increase in Artemisia, comprise the Dark Ages and the Medieval Climate Anomaly. Since ∼ 1300 to 1850 CE pronounced oscillations occur between relatively humid and arid conditions. Four periods depicted by relatively higher Pinus coinciding with the beginning and end of the Little Ice Age are interrupted by three arid events characterized by an increase in Artemisia. These alternating arid and humid shifts could be explained by centennial-scale changes in the North Atlantic Oscillation and solar activity

Correlated enhancement of Hc2 and Jc in carbon nanotube-doped MgB2

The use of MgB2 in superconducting applications still awaits for the development of a MgB2-based material where both current-carrying performance and critical magnetic field are optimized simultaneously. We achieved this by doping MgB2 with double-wall carbon nanotubes (DWCNT) as a source of carbon in polycrystalline samples. The optimum nominal DWCNT content for increasing the critical current density, Jc is in the range 2.5-10%at depending on field and temperature. Record values of the upper critical field, Hc2(4K) = 41.9 T (with extrapolated Hc2(0) ~ 44.4 T) are reached in a bulk sample with 10%at DWCNT content. The measured Hc2 vs T in all samples are successfully described using a theoretical model for a two-gap superconductor in the dirty limit first proposed by Gurevich et al.Comment: 12 pages, 3 figure

Reducing instruction fetch energy with backwards branch control information and buffering

Many emerging applications, e.g. in the embedded and DSP space, are often characterized by their loopy nature where a substantial part of the execution time is spent within a few program phases. Loop buffering techniques have been proposed for capturing and processing these loops in small buffers to reduce the processor‘s instruction fetch energy. However, these schemes are limited to straight-line or inner-most loops and fail to adequately handle complex loops. In this paper, we propose a dynamic loop buffering mech-anism that uses backwards branch control information to identify, capture and process complex loop structures. The DLB controller has been fully implemented in VHDL, syn-thesized and timed with the IBM Booledozer and Einstimer Synthesis tools, and analyzed for power with the Sequence PowerTheater tool. Our experiments show that the DLB approach, on average, results in a factor of 3 reduction in energy consumption compared to a traditional instruction memory design at an area overhead of about 9%

Lyapunov-based HOSM control

[EN] We give an overview of the methods of analysis and design of High-Order Sliding Mode Controllers (HOSM) and observers,  including also those taking advantage of a discontinuous integral action. First, discontinuous state feedback controllers enforcing a sliding mode of arbitrary order are described. Then a recent class of HOSM  controllers is presented, which consists of a continuousstate feedback controller and a discontinuous integral term. High-order sliding mode observers are also introduced,  which are able to estimate robustly and in finite time the states of the uncertain plant, and they allow the implementation of an output feedback control law. All described designs are based in explicit Lyapunov functions, what is a main contribution of the research group of the authors at the Universidad Nacional Aut´onoma de M´exico, in Mexico City. The paper is tutorial and only the basic  results are presented, leaving aside the rigorous mathematical formulation and proof. For this the appropriate literature is referred to. The results are illustrated using simulations and an experimental validation in a laboratory set up of a magnetic levitation system.[ES] En este trabajo se presenta una panorámica del desarrollo de los métodos básicos de análisis y diseño de controladores y observadores por modos deslizantes de orden superior. Inicialmente se describen los controladores por retroalimentación de estados con una ley de control discontinua, que generan un modo deslizante de cualquier orden. Posteriormente se presenta una nueva clase de algoritmos por modos deslizantes de orden superior, que consisten en una retroalimentación de estados continua y una acción de control integral discontinua. Se describen también observadores por modos deslizantes, que estiman los estados del sistema en tiempo finito, y que permiten obtener un controlador por retroalimentación de la salida. Todos los diseños presentados se basan en el uso de funciones de Lyapunov (explícitas), que constituyen una contribución importante del grupo de trabajo de los autores en la Universidad Nacional Autónoma de México. La presentación es tutorial y solo se dan los resultados, dejando a un lado la formalización rigurosa y las pruebas matemáticas. Para ello se refiere al lector a la literatura pertinente. Se ilustran los resultados mediante simulaciones y la validación experimental en un sistema de levitación magnética.PAPIIT-UNAM, proyecto IN102121Moreno, JA.; Fridman, L. (2022). Control por modos deslizantes de orden superior basado en funciones de Lyapunov. Revista Iberoamericana de Automática e Informática industrial. 19(4):394-406. https://doi.org/10.4995/riai.2022.17013OJS39440619