Periodic solutions with nonconstant sign in Abel equations of the second kind

The study of periodic solutions with constant sign in the Abel equation of the second kind can be made through the equation of the first kind. This is because the situation is equivalent under the transformation $x\mapsto x^{-1}$, and there are many results available in the literature for the first kind equation. However, the equivalence breaks down when one seeks for solutions with nonconstant sign. This note is devoted to periodic solutions with nonconstant sign in Abel equations of the second kind. Specifically, we obtain sufficient conditions to ensure the existence of a periodic solution that shares the zeros of the leading coefficient of the Abel equation. Uniqueness and stability features of such solutions are also studied.Comment: 10 page

Second-order odd-harmonic repetitive control and its application to active filter control

High order repetitive control has been introduced toovercomeperformance decay of repetitive control systems undervarying frequency of the signals to be tracked/rejected orimproving the interhamonic behavior. However, most highorder repetitive internal models used to improve frequencyuncertainty are unstable, as a consequence practicalimplementations are more difficult. In this work a stable,second order odd-harmonic repetitive control system ispresented and studied.The proposed internal model has been implemented andvalidated in a shunt active filter current controller. Thishigh order controller allows dealing with the gridfrequency variations without using adaptive schemes

Novel slow-fast behaviour in an oscillator driven by a frequency-switching force

When an oscillator switches abruptly between different frequencies, there is some ambiguity in deciding how the system should be modelled at the switch. Here we describe two seemingly natural models of a switch in a simple periodically-forced harmonic oscillator, which disagree starkly in their predictions of its long time behaviour. Attempting to resolve the disagreement by `regularizing' the switch not only preserves the disagreement, but shows it increases with time. One of the models corresponds to a conventional `Filippov' description of a nonsmooth system, while the second exhibits a structure that irreversibly ages, developing a number of novel multi-scale behaviours that we believe have not been reported before. These include slow-fast staircases, novel mixed-mode oscillations, and a synchronized canard explosion. These features are proven to exist using asymptotic analysis, but as they involve a slow-fast time-scale separation that increases with time, they lie beyond the reach of numerical methods

Ageing of an oscillator due to frequency switching

If an oscillator is driven by a force that switches between two frequencies, the dynamics it exhibits depends on the precise manner of switching. Here we take a one-dimensional oscillator and consider scenarios in which switching occurs: (i) between two driving forces which have different frequencies, or (ii) as a single forcing whose frequency switches between two values. The difference is subtle, but entirely changes the long term behaviour, and concerns whether the switch can be expressed linearly or nonlinearly in terms of a discontinuous quantity (such as a sign or Heaviside step function that represents the switch between frequencies). In scenario (i) the oscillator has a stable periodic orbit, and the system can be described as a Filippov system. In scenario (ii) the oscillator exhibits hidden dynamics, which lies outside the theory of Filippov's systems, and causes the system to be increasingly (as time passes) dominated by sliding along the frequency-switching threshold, and in particular if periodic orbits do exist, they too exhibit sliding. We show that the behaviour persists, at least asymptotically, if the systems are regularized (i.e. if the switch is modelled as a smooth transition in the manner of (i) or (ii))

Polynomial Interrupt Timed Automata

Interrupt Timed Automata (ITA) form a subclass of stopwatch automata where reachability and some variants of timed model checking are decidable even in presence of parameters. They are well suited to model and analyze real-time operating systems. Here we extend ITA with polynomial guards and updates, leading to the class of polynomial ITA (PolITA). We prove the decidability of the reachability and model checking of a timed version of CTL by an adaptation of the cylindrical decomposition method for the first-order theory of reals. Compared to previous approaches, our procedure handles parameters and clocks in a unified way. Moreover, we show that PolITA are incomparable with stopwatch automata. Finally additional features are introduced while preserving decidability

Program transformations using temporal logic side conditions

This paper describes an approach to program optimisation based on transformations, where temporal logic is used to specify side conditions, and strategies are created which expand the repertoire of transformations and provide a suitable level of abstraction. We demonstrate the power of this approach by developing a set of optimisations using our transformation language and showing how the transformations can be converted into a form which makes it easier to apply them, while maintaining trust in the resulting optimising steps. The approach is illustrated through a transformational case study where we apply several optimisations to a small program

Control adaptativo por modelo de referencia para un inversor basado en LCL con síntesis de controlador mínima

[Resumen] Un Control Adaptativo por Modelo de Referencia (MRAC) con Síntesis de Controlador Mínima (MCS), es desarrollado con el objetivo de controlar un Inversor monofásico basado en un Filtro LCL conectado a la Red Eléctrica y adaptar el inductor de la red, que es un parámetro desconocido y que genera incertidumbre, manteniendo las prestaciones y la robustez del sistema. Para ello primero se revisara el algoritmo de MCS y en función de este, se muestran todos los pasos a seguir y el desarrollo de los componentes necesarios para el funcionamiento de MCS en tiempo continuo. Se desarrolla un modelo de simulación promediado y se presentan los resultados obtenidos.Este trabajo ha sido realizado gracias al apoyo de la Secretaría Nacional de Educación Superior, Ciencia y Tecnología e Innovación del Ecuador (SENESCYT), a la Universidad de Cuenca, y a los proyectos DPI2013-41224-P y DPI2015-69286-C3-2-R (MINECO/FEDER) y 2014 SGR 267 de la agencia AGAUR de la Generalitat de CatalunyaGeneralitat de Catalunya; 2014 SGR 267https://doi.org/10.17979/spudc.978849749808

Characterising Probabilistic Processes Logically

In this paper we work on (bi)simulation semantics of processes that exhibit both nondeterministic and probabilistic behaviour. We propose a probabilistic extension of the modal mu-calculus and show how to derive characteristic formulae for various simulation-like preorders over finite-state processes without divergence. In addition, we show that even without the fixpoint operators this probabilistic mu-calculus can be used to characterise these behavioural relations in the sense that two states are equivalent if and only if they satisfy the same set of formulae.Comment: 18 page

The role of ethanol oxidation during carboxydotrophic growth of clostridium autoethanogenum

The WoodLjungdahl pathway is an ancient metabolic route used by acetogenic carboxydotrophs to convert CO into acetate, and some cases ethanol. When produced, ethanol is generally seen as an end product of acetogenic metabolism, but here we show that it acts as an important intermediate and co-substrate during carboxydotrophic growth of Clostridium autoethanogenum. Depending on CO availability, C. autoethanogenum is able to rapidly switch between ethanol production and utilization, hereby optimizing its carboxydotrophic growth. The importance of the aldehyde ferredoxin:oxidoreductase (AOR) route for ethanol production in carboxydotrophic acetogens is known; however, the role of the bifunctional alcohol dehydrogenase AdhE (AldAdh) route in ethanol metabolism remains largely unclear. We show that the mutant strain C. autoethanogenum adhE1a, lacking the Ald subunit of the main bifunctional aldehyde/alcohol dehydrogenase (AdhE, CAETHG\_3747), has poor ethanol oxidation capabilities, with a negative impact on biomass yield. This indicates that the AdhAld route plays a major role in ethanol oxidation during carboxydotrophic growth, enabling subsequent energy conservation via substrate-level phosphorylation using acetate kinase. Subsequent chemostat experiments with C. autoethanogenum show that the wild type, in contrast to adhE1a, is more resilient to sudden changes in CO supply and utilizes ethanol as a temporary storage for reduction equivalents and energy during CO-abundant conditions, reserving these stored assets for more CO-limited conditions. This shows that the direction of the ethanol metabolism is very dynamic during carboxydotrophic acetogenesis and opens new insights in the central metabolism of C. autoethanogenum and similar acetogens.info:eu-repo/semantics/publishedVersio