High-feedback Operation of Power Electronic Converters

electronic

Integrate and Fire Neural Networks, Piecewise Contractive Maps and Limit Cycles

We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the stable asymptotic dynamics consists of limit cycles. We also find sufficient conditions for the synchronization of networks containing excitatory neurons. The proofs are based on the analysis of the equivalent dynamics of a piecewise continuous Poincar\'e map associated to the system. We show that for strong interactions the Poincar\'e map is piecewise contractive. Using this contraction property, we prove that there exist a countable number of limit cycles attracting all the orbits dropping into the stable subset of the phase space. This result applies not only to the Poincar\'e map under study, but also to a wide class of general n-dimensional piecewise contractive maps.Comment: 46 pages. In this version we added many comments suggested by the referees all along the paper, we changed the introduction and the section containing the conclusions. The final version will appear in Journal of Mathematical Biology of SPRINGER and will be available at http://www.springerlink.com/content/0303-681

Adomian decomposition method, nonlinear equations and spectral solutions of burgers equation

Tese de doutoramento. Ciências da Engenharia. 2006. Faculdade de Engenharia. Universidade do Porto, Instituto Superior Técnico. Universidade Técnica de Lisbo

Data Driven Techniques for Modeling Coupled Dynamics in Transient Processes

We study the problem of modeling coupled dynamics in transient processes that happen in a network. The problem is considered at two levels. At the node level, the coupling between underlying sub-processes of a node in a network is considered. At the network level, the direct influence among the nodes is considered. After the model is constructed, we develop a network-based approach for change detection in high dimension transient processes. The overall contribution of our work is a more accurate model to describe the underlying transient dynamics either for each individual node or for the whole network and a new statistic for change detection in multi-dimensional time series. Specifically, at the node level, we developed a model to represent the coupled dynamics between the two processes. We provide closed form formulas on the conditions for the existence of periodic trajectory and the stability of solutions. Numerical studies suggest that our model can capture the nonlinear characteristics of empirical data while reducing computation time by about 25% on average, compared to a benchmark modeling approach. In the last two problems, we provide a closed form formula for the bound in the sparse regression formulation, which helps to reduce the effort of trial and error to find an appropriate bound. Compared to other benchmark methods in inferring network structure from time series, our method reduces inference error by up to 5 orders of magnitudes and maintain better sparsity. We also develop a new method to infer dynamic network structure from a single time series. This method is the basis for introducing a new spectral graph statistic for change detection. This statistic can detect changes in simulation scenario with modified area under curve (mAUC) of 0.96. When applying to the problem of detecting seizure from EEG signal, our statistic can capture the physiology of the process while maintaining a detection rate of 40% by itself. Therefore, it can serve as an effective feature to detect change and can be added to the current set of features for detecting seizures from EEG signal

Dynamical systems techniques in the analysis of neural systems

As we strive to understand the mechanisms underlying neural computation, mathematical models are increasingly being used as a counterpart to biological experimentation. Alongside building such models, there is a need for mathematical techniques to be developed to examine the often complex behaviour that can arise from even the simplest models. There are now a plethora of mathematical models to describe activity at the single neuron level, ranging from one-dimensional, phenomenological ones, to complex biophysical models with large numbers of state variables. Network models present even more of a challenge, as rich patterns of behaviour can arise due to the coupling alone. We first analyse a planar integrate-and-fire model in a piecewise-linear regime. We advocate using piecewise-linear models as caricatures of nonlinear models, owing to the fact that explicit solutions can be found in the former. Through the use of explicit solutions that are available to us, we categorise the model in terms of its bifurcation structure, noting that the non-smooth dynamics involving the reset mechanism give rise to mathematically interesting behaviour. We highlight the pitfalls in using techniques for smooth dynamical systems in the study of non-smooth models, and show how these can be overcome using non-smooth analysis. Following this, we shift our focus onto the use of phase reduction techniques in the analysis of neural oscillators. We begin by presenting concrete examples showcasing where these techniques fail to capture dynamics of the full system for both deterministic and stochastic forcing. To overcome these failures, we derive new coordinate systems which include some notion of distance from the underlying limit cycle. With these coordinates, we are able to capture the effect of phase space structures away from the limit cycle, and we go on to show how they can be used to explain complex behaviour in typical oscillatory neuron models

Emergent coordination between humans and robots

Emergent coordination or movement synchronization is an often observed phenomenon in human behavior. Humans synchronize their gait when walking next to each other, they synchronize their postural sway when standing closely, and they also synchronize their movement behavior in many other situations of daily life. Why humans are doing this is an important question of ongoing research in many disciplines: apparently movement synchronization plays a role in children’s development and learning; it is related to our social and emotional behavior in interaction with others; it is an underlying principle in the organization of communication by means of language and gesture; and finally, models explaining movement synchronization between two individuals can also be extended to group behavior. Overall, one can say that movement synchronization is an important principle of human interaction behavior. Besides interacting with other humans, in recent years humans do more and more interact with technology. This was first expressed in the interaction with machines in industrial settings, was taken further to human-computer interaction and is now facing a new challenge: the interaction with active and autonomous machines, the interaction with robots. If the vision of today’s robot developers comes true, in the near future robots will be fully integrated not only in our workplace, but also in our private lives. They are supposed to support humans in activities of daily living and even care for them. These circumstances however require the development of interactional principles which the robot can apply to the direct interaction with humans. In this dissertation the problem of robots entering the human society will be outlined and the need for the exploration of human interaction principles that are transferable to human-robot interaction will be emphasized. Furthermore, an overview on human movement synchronization as a very important phenomenon in human interaction will be given, ranging from neural correlates to social behavior. The argument of this dissertation is that human movement synchronization is a simple but striking human interaction principle that can be applied in human-robot interaction to support human activity of daily living, demonstrated on the example of pick-and-place tasks. This argument is based on five publications. In the first publication, human movement synchronization is explored in goal-directed tasks which bare similar requirements as pick-and-place tasks in activities of daily living. In order to explore if a merely repetitive action of the robot is sufficient to encourage human movement synchronization, the second publication reports a human-robot interaction study in which a human interacts with a non-adaptive robot. Here however, movement synchronization between human and robot does not emerge, which underlines the need for adaptive mechanisms. Therefore, in the third publication, human adaptive behavior in goal-directed movement synchronization is explored. In order to make the findings from the previous studies applicable to human-robot interaction, in the fourth publication the development of an interaction model based on dynamical systems theory is outlined which is ready for implementation on a robotic platform. Following this, a brief overview on a first human-robot interaction study based on the developed interaction model is provided. The last publication describes an extension of the previous approach which also includes the human tendency to make use of events to adapt their movements to. Here, also a first human-robot interaction study is reported which confirms the applicability of the model. The dissertation concludes with a discussion on the presented findings in the light of human-robot interaction and psychological aspects of joint action research as well as the problem of mutual adaptation.Spontan auftretende Koordination oder Bewegungssynchronisierung ist ein häufig zu beobachtendes Phänomen im Verhalten von Menschen. Menschen synchronisieren ihre Schritte beim nebeneinander hergehen, sie synchronisieren die Schwingbewegung zum Ausgleich der Körperbalance wenn sie nahe beieinander stehen und sie synchronisieren ihr Bewegungsverhalten generell in vielen weiteren Handlungen des täglichen Lebens. Die Frage nach dem warum ist eine Frage mit der sich die Forschung in der Psychologie, Neuro- und Bewegungswissenschaft aber auch in der Sozialwissenschaft nach wie vor beschäftigt: offenbar spielt die Bewegungssynchronisierung eine Rolle in der kindlichen Entwicklung und beim Erlernen von Fähigkeiten und Verhaltensmustern; sie steht in direktem Bezug zu unserem sozialen Verhalten und unserer emotionalen Wahrnehmung in der Interaktion mit Anderen; sie ist ein grundlegendes Prinzip in der Organisation von Kommunikation durch Sprache oder Gesten; außerdem können Modelle, die Bewegungssynchronisierung zwischen zwei Individuen erklären, auch auf das Verhalten innerhalb von Gruppen ausgedehnt werden. Insgesamt kann man also sagen, dass Bewegungssynchronisierung ein wichtiges Prinzip im menschlichen Interaktionsverhalten darstellt. Neben der Interaktion mit anderen Menschen interagieren wir in den letzten Jahren auch zunehmend mit der uns umgebenden Technik. Hier fand zunächst die Interaktion mit Maschinen im industriellen Umfeld Beachtung, später die Mensch-Computer-Interaktion. Seit kurzem sind wir jedoch mit einer neuen Herausforderung konfrontiert: der Interaktion mit aktiven und autonomen Maschinen, Maschinen die sich bewegen und aktiv mit Menschen interagieren, mit Robotern. Sollte die Vision der heutigen Roboterentwickler Wirklichkeit werde, so werden Roboter in der nahen Zukunft nicht nur voll in unser Arbeitsumfeld integriert sein, sondern auch in unser privates Leben. Roboter sollen den Menschen in ihren täglichen Aktivitäten unterstützen und sich sogar um sie kümmern. Diese Umstände erfordern die Entwicklung von neuen Interaktionsprinzipien, welche Roboter in der direkten Koordination mit dem Menschen anwenden können. In dieser Dissertation wird zunächst das Problem umrissen, welches sich daraus ergibt, dass Roboter zunehmend Einzug in die menschliche Gesellschaft finden. Außerdem wird die Notwendigkeit der Untersuchung menschlicher Interaktionsprinzipien, die auf die Mensch-Roboter-Interaktion transferierbar sind, hervorgehoben. Die Argumentation der Dissertation ist, dass die menschliche Bewegungssynchronisierung ein einfaches aber bemerkenswertes menschliches Interaktionsprinzip ist, welches in der Mensch-Roboter-Interaktion angewendet werden kann um menschliche Aktivitäten des täglichen Lebens, z.B. Aufnahme-und-Ablege-Aufgaben (pick-and-place tasks), zu unterstützen. Diese Argumentation wird auf fünf Publikationen gestützt. In der ersten Publikation wird die menschliche Bewegungssynchronisierung in einer zielgerichteten Aufgabe untersucht, welche die gleichen Anforderungen erfüllt wie die Aufnahme- und Ablageaufgaben des täglichen Lebens. Um zu untersuchen ob eine rein repetitive Bewegung des Roboters ausreichend ist um den Menschen zur Etablierung von Bewegungssynchronisierung zu ermutigen, wird in der zweiten Publikation eine Mensch-Roboter-Interaktionsstudie vorgestellt in welcher ein Mensch mit einem nicht-adaptiven Roboter interagiert. In dieser Studie wird jedoch keine Bewegungssynchronisierung zwischen Mensch und Roboter etabliert, was die Notwendigkeit von adaptiven Mechanismen unterstreicht. Daher wird in der dritten Publikation menschliches Adaptationsverhalten in der Bewegungssynchronisierung in zielgerichteten Aufgaben untersucht. Um die so gefundenen Mechanismen für die Mensch-Roboter Interaktion nutzbar zu machen, wird in der vierten Publikation die Entwicklung eines Interaktionsmodells basierend auf Dynamischer Systemtheorie behandelt. Dieses Modell kann direkt in eine Roboterplattform implementiert werden. Anschließend wird kurz auf eine erste Studie zur Mensch- Roboter Interaktion basierend auf dem entwickelten Modell eingegangen. Die letzte Publikation beschreibt eine Weiterentwicklung des bisherigen Vorgehens welche der Tendenz im menschlichen Verhalten Rechnung trägt, die Bewegungen an Ereignissen auszurichten. Hier wird außerdem eine erste Mensch-Roboter- Interaktionsstudie vorgestellt, die die Anwendbarkeit des Modells bestätigt. Die Dissertation wird mit einer Diskussion der präsentierten Ergebnisse im Kontext der Mensch-Roboter-Interaktion und psychologischer Aspekte der Interaktionsforschung sowie der Problematik von beiderseitiger Adaptivität abgeschlossen