435 research outputs found
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Control Theory: Mathematical Perspectives on Complex Networked Systems
Control theory is an interdisciplinary field that is located at the crossroads of pure and applied mathematics with systems engineering and the sciences. Its range of applicability and its techniques evolve rapidly with new developments in communication systems and electronic data processing. Thus, in recent years networked control systems emerged as a new fundamental topic, which combines complex communication structures with classical control methods and requires new mathematical methods. A substantial number of contributions to this workshop was devoted to the control of networks of systems. This was complemented by a series of lectures on other current topics like fundamentals of nonlinear control systems, model reduction and identification, algorithmic aspects in control, as well as open problems in control
Curvature and the equivalence problem in sub-Riemannian geometry
summary:These notes give an introduction to the equivalence problem of sub-Riemannian manifolds. We first introduce preliminaries in terms of connections, frame bundles and sub-Riemannian geometry. Then we arrive to the main aim of these notes, which is to give the description of the canonical grading and connection existing on sub-Riemann manifolds with constant symbol. These structures are exactly what is needed in order to determine if two manifolds are isometric. We give three concrete examples, which are Engel (2,3,4)-manifolds, contact manifolds and Cartan (2,3,5)-manifolds. These notes are an edited version of a lecture series given at the 42nd Winter school: Geometry and Physics, SrnĂ, Czech Republic, mostly based on [8] and other earlier work. However, the work on Engel (2,3,4)-manifolds is original research, and illustrate the important special case were our model has the minimal set of isometries
Inverse dynamics of underactuated flexible mechanical systems governed by quasi-linear hyperbolic partial differential equations
Diese Arbeit befasst sich mit der inversen Dynamik unteraktuierter, flexibler, mechanischer Systeme, welche durch quasi-lineare hyperbolische partielle Differentialgleichungen beschrieben werden können. Diese Gleichungnen, sind zeitlich verĂ€nderlichen Dirichlet-Randbedingungen unterworfen, welche durch unbekannte, rĂ€umlich disjunkte, also nicht kollokierte Neumann-Randbedingungen erzwungen werden. Die zugrundeliegenden Gleichungen werden zunĂ€chst abstrakt hergeleitet, bevor verschiedene mechanische Systeme vorgestellt werden können, die mit der eingangs postulierten Formulierung ĂŒbereinstimmen. Hierzu werden geometrisch exakte Theorien hergeleitet, welche in der Lage sind groĂe Bewegungen schlanker Strukturen wie Seile und Balken, aber auch ganz allgemein, dreidimensionaler Festkörper zu beschreiben.
In der Regel werden Anfangs-Randwertprobleme, die in der nichtlinearen Strukturdynamik auftreten, durch Anwendung einer sequentiellen Diskretisierung in Raum und Zeit gelöst. Diese Verfahren basieren fĂŒr gewöhnlich auf einer rĂ€umlichen Diskretisierung mit finiten Elementen, gefolgt von einer geeigneten zeitlichen Diskretisierung, welche meist auf finiten Differenzen beruht. Ein kurzer Ăberblick ĂŒber derartige sequentielle Integrationsverfahren fĂŒr das vorliegende Anfangs-Randwertproblem wird zunĂ€chst anhand der direkten Formulierung des Problems gegeben werden. D.h. es wird zunĂ€chst das reine Neumann-Randproblem betrachtet, bevor anschlieĂend ganz allgemein, verschiedene Möglichkeiten zur Einbindung etwaiger Dirichlet-Randbedingungen diskutiert werden. Darauf aufbauend wird das Problem der inversen Dynamik im Kontext rĂ€umlich diskreter mechanischer Systeme, welche rheonom-holonomen Servo-Bindungen unterliegen, eingefĂŒhrt. Eine ausfĂŒhrliche Untersuchung dieser Art von gebundenen Systemen soll die grundlegenden Unterschiede zwischen Servo-Bindungen und klassischen Kontakt-Bindungen herausarbeiten. Die daraus resultierenden Folgen fĂŒr die Entwicklung geeigneter numerisch stabiler Integrationsverfahren können dabei ebenfalls angesprochen werden, bevor zahlreich ausgewĂ€hlte Beispiele vorgestellt werden können.
Aufgrund der sehr eingeschrĂ€nkten Anwendbarkeit der sequentiellen Lösung der inversen Dynamik in Raum und Zeit, wird eine eingehende Analyse des vorliegenden Anfangs-Randwertproblems unternommen. Vor allem durch die Freilegung der hyperbolischen Struktur der zugrundeliegenden partiellen Differentialgleichungen werden sich weitere Einblicke in das vorliegende Problem erhofft. Die Erforschung der daraus resultierenden Mechanismen der Wellenausbreitung in kontinuierlichen Strukturen öffnet die TĂŒr zur Entwicklung numerisch stabiler Integrationsverfahren fĂŒr die inverse Dynamik. So kann unter anderem eine Methode vorgestellt werden, die auf der Integration der partiellen Differentialgleichungen entlang charakteristischer Mannigfaltigkeiten beruht. Dies regt zu der Entwicklung neuartiger Galerkinverfahren an, die ebenfalls in dieser Arbeit vorgestellt werden können.
Diese neu entwickelten Methoden können anschlie\ss end auf die Steuerung verschiedener mechanischer Systeme angewendet werden. DarĂŒber hinaus können die neuartigen Integrationsverfahren auch auf flexible Mehrkörpersysteme ĂŒbertragen werden. AngefĂŒhrt seien hier beispielsweise die kooperative Steuerung eines an mehreren flexiblen Seilen aufgehĂ€ngten starren Körpers oder die Steuerung des Endeffektors eines flexiblen mehrgliedrigen Schwenkarms.
AusgewÀhlte numerische Beispiele verdeutlichen die Relevanz der hier vorgeschlagenen, in Raum und Zeit simultanen Integration des vorliegenden Anfangs-Randwertproblems
Complete spelling rules for the Monster tower over three-space
The Monster tower, also known as the Semple tower, is a sequence of manifolds
with distributions of interest to both differential and algebraic geometers.
Each manifold is a projective bundle over the previous. Moreover, each level is
a fiber compactified jet bundle equipped with an action of finite jets of the
diffeomorphism group. There is a correspondence between points in the tower and
curves in the base manifold. These points admit a stratification which can be
encoded by a word called the RVT code. Here, we derive the spelling rules for
these words in the case of a three dimensional base. That is, we determine
precisely which words are realized by points in the tower. To this end, we
study the incidence relations between certain subtowers, called Baby Monsters,
and present a general method for determining the level at which each Baby
Monster is born. Here, we focus on the case where the base manifold is three
dimensional, but all the methods presented generalize to bases of arbitrary
dimension.Comment: 14 pages, 4 figures; new titl
Infinite-Dimensional Modelling and Control of a MEMS Deformable Mirror with Applications in Adaptive Optics
RĂSUMĂ Le contrĂŽle de dĂ©formation est un problĂšme Ă©mergent dans les micro structures intelligentes.
Une des applications type est le contrĂŽle de la dĂ©formation de miroirs dans lâoptique adaptative dans laquelle on oriente la face du miroir selon une gĂ©omĂ©trie prĂ©cise en utilisant une gamme de micro-vĂ©rins afin dâĂ©liminer la distortion lumineuse. Dans cette thĂšse, le
problĂšme de la conception du contrĂŽle du suivi est considĂ©rĂ© directement avec les modĂšles dĂ©crits par des Ă©quations aux dĂ©rivĂ©es partielles dĂ©finies dans lâespace de dimension infinie. Lâarchitecture du contrĂŽleur proposĂ©e se base sur la stabilisation par retour des variables et le suivi des trajectoires utilisant la thĂ©orie des systĂšmes diffĂ©rentiellement plats. La combinaison de la commande par rĂ©troaction et la planification des trajectoires permet de rĂ©duire
la complexitĂ© de la structure du contrĂŽleur pour que ce dernier puisse ĂȘtre implĂ©mentĂ©e dans les microsystĂšmes avec les techniques disponibles de nos jours. Pour aboutir Ă une architecture implĂ©mentable dans les applications en temps rĂ©el, la fonction de Green est considĂ©rĂ©e comme une fonction de test pour concevoir le contrĂŽleur et pour reprĂ©senter les trajectoires
de référence dans la planification de mouvements.----------ABSTRACT Deformation control is an emerging problem for micro-smart structures. One of its exciting applications is the control of deformable mirrors in adaptive optics systems, in which the mirror face-sheet is steered to a desired shape using an array of micro-actuators in order to remove light distortions. This technology is an enabling key for the forthcoming extremely large ground-based telescopes. Large-scale deformable mirrors typically exhibit complex dynamical behaviors mostly due to micro-actuators distributed in the domain of the system which in particular complicates control design.
A model of this device may be described by a fourth-order in space/second-order in time partial differential equation for the mirror face-sheet with Dirac delta functions located in the domain of the system to represent the micro-actuators. Most of control design methods dealing with partial differential equations are performed on lumped models, which often leads to high-dimensional and complex feedback control structures. Furthermore, control designs achieved based on partial differential equation models correspond to boundary control problems. In this thesis, a tracking control scheme is designed directly based on the infinite-dimensional model of the system. The control scheme is introduced based on establishing a relationship
between the original nonhomogeneous model and a target system in a standard boundary control form. Thereby, the existing boundary control methods may be applicable. For the control design, we apply the tool of differential flatness to a partial differential equation system
controlled by multiple actuators, which is essentially a multiple-input multiple-output partial differential equation problem. To avoid early lumping in the motion planning, we use the properties of the Greenâs function of the system to represent the reference trajectories.
A finite set of these functions is considered to establish a one-to-one map between the input
space and output space. This allows an implementable scheme for real-time applications. Since pure feedforward control is only applicable for perfectly known, and stable systems, feedback control is required to account for instability, model uncertainties, and disturbances.
Hence, a stabilizing feedback is designed to stabilize the system around the reference trajectories.
The combination of differential flatness for motion planning and stabilizing feedback provides a systematic control scheme suitable for the real-time applications of large-scale deformable mirrors
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On-Chip Micro Temperature Controllers Based on Freestanding Thermoelectric Nano Films for Low-Power Electronics
Dense and flat freestanding Bi2Te3-based thermoelectric nano films were successfully fabricated by sputtering technology using a newly developed nano graphene oxide membrane as a substrate. On-chip micro temperature controllers were integrated using conventional micro-electromechanical system technology, to achieve energy-efficient temperature control for low-power electronics. The tunable equivalent thermal resistance enables an ultrahigh temperature control capability of 100 K mWâ1 and an ultra-fast cooling rate exceeding 2000 K sâ1, as well as excellent reliability of up to 1 million cycles
Critical Behavior in Doping-Driven MetalInsulator Transition on Single-Crystalline Organic Mott-FET
We present the carrier transport properties in the vicinity of a
doping-driven Mott transition observed at a field-effect transistor (FET)
channel using a single crystal of the typical two-dimensional organic Mott
insulator -(BEDT-TTF)CuN(CN)Cl (-Cl).The FET shows a
continuous metalinsulator transition (MIT) as electrostatic doping proceeds.
The phase transition appears to involve two-step crossovers, one in Hall
measurement and the other in conductivity measurement. The crossover in
conductivity occurs around the conductance quantum , and hence is not
associated with "bad metal" behavior, which is in stark contrast to the MIT in
half-filled organic Mott insulators or that in doped inorganic Mott insulators.
Through in-depth scaling analysis of the conductivity, it is found that the
above carrier transport properties in the vicinity of the MIT can be described
by a high-temperature Mott quantum critical crossover, which is theoretically
argued to be a ubiquitous feature of various types of Mott transitions. [This
document is the unedited Authors' version of a Submitted Work that was
subsequently accepted for publication in Nano Letters, copyright \copyright
American Chemical Society after peer review. To access the final edited and
published work see http://dx.doi.org/10.1021/acs.nanolett.6b03817]Comment: 40 pages, 16 figures in Nano Letters, ASAP (2017
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