Synchronization with partial state coupling on SO(n)

This paper studies autonomous synchronization of k agents whose states evolve on SO(n), but which are only coupled through the action of their states on one "reference vector" in Rn for each link. Thus each link conveys only partial state information at each time, and to reach synchronization agents must combine this information over time or throughout the network. A natural gradient coupling law for synchronization is proposed. Extensive convergence analysis of the coupled agents is provided, both for fixed and time-varying reference vectors. The case of SO(3) with fixed reference vectors is discussed in more detail. For comparison, we also treat the equivalent setting in Rn, i.e. with states in Rn and connected agents comparing scalar product of their states with a reference vector.Comment: to be submitted to SIAM Journal on Control and Optimizatio

Decompounding on compact Lie groups

Noncommutative harmonic analysis is used to solve a nonparametric estimation problem stated in terms of compound Poisson processes on compact Lie groups. This problem of decompounding is a generalization of a similar classical problem. The proposed solution is based on a char- acteristic function method. The treated problem is important to recent models of the physical inverse problem of multiple scattering.Comment: 26 pages, 3 figures, 25 reference

Training Neurodegenerative Disease Support Group Leaders: A New Support Group Functioning Scale

Support group leaders play pivotal roles in maintaining healthy community support groups; however, these leaders also have personal support needs and typically lack formal training in managing complex behaviors of neurodegenerative disorders. A support group well-being questionnaire, assessing support group functioning, was developed and piloted among participants of an educational training program designed for support group leaders of various neurodegenerative disorder-specific support groups. An exploratory factor analysis evaluated the questionnaire’s psychometric properties and identified a reliable single factor five-item solution, which was titled the Support Group Functioning Scale (SGFS). Preliminary interpretation guidelines were proposed. Development of this scale is a first step in identifying support group leaders’ needs as they provide frontline assistance to caregivers and individuals with neurodegenerative illnesses. This tool shows promise as an efficient way to identify support groups in need of assistance and to assess the impact of trainings on support group functioning. Further validation of the scale is needed

Strukturpolitik im Wandel: Die Suche nach der richtigen Balance zwischen Wachstum und Ausgleich

Die EU-Strukturfondsförderung ist mit Finanzmitteln von rund 2 Mrd. Euro in den Jahren 2000 bis 2006 ein tragender Baustein der Strukturpolitik in Nordrhein-Westfalen gewesen. Dies wird aller Voraussicht nach auch so bleiben, denn die für die künftige Förderperiode 2007 bis 2012 vorgesehenen Mittel sind in ähnlicher Höhe angesetzt. Vor diesem Hintergrund erscheint die Hitzigkeit der aktuell in NRW geführten Debatte zur Strukturpolitik recht überraschend. Bei näherem Hinsehen entpuppt sich diese Kontroverse jedoch als ein grundsätzliches Ringen um die künftige Ausrichtung staatlicher Förderpolitik im größten deutschen Bundesland. Insbesondere geht es darum, ob auch in Zukunft die EU-gestützte Förderung mehr im politischen Verteilungskampf als durch Projektqualität erobert werden soll und kann. Dieser Beitrag diskutiert aus regionalökonomischer Sicht die drei zentralen Aspekte dieser Debatte, (i) die Frage der Ausgestaltung der Förderinstrumente, (ii) die Frage der Wirkungen strukturpolitischer Fördermaßnahmen und (iii) die sicherlich am heftigsten diskutierte Frage Ruhrgebiet und Cluster-Förderung. Insbesondere betonen wir die Erkenntnisprobleme, die eine nüchterne empirische Analyse der Strukturförderung erschweren und ziehen vor diesem Hintergrund ein vorsichtiges Fazit. Es ist unserer Ansicht nach sehr zu begrüßen, dass im Zuge der Lissabon-Strategie der EU wettbewerbliche Elemente bei der Vergabe der Fördermittel mehr Gewicht erhalten sollen als in der Vergangenheit. Um diese Förderphilosophie allerdings tatsächlich in mehr Wachstum vor allem für das Ruhrgebiet umzusetzen, muss sie mit ebenso viel Konsequenz wie Fingerspitzengefühl umgesetzt werden

Observers for invariant systems on Lie groups with biased input measurements and homogeneous outputs

This paper provides a new observer design methodology for invariant systems whose state evolves on a Lie group with outputs in a collection of related homogeneous spaces and where the measurement of system input is corrupted by an unknown constant bias. The key contribution of the paper is to study the combined state and input bias estimation problem in the general setting of Lie groups, a question for which only case studies of specific Lie groups are currently available. We show that any candidate observer (with the same state space dimension as the observed system) results in non-autonomous error dynamics, except in the trivial case where the Lie-group is Abelian. This precludes the application of the standard non-linear observer design methodologies available in the literature and leads us to propose a new design methodology based on employing invariant cost functions and general gain mappings. We provide a rigorous and general stability analysis for the case where the underlying Lie group allows a faithful matrix representation. We demonstrate our theory in the example of rigid body pose estimation and show that the proposed approach unifies two competing pose observers published in prior literature.Comment: 11 page

Synchronization with partial state feedback on SO(n),

peer reviewedThis paper considers the problem of constructing a distributed feedback law to achieve synchronization for a group of k agents whose states evolve on SO(n) and which exchange only partial state information along communication links. The partial state information is given by the action of the state on reference vectors in Rn. We propose a gradient based control law which achieves exponential local convergence to a synchronization configuration under a rank condition on a generalized Laplacian matrix. Furthermore, we discuss the case of time-varying reference vectors and provide a convergence result for this case. The latter helps reach synchronization, requiring less communication links and weaker conditions on the instantaneous reference vectors. Our methods are illustrated on an attitude synchronization problem where agents exchange only their relative positions observed in the respective body frames