Towards a minimal order distributed observer for linear systems

In this paper we consider the distributed estimation problem for continuous-time linear time-invariant (LTI) systems. A single linear plant is observed by a network of local observers. Each local observer in the network has access to only part of the output of the observed system, but can also receive information on the state estimates of its neigbours. Each local observer should in this way generate an estimate of the plant state. In this paper we study the problem of existence of a reduced order distributed observer. We show that if the observed system is observable and the network graph is a strongly connected directed graph, then a distributed observer exists with state space dimension equal to $Nn - \sum_{i =1}^N p_i$, where $N$ is the number of network nodes, $n$ is the state space dimension of the observed plant, and $p_i$ is the rank of the output matrix of the observed output received by the $i$th local observer. In the case of a single observer, this result specializes to the well-known minimal order observer in classical observer design.Comment: 12 pages, 1 figur

Priming effects on labile and stable soil organic carbon decomposition: Pulse dynamics over two years.

Soil organic carbon (SOC) is a major component in the global carbon cycle. Yet how input of plant litter may influence the loss of SOC through a phenomenon called priming effect remains highly uncertain. Most published results about the priming effect came from short-term investigations for a few weeks or at the most for a few months in duration. The priming effect has not been studied at the annual time scale. In this study for 815 days, we investigated the priming effect of added maize leaves on SOC decomposition of two soil types and two treatments (bare fallow for 23 years, and adjacent old-field, represent stable and relatively labile SOC, respectively) of SOC stabilities within each soil type, using a natural 13C-isotope method. Results showed that the variation of the priming effect through time had three distinctive phases for all soils: (1) a strong negative priming phase during the first period (≈0-90 days); (2) a pulse of positive priming phase in the middle (≈70-160 and 140-350 days for soils from Hailun and Shenyang stations, respectively); and (3) a relatively stabilized phase of priming during the last stage of the incubation (>160 days and >350 days for soils from Hailun and Shenyang stations, respectively). Because of major differences in soil properties, the two soil types produced different cumulative priming effects at the end of the experiment, a positive priming effect of 3-7% for the Mollisol and a negative priming effect of 4-8% for the Alfisol. Although soil types and measurement times modulated most of the variability of the priming effect, relative SOC stabilities also influenced the priming effect for a particular soil type and at a particular dynamic phase. The stable SOC from the bare fallow treatment tended to produce a narrower variability during the first phase of negative priming and also during the second phase of positive priming. Averaged over the entire experiment, the stable SOC (i.e., the bare fallow) was at least as responsive to priming as the relatively labile SOC (i.e., the old-field) if not more responsive. The annual time scale of our experiment allowed us to demonstrate the three distinctive phases of the priming effect. Our results highlight the importance of studying the priming effect by investigating the temporal dynamics over longer time scales

Distributed H_/L∞ fault detection observer design for linear systems:Proceedings

This paper studies the distributed fault detection problem for linear time-invariant (LTI) systems with distributed measurement output. A distributed H_/L∞ fault detection observer (DFDO) design method is proposed to detect actuator faults of the monitored system in the presence of a bounded process disturbances. The DFDO consists of a network of local fault detection observers, which communicate with their neighbors as prescribed by a given network graph. By using finite-frequency H_ performance, the residual in fault detection is sensitive to fault in the interested frequency-domain. The residual is robust against effects of the external process disturbance by L∞ analysis. A systematic algorithm for DFDO design is addressed and the residual thresholds are calculated in our distributed fault detection scheme. Finally, we use a numerical simulation to demonstrate the effectiveness of the proposed distributed fault detection approach

Distributed fault estimation for linear systems with actuator faults

This article investigates the problem of designing a distributed fault estimation observer (DFEO) for a given linear time invariant observed system with disturbances. The DFEO consists of a network of local fault estimation observers. The local observers at the network nodes are physically distributed and hence each of them has access to only part of the output of the observed system. Each local fault estimation observer communicates with its neighbors as prescribed by the given network graph. Both full order and reduced order DFEO's are presented in this article. A systematic design procedure for DFEO gains is addressed, enabling the estimation error dynamics to be robust against the effects of the external process disturbance and the derivative of the fault. The numerical design of our DFEO is amounts to solving an optimization problem with constraints of a bank of linear matrix inequalities. Finally, we illustrate the effectiveness of the proposed distributed fault estimation approach by means of a number of simulation results

Mutationsanalyse des Pro-Opiomelanocortin-Gens bei extrem adipösen Kindern und Jugendlichen

Adipositas stellt in der heutigen Gesellschaft ein ernstzunehmendes gesundheitspolitisches Problem dar. Untersuchungen des ?National Center for Health Statistics? zwischen den Jahren 1960-94 zeigen, daß der Anteil an übergewichtigen Personen in den USA in diesem Zeitraum stetig zunahm. Neben einer erhöhten Nahrungsmittelverfügbarkeit und einer Abnahme der individuellen körperlichen Aktivität sind genetische Faktoren für die Entwicklung einer Adipositas verantwortlich. Adoptions- und Zwillingsstudien zeigen dies eindrucksvoll. Formalgenetische Studien belegen den genetischen Beitrag zur phänotypischen Varianz des Körpergewichts. Zudem brachten vor allem die verschiedenen Mausmodelle neue Erkenntnisse. Das Ende 1994 identifizierte Hormon Leptin, das von Fettzellen produziert wird, erhärtete die These einer hormonellen Rückkopplung und zentralen Steuerung der Gewichtsregulation. Auch beim Menschen konnten relevante Mutationen im Leptin-Gen bei einzelnen extrem adipösen Menschen identifiziert werden. Andere im ZNS produzierte Hormone interagieren mit diesem Regelkreis und sind somit höchstwahrscheinlich an der Gewichtsregulation mitbeteiligt. Der Melanocortin-4-Rezeptor spielt hierbei eine wichtige Rolle. Sowohl Tiermodelle als auch Studien am Menschen zeigen, daß spezifische Mutationen des MC4-Rezeptors mit Adipositas einhergehen. Das hier untersuchte Proopiomelanocortin-Gen (POMC) stellt die Matrize für den natürlichen Liganden des MC4-Rezeptors, das alpha-MSH, dar. Außer dem alpha-MSH werden die ebenfalls vor allem zentral exprimierten Hormone ACTH, beta-und gamma-Lipotropin, beta- und gamma-MSH, beta-Endorphin und das 16-K-Fragment vom POMC-Gen kodiert. Kopplungsanalysen dreier verschiedener Kohorten mit unterschiedlichen ethischen Ursprüngen zeigten eine Kopplung von Plasma-Leptin-Spiegeln und dem Bereich des Chromosoms 2p, in dem das POMC-Gen liegt. Krude et al. identifizierten 1998 bei zwei Kindern mit Pigmentierungsstörungen, ACTH-Mangel und extremer Adipositas Mutationen im POMC-Gen. Bezugnehmend auf diese Ergebnisse wurde in dieser Arbeit mit Hilfe molekulargenetischer Methoden (Polymerase-Chain-Reaktion, Single-Strand-Conformation-Analysis) ein Mutationsscreen des POMC-Gens an einer Gruppe 96 extrem adipöser Kinder und Jugendlicher durchgeführt. Es wurden acht verschiedene Varianten mittels Single-Strand-Conformation-Analysis gefunden und durch Sequenzierung identifiziert: Eine 9-Basenpaar-Insertion (AGC-AGC-GGC) sowie eine 18-Basenpaar-Insertion (AGC-AGC-GGC)2 zwischen Position 6997/6998 der Sequenz nach Takahashi im Bereich des 16-K-Fragments, eine 6-Basenpaar-Insertion (GGG-CCC) zwischen Position 7304/7305 der Sequenz nach Takahashi im für das gamma-Lipotropin kodierenden Bereich, zwei Punktvarianten (Guanin zu Thymin an Position 7316 und Adenin zu Guanin an Position 7341 der Sequenz nach Takahashi) im für das gamma-Lipotropin kodierenden Bereich, von denen eine zu einem Kettenabbruch führt (Nonsensemutation), und fünf Basenpaar-Austausche, bei denen sich die ursprüngliche Aminosäuresequenz nicht ändert. Assoziationsstudien zu diesen Varianten in einer Kontrollgruppe von 60 untergewichtigen Studenten waren negativ. Somit haben Varianten im POMC-Gen in der hier untersuchten Studiengruppe keinen generellen Einfluss auf den Phänotyp Adipositas