Graph rigidity-based formation control of planar multi-agent systems

A multi-agent system is a network of interacting agents that collectively perform a complex task. This dissertation is concerned with the decentralized formation control of multi-agent systems moving in the plane. The formation problem is defined as designing control inputs for the agents so that they form and maintain a pre-defined, planar geometric shape. The focus is on three related problems with increasing level of complexity: formation acquisition, formation maneuvering, and target interception. Three different dynamic models, also with increasing level of complexity, are considered for the motion of the agents: the single-integrator model, the double-integrator model, and the full mechanical dynamic model. Rigid graph theory and Lyapunov theory are the primary tools utilized in this work for solving the aforementioned formation problems for the three models. The backstepping control technique also plays a key role in the cases of the double-integrator and full dynamic models. Starting with the single-integrator model, a basic formation acquisition controller is proposed that is only a function of the relative position of agents in an infinitesimally and minimally rigid graph. A Lyapunov analysis shows that the origin of the inter-agent distance error system is exponentially stable. It is then shown how an extra term can be added to the controller to enable formation maneuvering or target interception. The three controllers for the single-integrator model are used as a stepping stone and extended to the double-integrator model with the aid of backstepping. Finally, an actuator-level, formation acquisition control law is developed for multiple robotic vehicles that accounts for the vehicle dynamics. Specifically, a class of underactuated vehicles modeled by Euler-Lagrange-like equations is considered. The backstepping technique is again employed while exploiting the structural properties of the system dynamics. Computer simulations are provided throughout the dissertation to show the proposed control laws in action

Novel therapeutic strategies for osteochondral repair ex vivo and in vivo

Adult articular cartilage, a highly specialized connective tissue, does not regenerate upon injury. Articular cartilage defects may further initiate the development of osteoarthritis (OA), a clinically and socioeconomically debilitating joint disorder. Gene transfer of growth and transcription factors is a therapeutic strategy to improve the repair of articular cartilage defects. Advanced biomaterial- guided delivery of gene carriers such as those based on the clinically adapted recombinant adeno-associated virus (rAAV) vector is an exceptionally attractive treatment protocol to improve cartilage repair via minimally invasive, controlled delivery of therapeutic genes in a spatiotemporally precise manner, reducing intra-articular vector spread and a possible loss of the therapeutic gene product. Here, a thermosensitive hydrogel based on poly(ethylene oxide) and poly(propylene oxide) was first used to release an rAAV vector coding for the chondrogenic sex-determining region Y- type high-mobility group box 9 (SOX9) transcription factor in clinically relevant, full-thickness chondral defects in minipigs to evaluate its potential beneficial effects on cartilage repair in vivo. Delivery of a therapeutic rAAV construct coding for the reparative insulin-like growth factor I (IGF-I) via an alginate (AlgPH155) hydrogel was also tested in similar minipig chondral defects to further evidence workable approaches to enhance cartilage repair in vivo. As an alternative to hydrogel systems, a focus was also given to rAAV-mediated delivery of the chondrogenic transforming growth factor beta (TGF-b) using solid poly(e-caprolactone) (PCL) films to test the ability of this system to trigger chondroreparative processes in human bone marrow aspirates ex vivo as future implantable platforms in cartilage defects. Effective release of the rAAV SOX9 and IGF-I vectors using thermosensitive or alginate hydrogels, respectively, improved cartilage repair for at least 4 weeks (SOX9) and one year (IGF- I), with a reduction of perifocal OA when using IGF-I over a longer period of time. Effective release of the rAAV TGF-b vector using PCL films (especially those grafted with poly(sodium styrene sulfonate) - pNaSS) activated the chondrogenic differentiation of human bone marrow aspirates for at least 3 weeks. These data support the concept of applying biomaterial-guided rAAV gene delivery as an off-the-shelf, minimally invasive option for cartilage repair in translational applications.Der adulte hyaline Gelenkknorpel, ein hochspezialisiertes Bindegewebe, regeneriert nicht nach einer Verletzung. Knorpeldefekte können zudem die Entstehung der klinisch und sozioökonomisch folgenschweren Arthrose einleiten. Die biomaterialgesteuerte Abgabe von Genvektoren, die auf klinisch adaptierten rekombinanten adeno-assoziierten viralen (rAAV) Vektoren basieren, ist eine attraktive Strategie zur Verbesserung der Knorpelreparatur durch eine minimalinvasive und kontrollierte Abgabe therapeutischer Gene in zeitlich und räumlich präziser Weise, welche eine intraartikuläre Vektorausbreitung und möglichen Verlust des therapeutischen Genprodukts reduziert. Die vorliegende Arbeit verwendete ein thermosensitiven Hydrogel auf Basis von Polyethylenoxid und Polypropylenoxid, um einen rAAV-Vektor, der für das Gen des chondrogenen Transkriptionsfaktors SOX9 (geschlechtsbestimmende Region Y-Typ- Hochmobilitätsgruppenbox 9) kodiert, in vollschichtige chondrale Defekte in Minischweinen freizusetzen, um seinen Effekt auf die Knorpelreparatur in vivo zu analysieren. Zudem wurde die Abgabe eines therapeutischen rAAV-Konstrukts, das für den insulinartigen Wachstumsfaktor I (IGF-I) kodiert, über ein Alginat (AlgPH155)-Hydrogel im gleichen Tiermodell als weiterer Ansatz zur Verbesserung der Knorpelreparatur in vivo getestet. Als Alternative zu Hydrogelsystemen wurde ein zusätzlicher Schwerpunkt auf die rAAV-vermittelte Abgabe des transformierenden Wachstumsfaktors b (TGF-b) unter Verwendung fester Poly(e-Caprolacton) (PCL)-Filme gelegt, um die Fähigkeit dieses Systems zu überprüfen, chondroreparative Prozesse in humanen Knochenmarkaspiraten ex vivo als zukünftige implantierbare Plattformen in Knorpeldefekte zu initiieren. Die Ergebnisse zeigen, daß die effektive Freisetzung der rAAV-SOX9- und IGF-I- Vektoren durch thermosensitive bzw. Alginat-Hydrogele die Knorpelreparatur für mindestens 4 Wochen (SOX9) bzw. ein Jahr (IGF-I) signifikant verbesserte. Zudem führt IGF-I zu gleichzeitiger signifikanter Verringerung der perifokalen Arthrose über einen längeren Zeitraum. Die wirksame Freisetzung des rAAV-TGF-b-Vektors unter Verwendung von PCL-Filmen (insbesonders wenn mit Polynatriumstyrolsulfonat - pNaSS liiert) aktivierte die chondrogene Differenzierung humaner Knochenmarkaspirate für mindestens 3 Wochen. Diese Daten unterstützen das Konzept einer Anwendung von biomaterialgesteuerter rAAV-Genabgabe als vielversprechende minimalinvasive Option für die klinische Knorpelreparatur

An Arnoldi-frontal approach for the stability analysis of flows in a collapsible channel

In this paper, we present a new approach based on a combination of the Arnoldi and frontal methods for solving large sparse asymmetric and generalized complex eigenvalue problems. The new eigensolver seeks the most unstable eigensolution in the Krylov subspace and makes use of the efficiency of the frontal solver developed for the finite element methods. The approach is used for a stability analysis of flows in a collapsible channel and is found to significantly improve the computational efficiency compared to the traditionally used QZ solver or a standard Arnoldi method. With the new approach, we are able to validate the previous results obtained either on a much coarser mesh or estimated from unsteady simulations. New neutral stability solutions of the system have been obtained which are beyond the limits of previously used methods

A Two-stage Classification Method for High-dimensional Data and Point Clouds

High-dimensional data classification is a fundamental task in machine learning and imaging science. In this paper, we propose a two-stage multiphase semi-supervised classification method for classifying high-dimensional data and unstructured point clouds. To begin with, a fuzzy classification method such as the standard support vector machine is used to generate a warm initialization. We then apply a two-stage approach named SaT (smoothing and thresholding) to improve the classification. In the first stage, an unconstraint convex variational model is implemented to purify and smooth the initialization, followed by the second stage which is to project the smoothed partition obtained at stage one to a binary partition. These two stages can be repeated, with the latest result as a new initialization, to keep improving the classification quality. We show that the convex model of the smoothing stage has a unique solution and can be solved by a specifically designed primal-dual algorithm whose convergence is guaranteed. We test our method and compare it with the state-of-the-art methods on several benchmark data sets. The experimental results demonstrate clearly that our method is superior in both the classification accuracy and computation speed for high-dimensional data and point clouds.Comment: 21 pages, 4 figure

A double-distribution-function lattice Boltzmann method for bed-load sediment transport

The governing equations of bed-load sediment transport are the shallow water equations and the Exner equation. To embody the advantages of the lattice Boltzmann method (e.g., simplicity, efficiency), the three-velocity (D1Q3) and five-velocity (D1Q5) double-distribution-function lattice Boltzmann models (DDF-LBMs), which can present the numerical solution for one-dimensional bed-load sediment transport, are proposed here based on the quasi-steady approach. The so-called DDF-LBM means we use two distribution functions to describe the movement of the two components, respectively. By using the Chapman–Enskog expansion, the governing equations can be recovered correctly from the DDF-LBMs. To illustrate the efficiency of these, two benchmark tests are used, and excellent agreements between the numerical and analytical solutions are demonstrated. In addition, we show that the D1Q5 DDF-LBM has better accuracy compared to the Hudson’s method