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Publication Effects of Delay on the Functionality of Large-scale Networks(2008-02-01) Papachristodoulou, Antonis; Jadbabaie, AliNetworked systems are common across engineering and the physical sciences. Examples include the Internet, coordinated motion of multi-agent systems, synchronization phenomena in nature etc. Their robust functionality is important to ensure smooth operation in the presence of uncertainty and unmodelled dynamics. Many such networked systems can be viewed under a unified optimization framework and several approaches to assess their nominal behaviour have been developed. In this paper, we consider what effect multiple, non-commensurate (heterogeneous) communication delays can have on the functionality of large-scale networked systems with nonlinear dynamics. We show that for some networked systems, the structure of the delayed dynamics allows functionality to be retained for arbitrary communication delays, even for switching topologies under certain connectivity conditions; whereas in other cases the loop gains have to be compensated for by the delay size, in order to render functionality delay-independent for arbitrary network sizes. Consensus reaching in multi-agent systems and stability of network congestion control for the Internet are used as examples. The differences and similarities of the two cases are explained in detail, and the application of the methodology to other technological and physical networks is discussed.Publication Incremental Phi*: Incremental Any-Angle Path Planning on Grids(2009-07-11) Nash, Alex; Koenig, Sven; Likhachev, MaximWe study path planning on grids with blocked and unblocked cells. Any-angle path-planning algorithms find short paths fast because they propagate information along grid edges without constraining the resulting paths to grid edges. Incremental path-planning algorithms solve a series of similar path-planning problems faster than repeated single-shot searches because they reuse information from the previous search to speed up the next one. In this paper, we combine these ideas by making the any-angle path-planning algorithm Basic Theta* incremental. This is non-trivial because Basic Theta* does not fit the standard assumption that the parent of a vertex in the search tree must also be its neighbor. We present Incremental Phi* and show experimentally that it can speed up Basic Theta* by about one order of magnitude for path planning with the freespace assumption.Publication Distributed Topology Control of Dynamic Networks(2008-06-11) Zavlanos, Michael M; Tahbaz-Salehi, Alireza; Jadbabaie, Ali; Pappas, George JIn this paper, we present a distributed control framework for controlling the topology of dynamic multi-agent networks. Agents are equipped with local sensing and wireless communication capabilities, however, due to power constraints, they are required to switch between two modes of operation, namely active and sleep. The control objective investigated in this paper is to determine distributed coordination protocols that regulate switching between the operation modes of every agent such that the overall network guarantees multi-hop communication links among a subset of so called boundary agents. In the proposed framework, coordination is based on a virtual market where every request to switch off is associated with a bid. Combinations of requests are verified with respect to connectivity and the one corresponding to the highest aggregate bid is finally served. Other than nearest neighbor information, our approach assumes no knowledge of the network topology, while verification of connectivity relies on notions of algebraic graph theory as well as gossip algorithms run over the network. Integration of the individual controllers results in an asynchronous networked control system for which we show that it satisfies the connectivity specification almost surely. We finally illustrate efficiency of our scalable approach in nontrivial computer simulations.Publication Metabolic Networks Analysis using Convex Optimization(2008-12-09) Julius, A. Agung; Imielinski, Marcin; Pappas, George JMetabolic networks map the biochemical reactions in a living cell to the flow of various chemical substances in the cell, which are called metabolites. A standard model of a metabolic network is given as a linear map from the reaction rates to the change in metabolites concentrations. We study two problems related to the analysis of metabolic networks, the minimal network problem and the minimal knockout problem.Publication Single Cell Manipulation using Ferromagnetic Composite Microtransporters(2010-01-29) Sakar, Mahmut Selman; Steager, Edward B; Pappas, George J; Kumar, Vijay; Kim, Dal Hyung; Kim, Min JunFor biomedical applications, such as single cell manipulation, it is important to fabricate microstructures that can be powered and controlled wirelessly in fluidic environments. In this letter, we describe the construction and operation of truly micron-sized, biocompatible ferromagnetic microtransporters driven by external magnetic fields. Microtransporters were fabricated using a simple, single step fabrication method and can be produced in large numbers. We demonstrate that they can be navigated to manipulate single cells with micron-size precision without disturbing the local environment.Publication Solving Image Registration Problems Using Interior Point Methods(2008-10-12) Taylor, Camillo J; Bhusnurmath, ArvindThis paper describes a novel approach to recovering a parametric deformation that optimally registers one image to another. The method proceeds by constructing a global convex approximation to the match function which can be optimized using interior point methods. The paper also describes how one can exploit the structure of the resulting optimization problem to develop efficient and effective matching algorithms. Results obtained by applying the proposed scheme to a variety of images are presented.Publication Target Enumeration via Euler Characteristic Integrals(2009-07-01) Baryshnikov, Yury; Ghrist, RobertWe solve the problem of counting the total number of observable targets (e.g., persons, vehicles, landmarks) in a region using local counts performed by a network of sensors, each of which measures the number of targets nearby but neither their identities nor any positional information. We formulate and solve several such problems based on the types of sensors and mobility of the targets. The main contribution of this paper is the adaptation of a topological sheaf integration theory — integration with respect to Euler characteristic — to yield complete solutions to these problems.Publication Three examples of applied and computational homology(2008-06-01) Ghrist, RobertComputational algebraic topology has already existed for some decades, with as its main objective the generation of examples. Nowadays, the field is rapidly changing into an applied branch of mathematics that is important in its own right. Robert Ghrist, topologist at the University of Illinois and one of the winners of the 2007 Scientific American 50 award, gives us three examples that illustrate this development, each with a different origin.Publication Elastic Multi-Particle Systems for Bounded-Curvature Path Planning(2008-06-11) Ahmadzadeh, Ali; Jadbabaie, Ali; Pappas, George J; Kumar, VijayThis paper investigates a path planning algorithm for Dubins vehicles. Our approach is based on approximation of the trajectories of vehicles using sequence of waypoints and treating each way point as a moving particle in the space. We define interaction forces between the particles such that the resulting multi-particle system will be stable, moreover, the trajectories generated by the waypoints in the equilibria of the multi-particle system will satisfy all of the hard constraint such as bounded-curvature constraint and obstacle avoidance.Publication Distributed Quadratic Programming over Arbitrary Graphs(2007-01-01) Motee, Nader; Jadbabaie, AliIn this paper, the locality features of infinitedimensional quadratic programming (QP) optimization problems are studied. Our approach is based on tools from operator theory and ideas from Multi Parametric Quadratic Programming (MPQP). The key idea is to use the spatially decaying operators (SD), which has been recently developed to study spatially distributed systems in [1], to capture couplings between optimization variables in the quadratic cost functional and linear constraints. As an application, it is shown that the problem of receding horizon control of spatially distributed systems with heterogeneous subsystems, input and state constraints, and arbitrary interconnection topologies can be modeled as an infinitedimensional QP problem. Furthermore, we prove that for a convex infinite-dimensional QP in which the couplings are through SD operators, optimal solution is piece-wise affine– represented as convolution sums. More importantly, we prove that the kernel of each convolution sum decays in the spatial domain at a rate proportional to the inverse of the corresponding coupling function of the optimization problem, thereby providing evidence that even centralized solutions to the infinite-dimensional QP has inherent spatial locality.