Institute for Systems Research Technical Reports
Permanent URI for this collectionhttp://hdl.handle.net/1903/4376
This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.
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Item A GENERAL FRAMEWORK FOR CONSENSUS NETWORKS(2015-03-10) Somarakis, Christoforos; Baras, JohnA new framework for the analysis of consensus networks is developed. The theory consists of necessary and sufficient conditions and it is flexible enough to comprise a variety of consensus systems. Under mild connectivity assumptions, the discussion ranges from linear, nonlinear, ordinary, functional and leader-follower models. The establishment of explicit estimates on the rate of convergence is the central objective. Our work extends and unifies past related works in the literature. Illustrative examples and simulations are presented to outline the theoretical results.Item Towards a unified theory of consensus(2014-10-12) Somarakis, Christoforos; Baras, JohnWe revisit the classic multi-agent distributed consensus problem under mild connectivity assumptions and non-uniformly bounded weights. The analysis is based on a novel application of the standard results from the non-negative matrix theory. It is a simple, yet unifying, approach that yields generalized results. We apply these results to a wide variety of linear, non-linear consensus and flocking algorithms proposed in the literature and we obtain new conditions for asymptotic consensus. Our framework is developed in both discrete and continuous time. Furthermore we extend the discussion to stochastic settings.Item Stability by Fixed Point Theory in Consensus Dynamics(2014-08-22) Somarakis, Christoforos; Baras, John; Paraskevas, Evripidis; Baras, JohnWe study the stability of linear time invariant distributed consensus dynamics in the presence of multiple propagation and processing delays. We employ fixed point theory (FPT) methods and derive sufficient conditions for asymptotic convergence to a common value while the emphasis is given in estimating the rate of convergence. We argue that this approach is novel in the field of networked dynamics as it is also flexible and thus capable of analyzing a wide variety of consensus based algorithms for which conventional Lyapunov methods are either too restrictive or unsuccessful.Item On the dynamics of linear functional differential equations with asymptotically constant solutions(2014-08-22) Somarakis, Christoforos; Baras, John; Paraskevas, Evripidis; Baras, JohnWe discuss the dynamics of general linear functional differential equations with solutions that exhibit asymptotic constancy. We apply fixed point theory methods to study the stability of these solutions and we provide sufficient conditions of asymptotic stability with emphasis on the rate of convergence. Several examples are provided to illustrate the claim that the derived results generalize, unify and in some cases improve the existing ones.Item A Fixed Point Theory Approach to Multi-Agent Consensus Dynamics With Delays(2013-01-01) Somarakis, Christoforos; Baras, JohnThe classic linear time-invariant multi-agent consensus scheme is revisited in the presence of constant and distributed bounded delays. We create a fixed point argument and prove exponential convergence with specific rate that depends both on the topology of the communication graph and the upper bound of the allowed delay.Item Linear Processes Under Vanishing Communications - The Consensus Problem(2012-04-07) Somarakis, ChristoforosIn this report, we revisit the classical multi-agent distributed consensus problem under the dropping of the general assumption that the existence of a connection between agent implies weights uniformly bounded away from zero. We reformulate and study the problem by establishing global convergence results both in discrete and continuous time, under fixed, switching and random topologies.Item A randomized gossip consensus algorithm on convex metric spaces(2012-02-20) Matei, Ion; Somarakis, Christoforos; Baras, JohnA consensus problem consists of a group of dynamic agents who seek to agree upon certain quantities of interest. This problem can be generalized in the context of convex metric spaces that extend the standard notion of convexity. In this paper we introduce and analyze a randomized gossip algorithm for solving the generalized consensus problem on convex metric spaces. We study the convergence properties of the algorithm using stochastic differential equations theory. We show that the dynamics of the distances between the states of the agents can be upper bounded by the dynamics of a stochastic differential equation driven by Poisson counters. In addition, we introduce instances of the generalized consensus algorithm for several examples of convex metric spaces together with numerical simulations.Item The Dynamics Of A Simple Rational Map(2011-07-17) Somarakis, ChristoforosThe dynamics of the 2-D rational map are studied for various values of it's control parameters. Despite it's simple structure this model is very rich in non-linear phenomena such as, multi-scroll strange attrac- tors, transitions to chaos via period doubling bifurcations, quasi-periodicity as well as intermittency, interior crisis, hyper-chaos etc. In this work, strange attractors, bifurcation diagrams, periodic windows, invariant characteristics are investigated both analytically and numerically.