Stacy Patterson

Bio: Stacy Patterson is an academic researcher from Rensselaer Polytechnic Institute. The author has contributed to research in topics: Consensus dynamics & Network topology. The author has an hindex of 18, co-authored 104 publications receiving 1758 citations. Previous affiliations of Stacy Patterson include Technion – Israel Institute of Technology & Montana State University.

Coherence in Large-Scale Networks: Dimension-Dependent Limitations of Local Feedback

Abstract: We consider distributed consensus and vehicular formation control problems. Specifically we address the question of whether local feedback is sufficient to maintain coherence in large-scale networks subject to stochastic disturbances. We define macroscopic performance measures which are global quantities that capture the notion of coherence; a notion of global order that quantifies how closely the formation resembles a solid object. We consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1, 2, and higher dimensions, with vehicular platoons corresponding to the 1-D case. A common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures, with a dimensions of 3 being necessary to achieve coherence in consensus and vehicular formations under certain conditions. In particular, we show that it is impossible to have large coherent 1-D vehicular platoons with only local feedback. We analyze these effects in terms of the underlying energetic modes of motion, showing that they take the form of large temporal and spatial scales resulting in an accordion-like motion of formations. A conclusion can be drawn that in low spatial dimensions, local feedback is unable to regulate large-scale disturbances, but it can in higher spatial dimensions. This phenomenon is distinct from, and unrelated to string instability issues which are commonly encountered in control problems for automated highways.

Leader selection for optimal network coherence

Abstract: We consider the problem of leader-based distributed coordination in networks where agents are subject to stochastic disturbances, but where certain designated leaders are immune to those disturbances. Specifically, we address the effect of leader selection on the coherence of the network, defined in terms of an H 2 norm of the system. This quantity captures the level of agreement of the nodes in the face of the external disturbances. We show that network coherence depends on the eigenvalues of a principal submatrix of the Laplacian matrix, and we formulate an optimization problem to select the set of leaders that results in the highest coherence. As this optimization problem is combinatorial in nature, we also present several greedy algorithms for leader selection that rely on more easily computable bounds of the H 2 norm and the eigenvalues of the system. Finally, we illustrate the effectiveness of these algorithms using several network examples.

Convergence Rates of Distributed Average Consensus With Stochastic Link Failures

Abstract: We consider a distributed average consensus algorithm over a network in which communication links fail with independent probability. In such stochastic networks, convergence is defined in terms of the variance of deviation from average. We first show how the problem can be recast as a linear system with multiplicative random inputs which model link failures. We then use our formulation to derive recursion equations for the second order statistics of the deviation from average in networks with and without additive noise. We give expressions for the convergence behavior in the asymptotic limits of small failure probability and large networks. We also present simulation-free methods for computing the second order statistics in each network model and use these methods to study the behavior of various network examples as a function of link failure probability.

Distributed Compressed Sensing for Static and Time-Varying Networks

Abstract: We consider the problem of in-network compressed sensing from distributed measurements. Every agent has a set of measurements of a signal x, and the objective is for the agents to recover x from their collective measurements using only communication with neighbors in the network. Our distributed approach to this problem is based on the centralized Iterative Hard Thresholding algorithm (IHT). We first present a distributed IHT algorithm for static networks that leverages standard tools from distributed computing to execute in-network computations with minimized bandwidth consumption. Next, we address distributed signal recovery in networks with time-varying topologies. The network dynamics necessarily introduce inaccuracies to our in-network computations. To accommodate these inaccuracies, we show how centralized IHT can be extended to include inexact computations while still providing the same recovery guarantees as the original IHT algorithm. We then leverage these new theoretical results to develop a distributed version of IHT for time-varying networks. Evaluations show that our distributed algorithms for both static and time-varying networks outperform previously proposed solutions in time and bandwidth by several orders of magnitude.

Consensus and Coherence in Fractal Networks

Abstract: We consider first- and second-order consensus algorithms in networks with stochastic disturbances. We quantify the deviation from consensus using the notion of network coherence, which can be expressed as an $H_{2}$ norm of the stochastic system. We use the setting of fractal networks to investigate the question of whether a purely topological measure, such as the fractal dimension, can capture the asymptotics of coherence in the large system size limit. Our analysis for first-order systems is facilitated by connections between first-order stochastic consensus and the global mean first passage time of random walks. We then show how to apply similar techniques to analyze second-order stochastic consensus systems. Our analysis reveals that two networks with the same fractal dimension can exhibit different asymptotic scalings for network coherence. Thus, this topological characterization of the network does not uniquely determine coherence behavior. The question of whether the performance of stochastic consensus algorithms in large networks can be captured by purely topological measures, such as the spatial dimension, remains open.

Random graphs

Abstract: We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms

Abstract: This self-contained introduction to the distributed control of robotic networks offers a distinctive blend of computer science and control theory. The book presents a broad set of tools for understanding coordination algorithms, determining their correctness, and assessing their complexity; and it analyzes various cooperative strategies for tasks such as consensus, rendezvous, connectivity maintenance, deployment, and boundary estimation. The unifying theme is a formal model for robotic networks that explicitly incorporates their communication, sensing, control, and processing capabilities--a model that in turn leads to a common formal language to describe and analyze coordination algorithms.Written for first- and second-year graduate students in control and robotics, the book will also be useful to researchers in control theory, robotics, distributed algorithms, and automata theory. The book provides explanations of the basic concepts and main results, as well as numerous examples and exercises.Self-contained exposition of graph-theoretic concepts, distributed algorithms, and complexity measures for processor networks with fixed interconnection topology and for robotic networks with position-dependent interconnection topology Detailed treatment of averaging and consensus algorithms interpreted as linear iterations on synchronous networks Introduction of geometric notions such as partitions, proximity graphs, and multicenter functions Detailed treatment of motion coordination algorithms for deployment, rendezvous, connectivity maintenance, and boundary estimation

Gossip Algorithms for Distributed Signal Processing

Abstract: Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This paper presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmitted messages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.

Distributed Control of Robotic Networks

Abstract: (i) You are allowed to freely download, share, print, or photocopy this document. (ii) You are not allowed to modify, sell, or claim authorship of any part of this document. (iii) We thank you for any feedback information, including suggestions, evaluations, error descriptions, or comments about teaching or research uses.