Consensus seeking in multiagent systems under dynamically changing interaction topologies
TL;DR: It is shown that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves.
Abstract: This note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies. Both discrete and continuous update schemes are proposed for information consensus. This note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves.
Citations
More filters
05 Mar 2007
TL;DR: A theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees is provided.
Abstract: This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations
9,715 citations
Cites methods from "Consensus seeking in multiagent sys..."
...Distributed computation over networks has a tradition in systems and control theory starting with the pioneering work of Borkar and Varaiya [10] and Tsitsiklis and Athens [90] on asynchronous asymptotic agreement problem for distributed decision-making systems....
[...]
TL;DR: A theoretical framework for design and analysis of distributed flocking algorithms, and shows that migration of flocks can be performed using a peer-to-peer network of agents, i.e., "flocks need no leaders."
Abstract: In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in free-space and presence of multiple obstacles are considered. We present three flocking algorithms: two for free-flocking and one for constrained flocking. A comprehensive analysis of the first two algorithms is provided. We demonstrate the first algorithm embodies all three rules of Reynolds. This is a formal approach to extraction of interaction rules that lead to the emergence of collective behavior. We show that the first algorithm generically leads to regular fragmentation, whereas the second and third algorithms both lead to flocking. A systematic method is provided for construction of cost functions (or collective potentials) for flocking. These collective potentials penalize deviation from a class of lattice-shape objects called /spl alpha/-lattices. We use a multi-species framework for construction of collective potentials that consist of flock-members, or /spl alpha/-agents, and virtual agents associated with /spl alpha/-agents called /spl beta/- and /spl gamma/-agents. We show that migration of flocks can be performed using a peer-to-peer network of agents, i.e., "flocks need no leaders." A "universal" definition of flocking for particle systems with similarities to Lyapunov stability is given. Several simulation results are provided that demonstrate performing 2-D and 3-D flocking, split/rejoin maneuver, and squeezing maneuver for hundreds of agents using the proposed algorithms.
4,693 citations
Cites background from "Consensus seeking in multiagent sys..."
...Recently, there has been a surge of interest among control scientists in consensus problems due to the work of Olfati-Saber and Murray [20], [21] and alignment on networks with variable topology by Jadbabaie et al. [22], Moreau [23], and Ren and Beard [24]....
[...]
...[22], Moreau [23], and Ren and Beard [24]....
[...]
TL;DR: Theoretical results regarding consensus-seeking under both time invariant and dynamically changing communication topologies are summarized in this paper, where several specific applications of consensus algorithms to multivehicle coordination are described.
Abstract: The purpose of this article is to provide a tutorial overview of information consensus in multivehicle cooperative control. Theoretical results regarding consensus-seeking under both time invariant and dynamically changing communication topologies are summarized. Several specific applications of consensus algorithms to multivehicle coordination are described
3,028 citations
Cites background from "Consensus seeking in multiagent sys..."
...sus algorithm has the form [S3], [24], [26], [31]...
[...]
...The most common continuous consensus algorithm [1], [5], [24]–[26] is given by...
[...]
...It can be shown that this condition is satisfied if there exists an infinite sequence of contiguous, uniformly bounded time intervals, with the property that across each interval, the union of the communication graphs has a rooted directed spanning tree [26], [28]....
[...]
[...]
TL;DR: In this paper, the basic laws describing the essential aspects of collective motion are reviewed and a discussion of the various facets of this highly multidisciplinary field, including experiments, mathematical methods and models for simulations, are provided.
Abstract: We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior Our aim is to provide a balanced discussion of the various facets of this highly multidisciplinary field, including experiments, mathematical methods and models for simulations, so that readers with a variety of background could get both the basics and a broader, more detailed picture of the field The observations we report on include systems consisting of units ranging from macromolecules through metallic rods and robots to groups of animals and people Some emphasis is put on models that are simple and realistic enough to reproduce the numerous related observations and are useful for developing concepts for a better understanding of the complexity of systems consisting of many simultaneously moving entities As such, these models allow the establishing of a few fundamental principles of flocking In particular, it is demonstrated, that in spite of considerable differences, a number of deep analogies exist between equilibrium statistical physics systems and those made of self-propelled (in most cases living) units In both cases only a few well defined macroscopic/collective states occur and the transitions between these states follow a similar scenario, involving discontinuity and algebraic divergences
2,120 citations
TL;DR: In this article, a distributed observer-type consensus protocol based on relative output measurements is proposed to solve the consensus problem of multi-agent systems with a time-invariant communication topology consisting of general linear node dynamics.
Abstract: This paper addresses the consensus problem of multiagent systems with a time-invariant communication topology consisting of general linear node dynamics. A distributed observer-type consensus protocol based on relative output measurements is proposed. A new framework is introduced to address in a unified way the consensus of multiagent systems and the synchronization of complex networks. Under this framework, the consensus of multiagent systems with a communication topology having a spanning tree can be cast into the stability of a set of matrices of the same low dimension. The notion of consensus region is then introduced and analyzed. It is shown that there exists an observer-type protocol solving the consensus problem and meanwhile yielding an unbounded consensus region if and only if each agent is both stabilizable and detectable. A multistep consensus protocol design procedure is further presented. The consensus with respect to a time-varying state and the robustness of the consensus protocol to external disturbances are finally discussed. The effectiveness of the theoretical results is demonstrated through numerical simulations, with an application to low-Earth-orbit satellite formation flying.
2,096 citations
References
More filters
Book•
[...]
TL;DR: In this article, the authors present results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrate their importance in a variety of applications, such as linear algebra and matrix theory.
Abstract: Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: - New sections on the singular value and CS decompositions - New applications of the Jordan canonical form - A new section on the Weyr canonical form - Expanded treatments of inverse problems and of block matrices - A central role for the Von Neumann trace theorem - A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric-skew symmetric pair - Expanded index with more than 3,500 entries for easy reference - More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid - A new appendix provides a collection of problem-solving hints.
23,986 citations
TL;DR: A distinctive feature of this work is to address consensus problems for networks with directed information flow by establishing a direct connection between the algebraic connectivity of the network and the performance of a linear consensus protocol.
Abstract: In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.
11,658 citations
Book•
01 Jan 2009
TL;DR: The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.
Abstract: Graphs.- Groups.- Transitive Graphs.- Arc-Transitive Graphs.- Generalized Polygons and Moore Graphs.- Homomorphisms.- Kneser Graphs.- Matrix Theory.- Interlacing.- Strongly Regular Graphs.- Two-Graphs.- Line Graphs and Eigenvalues.- The Laplacian of a Graph.- Cuts and Flows.- The Rank Polynomial.- Knots.- Knots and Eulerian Cycles.- Glossary of Symbols.- Index.
8,307 citations
TL;DR: A theoretical explanation for the observed behavior of the Vicsek model, which proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
Abstract: In a recent Physical Review Letters article, Vicsek et al. propose a simple but compelling discrete-time model of n autonomous agents (i.e., points or particles) all moving in the plane with the same speed but with different headings. Each agent's heading is updated using a local rule based on the average of its own heading plus the headings of its "neighbors." In their paper, Vicsek et al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models. The Vicsek model proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
8,233 citations