Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition
TL;DR: Conditions for guaranteeing the cluster consensus control for generic linear multi-agent systems (MASs) under directed interaction topology via distributed feedback controller are presented in terms of purely the graphic topology conditions and thus are very easy to be verified.
About: This article is published in Automatica.The article was published on 2013-09-01. It has received 296 citations till now. The article focuses on the topics: Uniform consensus & Directed acyclic graph.
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TL;DR: Focusing on different kinds of constraints on the controller and the self-dynamics of each individual agent, as well as the coordination schemes, the recent results are categorized into consensus with constraints, event-based consensus, consensus over signed networks, and consensus of heterogeneous agents.
Abstract: In this paper, we mainly review the topics in consensus and coordination of multi-agent systems, which have received a tremendous surge of interest and progressed rapidly in the past few years. Focusing on different kinds of constraints on the controller and the self-dynamics of each individual agent, as well as the coordination schemes, we categorize the recent results into the following directions: consensus with constraints, event-based consensus, consensus over signed networks, and consensus of heterogeneous agents. We also review some applications of the very well developed consensus algorithms to the topics such as economic dispatch problem in smart grid and k -means clustering algorithms.
595 citations
Cites background or methods from "Cluster consensus control of generi..."
...ogy and coupling configuration for leaderless case, which includes the leader-following one studied in [70] and [109] as a special case....
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...A consistent and intuitive result obtained in [70], [109], and [110] for generic linear systems and in [67]–[69] for integrator agents...
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...This is what has been systematically investigated in [68], [70], [109], and [110], where the agents...
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...Qin and Yu [70] exploit pinning control technique to achieve cluster consensus under the assumption that the network topology is collectively acyclic....
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...In most works, Lyapunov method based analysis is a preference [65], [70], [95], [111], [119]....
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TL;DR: Time-varying formation tracking analysis and design problems for second-order Multi-Agent systems with switching interaction topologies are studied, and a formation tracking protocol is constructed based on the relative information of the neighboring agents.
Abstract: Time-varying formation tracking analysis and design problems for second-order Multi-Agent systems with switching interaction topologies are studied, where the states of the followers form a predefined time-varying formation while tracking the state of the leader. A formation tracking protocol is constructed based on the relative information of the neighboring agents. Necessary and sufficient conditions for Multi-Agent systems with switching interaction topologies to achieve time-varying formation tracking are proposed together with the formation tracking feasibility constraint based on the graph theory. An approach to design the formation tracking protocol is proposed by solving an algebraic Riccati equation, and the stability of the proposed approach is proved using the common Lyapunov stability theory. The obtained results are applied to solve the target enclosing problem of a multiquadrotor unmanned aerial vehicle (UAV) system consisting of one leader (target) quadrotor UAV and three follower quadrotor UAVs. A numerical simulation and an outdoor experiment are presented to demonstrate the effectiveness of the theoretical results.
566 citations
TL;DR: If each agent is asymptotically null controllable with bounded controls and the interaction topology described by a signed digraph is structurally balanced and contains a spanning tree, then the semi-global bipartite consensus can be achieved for the linear multiagent system by a linear feedback controller with the control gain being designed via the low gain feedback technique.
Abstract: The bipartite consensus problem for a group of homogeneous generic linear agents with input saturation under directed interaction topology is examined. It is established that if each agent is asymptotically null controllable with bounded controls and the interaction topology described by a signed digraph is structurally balanced and contains a spanning tree, then the semi-global bipartite consensus can be achieved for the linear multiagent system by a linear feedback controller with the control gain being designed via the low gain feedback technique. The convergence analysis of the proposed control strategy is performed by means of the Lyapunov method which can also specify the convergence rate. At last, the validity of the theoretical findings is demonstrated by two simulation examples.
272 citations
Cites background from "Cluster consensus control of generi..."
...Such a bipartite consensus framework is different from the group consensus phenomenon investigated in [19] and [20], in which there are multiple interacting clusters of agents and the interactions between different clusters may be either cooperative or competitive....
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...RECENTLY, great interest has been directed toward to the collective behavior of multiagent systems in various areas, such as biology, physics, computer science, and control engineering (see [1]–[20] and references therein)....
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...Lemma 5 [20]: For any nonzero vector x ∈ RNn, symmetric matrix Q ∈ RN×N , and symmetric positive-semidefinite matrix W ∈ Rn×n, there hold λmin(Q)x (IN ⊗ W)x ≤ xT(Q ⊗ W)x ≤ λmax(Q)x(IN ⊗ W)x...
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TL;DR: A discontinuous Lyapunov functional approach is developed to derive a design criterion on the existence of an admissible sampled-data CFP for cluster formation control for a networked multi-agent system in the simultaneous presence of aperiodic sampling and communication delays.
Abstract: This paper addresses the problem of cluster formation control for a networked multi-agent system (MAS) in the simultaneous presence of aperiodic sampling and communication delays. First, to fulfill multiple formation tasks, a group of agents are decomposed into $M$ distinct and nonoverlapping clusters. The agents in each cluster are then driven to achieve a desired formation, whereas the MAS as a whole accomplishes $ M $ cluster formations. Second, by a proper modeling of aperiodic sampling and communication delays, an aperiodic sampled-data cluster formation protocol (CFP) is delicately constructed such that the information exchanges among neighboring agents only occur intermittently at discrete instants of time. Third, a detailed theoretical analysis of cluster formability is carried out and a sufficient and necessary condition is provided such that the system is $M$ -cluster formable. Furthermore, a discontinuous Lyapunov functional approach is developed to derive a design criterion on the existence of an admissible sampled-data CFP. Finally, numerical simulations on a team of nonholonomic mobile robots are given to illustrate the effectiveness of the obtained theoretical result.
230 citations
TL;DR: It is shown in this paper that an affine formation is stabilizable over an undirected graph if and only if the undirecting graph is universally rigid, while an affines formation is stable over a directed graph in the d-dimensional space if andonly if the directed graph is (d + 1)-rooted.
Abstract: This paper introduces a new multi-agent control problem, called an affine formation control problem, with the objective of asymptotically reaching a configuration that preserves collinearity and ratios of distances with respect to a target configuration. Suppose each agent updates its own state using a weighted sum of its neighbor's relative states with possibly negative weights. Then the affine control problem can be solved for either undirected or directed interaction graphs. It is shown in this paper that an affine formation is stabilizable over an undirected graph if and only if the undirected graph is universally rigid, while an affine formation is stabilizable over a directed graph in the $d$ -dimensional space if and only if the directed graph is $(d + 1)$ -rooted. Rigorous analysis is provided, mainly relying on Laplacian associated with the interaction graph, which contain both positive and negative weights.
158 citations
Cites background from "Cluster consensus control of generi..."
...Moreover, the works by [13]–[15] consider negative weights as the inhibitory mechanism to desynchronize the interacting agents in different clusters....
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References
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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: 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.
6,135 citations