Stability of multiagent systems with time-dependent communication links
Citations
9,715 citations
Cites background or methods from "Stability of multiagent systems wit..."
...Recently, an extension of Theorem 6 with connectivity of the union of graphs over an infinite interval has been introduced by Moreau [14] (also, an extension is presented in [15] for weighted graphs)....
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...Proof: See the proof of Proposition 2 in [14]....
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...In this paper, we focus on the work described in five key papers—namely, Jadbabaie, Lin, and Morse [38], Olfati-Saber and Murray [70], Fax and Murray [28], Moreau [59], and Ren and Beard [74]— that have been instrumental in paving the way for more recent advances in study of self-organizing networked systems, or swarms....
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...Here, we rephrase a theorem due to Moreau and present it based our notation....
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...h Similarly, the algorithm analyzed in Proposition 2 of [14] does not solve the f -consensus problem....
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6,135 citations
4,693 citations
Cites background from "Stability of multiagent systems wit..."
...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]....
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...[22], Moreau [23], and Ren and Beard [24]....
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3,028 citations
Cites background or methods or result from "Stability of multiagent systems wit..."
...Using set-valued Lyapunov theory, [ 31 ] shows that the discrete-time consensus algorithm (S3) is uniformly globally attractive with respect to the collection of equilibrium solutions span{1} if and only if there exists K ≥ 0 such that the union of the communication graphs has a rooted directed spanning tree across each interval of length Kh, where h is the sample time....
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...The most common discrete-time consensus algorithm has the form [S3], [24], [26], [ 31 ]...
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...In addition, the result in [ 31 ] is extended to take into account bounded time delays in [40]....
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...Lyapunov Analysis of Consensus Algorithms Nonlinear analysis tools can also be used to study consensus algorithms [ 31 ]....
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...shown in [ 31 ] that V(t2) ⊆ V(t1) for all t2 ≥ t1, and that x(t) approaches an element of the set span{1}, which implies that consensus is reached....
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2,692 citations
Cites methods from "Stability of multiagent systems wit..."
...Related coordination problems with time-varying topologies have been studied in [21] using a switched linear system model, and in [27] using set-valued Lyapunov theory....
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References
11,658 citations
8,233 citations
"Stability of multiagent systems wit..." refers background or methods or result in this paper
...topology guaranteeing convergence of the individual agents’ states to a common value, thereby extending some of the results reported in [14], [27]–[29], and [31]....
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...The approach of the present paper applies to the linear swarming model of [14] as well as to the nonlinear model of [11] provided the initial orientation differences are sufficiently small....
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...Other studies that consider the connection between communication topology and system stability such as [14], [27]–[29], [31], [34], and [35] typically rely on algebraic graph theory, relating the graph topology with the algebraic structure of associated graph matrices....
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...1Within the context of swarming models [11], [14], agent i could be a particle moving at constant speed in two-dimensional space and x could represent its heading....
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...This is the swarming model studied in [14] and corresponds to the linear example of Section II with all weights equal to 1....
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6,514 citations
"Stability of multiagent systems wit..." refers background or methods in this paper
...Denote the direction of motion of particle by . The following model is studied in [ 11 ]:...
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...In the physics literature, swarming models are often individual-based with each individual being represented by a particle moving at constant speed, its direction of motion being updated according to nearest neighbor coupling; see, for example, [ 11 ]....
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...Example 4 (Swarming): Reference [ 11 ] proposes a simple model to investigate self-ordered motion in systems of particles with biologically motivated interaction....
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...1 Within the context of swarming models [ 11 ], [14], agent could be a particle moving at constant speed in two-dimensional space and could represent its heading....
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...The approach of the present paper applies to the linear swarming model of [14] as well as to the nonlinear model of [ 11 ] provided the initial orientation differences are sufficiently small....
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4,693 citations
"Stability of multiagent systems wit..." refers background in this paper
...In recent years, engineering applications such as formation control have increased the interest of engineers in swarming and collective motion patterns [12]–[26]....
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4,377 citations
"Stability of multiagent systems wit..." refers background in this paper
...Other studies that consider the connection between communication topology and system stability such as [14], [27]–[29], [31], [34], and [35] typically rely on algebraic graph theory, relating the graph topology with the algebraic structure of associated graph matrices....
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...(Leaderless coordination is also considered, for example, in [34]–[38])....
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