### Citations

1587 |
Optimization and nonsmooth analysis
- Clarke
- 1983
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Citation Context ... ∈ Rd, there exists a Filippov solution to (8)with the initial condition x(0) = x0. We also use the following notions of the generalized directional derivative and generalized gradient. Definition 2 (=-=[20]-=-). Assume f : Rd → R is locally Lipschitz near any given point x ∈ Rd. Then the generalized directional derivative of f at x in the direction ν ∈ Rd is defined by f 0(x; ν) ∆= lim sup y→x, t↓0 f (y+ t... |

852 | Algebraic Graph Theory
- Godsil, Royle
- 2001
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Citation Context ...elationships in terms of whether the position (resp. velocity) information can be exchanged between a pair of agents.Weuse aij and bij, 1 ≤ i, j ≤ N , to denote the elements of the adjacency matrices =-=[16]-=- of G1 and G2 respectively; in other words, aij (resp. bij) equals one if j is a neighbor of i in G1 (resp. G2) and zero otherwise. And we set aii = 0, bii = 0 for all i = 1, . . . ,N . In the sequel,... |

757 | Consensus and cooperation in networked multi-agent systems
- Olfati-Saber, Fax, et al.
- 2007
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Citation Context ...[q∗u(ri − rj)] + F [q∗u(rj − ri)] = q∗u(ri − rj)+ q∗u(rj − ri) = −δu (42) when ri − rj ≠ kδu, where k are integers, and F [q∗u(ri − rj)] + F [q∗u(rj − ri)] = [(k− 1)δu, kδu] + [−(k+ 1)δu,−kδu] = −δu =-=[0, 2]-=- (43) when ri − rj = kδu. From (43), we have N i=1 N j=1 aijF [q∗u(ri − rj)] 1 N N(a) ri(t)− r1(t), i = 2, 3, 4. (b) vi(t), i = 1, 2, 3, 4. Fig. 5. Synchronized motion with unbounded agent velocit... |

147 |
Lyapunov stability theory of nonsmooth systems
- Shevitz, Paden
- 1994
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Citation Context ...y of regular functions, each of which is regular at x, then for any nonnegative scalars λi, m i=1 λi fi(x) is regular at x. The following chain rule is useful for the calculations later on. Lemma 5 (=-=[21]-=-). Let x(·) be a Filippov solution to ẋ = X(x) on an interval containing t, and V : Rd → R be a Lipschitz and regular function. Then V (x(t)) is absolutely continuous and ddt V (x(t)) exists almost e... |

128 | Tsitsiklis, Distributed averaging algorithms and quantization effects. http://arxiv.org/abs/0803.1202
- Nedić, Olshevsky, et al.
- 2008
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Citation Context ... have been installed with identical quantizers. Remark 1. In the literature, when quantizers are applied to agents with first-order dynamics, different information has been quantized. For example, in =-=[6]-=- the quantization takes place after the relative positions have been summed up, namelyLetters 61 (2012) 1157–1167 ui = −q j∈N1(i) (ri − rj) ; in [10] the absolute position information in some gl... |

67 | Distributed consensus in multi-vehicle cooperative control - Ren, Beard - 2008 |

67 | On Consensus Algorithms for Double-integrator Dynamics
- Ren
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Citation Context ...ynamics as double-integrators are widely used for modeling mobile autonomous agents especially when the research focus is on the collective team dynamics instead of detailed individual agent dynamics =-=[13]-=-. Multi-agent systems with second-order agent dynamics can have ∗ Corresponding author. E-mail addresses: hui.liu@rug.nl (H. Liu), ming.cao@ieee.org, m.cao@rug.nl (M. Cao), c.de.persis@rug.nl (C. De P... |

32 |
Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems
- Yu, Chen, et al.
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Citation Context ... m.cao@rug.nl (M. Cao), c.de.persis@rug.nl (C. De Persis). dramatically different collective behavior than those with firstorder agent dynamics even when agents are coupled together in similarmanners =-=[14]-=-. However,while various quantized consensus schemes have been proposed for multi-agent systems with firstorder dynamics [7,10], less is known about the quantization effects on the consensus-type algor... |

32 |
Discontinuous dynamical systems
- Cortes
- 2008
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Citation Context ... equation ẋ(t) = X(x(t)) (8) whereX : Rd → Rd ismeasurable but discontinuous, the existence of a continuously differentiable solution is not guaranteed. In this paper, we adopt the Filippov solution =-=[19]-=-. lH. Liu et al. / Systems & Contro Definition 1. LetB(Rd) denote the collection of all subsets of Rd. The Filippov set-valued map F [X] : Rd → B(Rd) is defined by F [X](x) ∆= δ>0 µ(S)=0 co{X(B(x,... |

19 |
Stability analysis for multiagent systems using the incidence matrix: Quantized communication and formation control
- Dimarogonas, Johansson
- 2010
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Citation Context ...elyLetters 61 (2012) 1157–1167 ui = −q j∈N1(i) (ri − rj) ; in [10] the absolute position information in some global coordinate system is quantized, namely ui = − j∈N1(i) q(ri)− q(rj) . In =-=[17]-=-, the relative position information is quantized in a similar way for what we have done in (3) for second-order agent dynamics. But the coordination task is different, and thus the control goal is dif... |

12 |
Discontinuities and hysteresis in quantized average consensus
- Ceragioli, Persis, et al.
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Citation Context ...rder agent dynamics even when agents are coupled together in similarmanners [14]. However,while various quantized consensus schemes have been proposed for multi-agent systems with firstorder dynamics =-=[7,10]-=-, less is known about the quantization effects on the consensus-type algorithms for motion coordination in systems with higher-order dynamics. Recently some interesting sufficient and/or necessary con... |

12 | 2011, Network topology and communication data rate for consensusability of discrete-time multi-agent systems - You, Xie |

10 | Distributed leader-follower flocking control for multi-agent dynamical systems with time-varying velocities - Yu, Chen, et al. |

9 |
2005 Cooperative control
- Kumar, Leonard, et al.
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Citation Context ...ent dynamics. © 2012 Elsevier B.V. All rights reserved. 1. Introduction Recently significant research efforts have been made to study how to coordinate the motion of teams of mobile autonomous agents =-=[1]-=-. One popular approach is to use consensus-type algorithms to guide a team of agents to coincide with one another moving with the same velocity under the conditions that the relative position and/or r... |

9 |
On quantization and communication topologies in multi-vehicle rendezvous
- Johansson, Speranzon, et al.
- 2005
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Citation Context ...ositive number and ⌊a⌋, a ∈ R, denotes the greatest integer that is less than or equal to a. The uniform quantizer (4) is similar to those used in [8,17]. The asymmetric uniform quantizer we consider =-=[18]-=- is a map q∗u : R→ R such that q∗u(x) = δu x δu . (5) The logarithmic quantizer we use [8] is an odd map ql : R → R such that ql(x) = e qu(ln x) when x > 0; 0 when x = 0; −equ(ln(−x)) when x < ... |

5 | Quantized consensus, Automatica 43 - Kashyap, Basar, et al. - 2007 |

3 | On the passivity approach to quantized coordination problems, in - Persis |

1 |
Average consensus on networksLetters 61
- Frasca, Carli, et al.
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Citation Context ...rder agent dynamics even when agents are coupled together in similarmanners [14]. However,while various quantized consensus schemes have been proposed for multi-agent systems with firstorder dynamics =-=[7,10]-=-, less is known about the quantization effects on the consensus-type algorithms for motion coordination in systems with higher-order dynamics. Recently some interesting sufficient and/or necessary con... |

1 | Control of one-dimensional guided formations using coarsely quantized information, in - Persis, Liu, et al. |

1 | De Persis, Quantization effects on synchronization of mobile agentswith second-order dynamics - Liu, Cao, et al. |