Mean Square Consensus Control for Second Order Multi-Agent Systems under Fixed Topologies and Measurement Noises

Liu, Xue Liang; Xu, Bu Gong; Xie, Li

doi:10.4028/www.scientific.net/amr.403-408.4036

Cited by 8 publications

(6 citation statements)

References 16 publications

(22 reference statements)

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“…These results are more general and strong than that of Liu, Xu, and Xie (2011), where the topology is assumed strongly connected and balanced. In addition, they make the study of Sun et al (2013) a special case of ours, when the topology is balanced and the time delay is time-invariant.…”

Section: Downloaded By [New York University] At 06:30 23 June 2015mentioning

confidence: 63%

“…In Liu, Xu, and Xie (2011) and Sun et al (2013), due to the balancedness of the topology, all the agents' initial conditions contribute to the final consensus with equal probability. However, it is well known in distributed control of multi-agent systems that in many real applications, the topologies might not be strongly connected or balanced.…”

Section: Motivations and Contributionsmentioning

confidence: 98%

“…Continuous and discrete double-integrator * Correspondent author. Email: djaidjasaber@yahoo.fr consensus with noisy communication has been studied by Cheng, Hou, Tan, and Wang (2011), Cheng, Wang, Hou, Tan, and Cao (2013), Liu, Xu, and Xie (2011), Fang (2015a, 2015b), Wu, Peng, Xie, and Wen (2013), while continuous and discrete linear multi-agent consensus has been investigated by Cheng, Hou, and Tan (2014), , and Wang, Cheng, Ren, Hou, and Tan (2015).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Consensus seeking in multi-agent systems with noisy and delayed communication in digraphs having spanning tree

Djaidja

2015

International Journal of Systems Science

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This paper studies the consensus problem of continuous-time single-integrator multi-agent systems with measurement noises and time delays under directed fixed topologies. Each agent in the team receives imprecise and delayed information from its neighbours. The noises are considered white noises, and time delays are assumed to be uniform for all the received information states. An analysis framework based on graph theory and stochastic tools is followed to derive conditions under which the asymptotic unbiased mean square linear χ -consensus is achieved in directed fixed topologies having a spanning tree. Then, conditions to achieve asymptotic unbiased mean square average consensus are deduced for fixed balanced digraphs having a spanning tree. The effectiveness of the proposed algorithms is proved through some simulations.

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Section: Downloaded By [New York University] At 06:30 23 June 2015mentioning

confidence: 63%

Section: Motivations and Contributionsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Consensus seeking in multi-agent systems with noisy and delayed communication in digraphs having spanning tree

Djaidja

2015

International Journal of Systems Science

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“…However, in all these works, other constraints have been discussed and the measurement noises are not considered. (2) The switching topologies case is examined here, this issue has not been studied neither by Liu et al [20] nor by Cheng et al [21].…”

Section: Introductionmentioning

confidence: 99%

Consensus of double-integrator multi-agent systems without relative state derivatives under communication noises and directed topologies

Djaidja

Fang

2015

Journal of the Franklin Institute

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“…In the last decade, many research articles addressed the problem of distributed consensus under noisy measurements , to name a few. Their main goal was the design of a robust consensus protocol that is able to reduce the impact of measurement noises corrupting the information exchange between agents in a network, in the meantime, this consensus protocol should achieve agreement between the agents on a final random value.…”

Section: Introductionmentioning

confidence: 99%

Stochastic consensus of single-integrator multi-agent systems under relative state-dependent measurement noises and time delays

Djaidja

Cheng

2016

Int. J. Robust. Nonlinear Control

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This paper proposes a consensus algorithm for continuous-time single-integrator multi-agent systems with relative state-dependent measurement noises and time delays in directed fixed and switching topologies. Each agent's control input relies on its own information state and its neighbors' information states, which are delayed and corrupted by measurement noises whose intensities are considered a function of the agents' relative states. The time delays are considered time-varying and uniform. For directed fixed topologies, condition to ensure mean square linear -consensus (average consensus, respectively) are derived for digraphs having spanning tree (balanced digraphs having spanning tree, respectively). For directed switching topologies, conditions on both time delays and dwell time have been given to extend the mean square linear -consensus (average consensus, respectively) of fixed topologies to switching topologies. 861In references [1][2][3][4][5][6][7][8][9], the noises are considered additive noises whose intensities are constant and independent of the agents states. Recently, some research [10-12] considered a more reliable and practical model for the noises, which relies on the fact that the noises intensities are time-varying and dependent on the agents' states. [10] obtained sufficient conditions to ensure both mean square and almost sure consensus of high-dimensional first-order dynamics under relative state-depending measurement noises in undirected topologies, where the noise intensities are assumed a vector or a matrix function of agents' relative states.[11] studied the single-integrator consensus with measurement noises in directed topologies. The measurement noise intensities are considered a linear function proportional to the absolute agents' relative states. Conditions to achieve mean square convergence and strong convergence have been obtained for both fixed and time-varying topologies.[12] extended the results of [11] to the leader-following consensus in directed fixed and switching topologies and derived conditions to ensure the tracking in mean square.Motivations and contributions: The authors in [10][11][12] assumed that the information states obtained by an agent from its neighbors are undelayed. However, this statement is not practical because the communication in real physical systems is always subject to time delays caused by the limitation of the speed of acquisition and transmission [13]. Therefore, it is of great importance if one studies the problem of consensus under relative state-dependent measurement noises and time delays. To the best of our knowledge, this problem is not investigated in the literature. In fact, solving this problem is more challenging and is not trivial, because the closed-loop equation that describes the system is a stochastic delay differential equation that is difficult to analyze, because its perturbed term is also a function of the delayed relative states, and therefore, the usual techniques that are typically used with non-state depending measurement...

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Mean Square Consensus Control for Second Order Multi-Agent Systems under Fixed Topologies and Measurement Noises

Cited by 8 publications

References 16 publications

Consensus seeking in multi-agent systems with noisy and delayed communication in digraphs having spanning tree

Consensus seeking in multi-agent systems with noisy and delayed communication in digraphs having spanning tree

Consensus of double-integrator multi-agent systems without relative state derivatives under communication noises and directed topologies

Stochastic consensus of single-integrator multi-agent systems under relative state-dependent measurement noises and time delays

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