Consensus for double integrator dynamics in heterogeneous networks

Goldin, Darina; Attia, Sid Ahmed; Raisch, Jörg

doi:10.1109/cdc.2010.5717761

Cited by 14 publications

(17 citation statements)

References 11 publications

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“…Remark 4.5. Theorem 4.4 is closely related to recent results on partial consensus for double-integrator multi-agent systems [16,7], as will become clear from the discussion in Section 5.1.…”

Section: Stability Analysismentioning

confidence: 61%

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Port-Hamiltonian Systems on Graphs

Schaft

Maschke²

2013

SIAM J. Control Optim.

152

146

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In this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port-Hamiltonian systems on open graphs. Basic idea is to associate with the incidence matrix of the graph a Dirac structure relating the flow and effort variables associated to the edges, internal vertices, as well as boundary vertices of the graph, and to formulate energy-storing or energy-dissipating relations between the flow and effort variables of the edges and internal vertices. This allows for state variables associated to the edges, and formalizes the interconnection of networks. Examples from different origins such as consensus algorithms are shown to share the same structure. It is shown how the identified Hamiltonian structure offers systematic tools for the analysis of the resulting dynamics. * A.J. van der Schaft is with the Johann

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Section: Stability Analysismentioning

confidence: 61%

“…Hence in this case q ∈ im B T ⊂ Λ 1 . Note that the subspace im B T × Λ 0 ⊂ Λ 1 × Λ 0 is an invariant subspace with regard to the dynamics (16) or (17). We will return to this in Section 5.1.…”

Section: Mass-spring Systemsmentioning

confidence: 99%

Port-Hamiltonian Systems on Graphs

Schaft

Maschke²

2013

SIAM J. Control Optim.

152

146

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“…It is also of great interest to quantify how much damping is needed to avoid the natural oscillation of the double integrator dynamics. In [3] it was shown that in the linear case on R N , G a only needed to have one link for the dynamics to converge to the double consensus. However, here we require G a to be connected.…”

Section: Discussionmentioning

confidence: 99%

“…In the Euclidean counterpart of this problem it is possible to guarantee convergence when only two nodes share speed information [3]. In our case, we need to assume the undirected graph G a is connected.…”

Section: B Combining Synchronization Of Coupled Oscillators With Conmentioning

confidence: 99%

Distributed clock synchronization: Joint frequency and phase consensus

Mallada

Tang

2011

IEEE Conference on Decision and Control and European Control Conference

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Abstract-Distributed synchronization has gradually gained importance over the last two decades. The ad-hoc nature of new applications has increased the need for robust and scalable distributed solutions that are capable of generating high precision timing information. However, current solutions usually produce phase errors when the frequencies are heterogeneous. This paper proposes a distributed synchronization procedure that can achieve consensus in both frequency and phase. The algorithm uses only local information and is robust to frequency heterogeneity and network topology. A sufficient condition for global convergence is shown by leveraging recent results on coupled oscillators. We further characterize an invariant constant of the algorithm that relates the limiting frequency ω * with the harmonic mean of the clocks' natural frequencies. Simulations are provided to illustrate and verify these properties.

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“…Examples of this are the already quoted publication, the doctoral theses [14,31] and an increasing number of papers such as [1,2,15,16,18,32]. From a more mathematical perspective, some examples are [6,118,119,17,23,46] and the references within.…”

Section: Zusammenfassungmentioning

confidence: 99%

Consensus in Multi‐agent Systems

Wen

Chen

et al. 2016

Distributed Cooperative Control of Multi‐agent Systems

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A Carlos Elías y a Marina. AbstractDuring the last decade, the problem of consensus in multiagents systems has been studied with special emphasis on graph theoretical methods. Consensus can be regarded as a control objective in which is sought that all systems, or agents, in a network have an equivalent output value. This is achieved through a given control strategy usually referred to as consensus algorithm. The motivation to study such an objective comes from different areas, such as engineering, and social and natural sciences. In the control engineering field, important application examples are formation control of swarms of mobile robots and distributed electric generation. Most of the work in this area is done for agents with single or double integrator dynamics and algorithms derived as the Laplacian matrix of undirected graphs. That is, consensus is often studied as a property of particular networks and particular algorithms.In this thesis, we tackle the problem from a Control Theory perspective in an attempt to augment the class of systems that can be studied. For that we translate the consensus problem from its classical formulation for integrator systems into a general continuous time stability problem. From here, different algorithmic strategies under several dynamical assumptions of the agents can be studied through well known control theoretical tools -as Lyapunov's theory, linear matrix inequalities (LMI), or robust control -along with graph theoretical concepts. In particular, in this work we study consensus of agents with arbitrary linear dynamics under the influence of linear algorithms not necessarily derived from graphs. Furthermore, we include the possibility that the agents are disturbed by several factors as external signals, parameter uncertainties, switching dynamics, or communication failure. The theoretical analysis is also applied to the problem of power sharing in electric grids and to the analysis of distributed formation control.

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Consensus for double integrator dynamics in heterogeneous networks

Cited by 14 publications

References 11 publications

Port-Hamiltonian Systems on Graphs

Port-Hamiltonian Systems on Graphs

Distributed clock synchronization: Joint frequency and phase consensus

Consensus in Multi‐agent Systems

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