Utility of Edge-wise Funnel Coupling for Asymptotically Solving Distributed Consensus Optimization

Lee, Jin Gyu; Berger, Toby; Trenn, Stephan; Shim, Hyungbo

doi:10.23919/ecc51009.2020.9143983

Cited by 8 publications

(7 citation statements)

References 24 publications

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“…With the funnel coupling (47), it is shown in [41] that, under the assumption that no finite escape time exists, the state difference ν i j (t) evolves within the funnel:…”

Section: Edge-wise Funnel Couplingmentioning

confidence: 99%

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Design of heterogeneous multi-agent system for distributed computation

Lee,

Shim

2021

Preprint

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A group behavior of a heterogeneous multi-agent system is studied which obeys an "average of individual vector fields" under strong couplings among the agents. Under stability of the averaged dynamics (not asking stability of individual agents), the behavior of heterogeneous multi-agent system can be estimated by the solution to the averaged dynamics. A following idea is to "design" individual agent's dynamics such that the averaged dynamics performs the desired task. A few applications are discussed including estimation of the number of agents in a network, distributed least-squares or median solver, distributed optimization, distributed state estimation, and robust synchronization of coupled oscillators. Since stability of the averaged dynamics makes the initial conditions forgotten as time goes on, these algorithms are initialization-free and suitable for plug-and-play operation. At last, nonlinear couplings are also considered, which potentially asserts that enforced synchronization gives rise to an emergent behavior of a heterogeneous multi-agent system.

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“…With the funnel coupling (47), it is shown in [41] that, under the assumption that no finite escape time exists, the state difference ν i j (t) evolves within the funnel:…”

Section: Edge-wise Funnel Couplingmentioning

confidence: 99%

“…In practice, the funnel coupling (47) enforces approximate synchronization as in (48), and thus, the behavior of the network is not exactly the same as (50) but can be shown to be close to it. More details are found in [41].…”

Section: Edge-wise Funnel Couplingmentioning

confidence: 99%

Design of heterogeneous multi-agent system for distributed computation

Lee,

Shim

2021

Preprint

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“…The idea of an edge-wise funnel coupling law was first proposed in [3] and the specific use of this design to solve distributed consensus optimization can be found in [4]. Both this novel coupling law and the node-wise funnel coupling law (2) are inspired by the funnel control introduced in [5]; see also the recent works [6,7] and the literature review therein.…”

Section: Contribution Of the Present Papermentioning

confidence: 99%

Edge-wise funnel output synchronization of heterogeneous agents with relative degree one

Lee¹,

Berger²,

Trenn³

et al. 2021

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In a recent work by three of the authors, in order to enforce synchronization for scalar heterogeneous multi-agent systems with some useful characteristics, a node-wise funnel coupling law was proposed. The emergent dynamics, to which each of the agents synchronizes, was characterized and it was studied how networks can be synthesized which exhibit these emergent dynamics. The advantage of this synthesis is its suitability for plug-and-play operation. However, the aforementioned emergent dynamics under node-wise funnel coupling are determined by an algebraic equation which does not admit an explicit solution in general, and even its pointwise solution proves rather difficult. Furthermore, the contractivity assumption on the emergent dynamics, required to establish the synchronization, is hard to be checked without solving the algebraic equation. To resolve these drawbacks, in the present paper we present a new funnel coupling law that uses edge-wise output differences. Under this novel coupling the benign properties of node-wise funnel coupling are retained, but the emergent dynamics are given explicitly by the blended dynamics of the multi-agent system, which already proved an advantageous tool in the analysis and design of such networks. Additionally, our results are not restricted to scalar systems and treat the case that neighboring agents only communicate their output information, and not their complete state.

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“…In fact, unlike the internal model principle results, it is observed in this paper, that as the performance function approaches zero, the coupling term approaches to possibly non-zero time-varying signal, which compensates the heterogeneity of the individual agents. Specific use of this idea to solve distributed consensus optimization can be found in (Lee, Berger, Trenn, & Shim, 2020a). We want to emphasize that even when asymptotic synchronization is achieved, the input u i (t, ν i (t)) can still be bounded.…”

Section: Related Approachesmentioning

confidence: 99%

Synchronization with prescribed transient behavior: Heterogeneous multi-agent systems under funnel coupling Extended arXiv version

Lee,

Trenn,

Shim

2020

Preprint

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In this paper, we introduce a nonlinear time-varying coupling law, which can be designed in a fully decentralized manner and achieves approximate synchronization with arbitrary precision, under only mild assumptions on the individual vector fields and the underlying graph structure. Meanwhile, we consider undirected graphs and scalar input affine systems for simplicity. The proposed coupling law is motivated by the so called funnel control method studied in adaptive control under the observation that arbitrary precision synchronization can be achieved for heterogeneous multi-agent systems by the highgain coupling, and thus, we follow to call our coupling law as '(node-wise) funnel coupling.' By getting out of the conventional proof technique in the funnel control study, we now can obtain even asymptotic synchronization with the same funnel coupling law. Moreover, the emergent collective behavior that arises for a heterogeneous multi-agent system when enforcing arbitrary precision synchronization by the proposed funnel coupling law, has been analyzed in this paper. In particular, we introduce a single scalar dynamics called 'emergent dynamics' that is capable of illustrating the emergent synchronized behavior by its solution trajectory. Characterization of the emergent dynamics is important because, for instance, one can design the emergent dynamics first such that the solution trajectory behaves as desired, and then, provide a design guideline to each agent so that the constructed vector fields yield the desired emergent dynamics. A particular example illustrating the utility of the emergent dynamics is given also in the paper as a distributed median solver.

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Utility of Edge-wise Funnel Coupling for Asymptotically Solving Distributed Consensus Optimization

Cited by 8 publications

References 24 publications

Design of heterogeneous multi-agent system for distributed computation

Design of heterogeneous multi-agent system for distributed computation

Edge-wise funnel output synchronization of heterogeneous agents with relative degree one

Synchronization with prescribed transient behavior: Heterogeneous multi-agent systems under funnel coupling Extended arXiv version

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