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Design of Heterogeneous Multi-agent System for Distributed Computation

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Trends in Nonlinear and Adaptive Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 488))

Abstract

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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Notes

  1. 1.

    More appropriate name could be “averaged dynamics,” which may however confuse the reader with the averaged dynamics in the well-known averaging theory [18] that deals with time average.

  2. 2.

    \(\dot{x} = f(t,x)\) is contractive if \(\exists \varTheta > 0\) such that \(\varTheta \frac{\partial f}{\partial x}(t,x) + \frac{\partial f}{\partial x}(t,x)^T \varTheta \le - I\) for all x and t [20].

  3. 3.

    The condition for w in \({\mathscr {D}}_x\) can be understood by recalling that \(\mathrm{col}(x_1,\ldots ,x_N) = 1_N \otimes s + (R \otimes I_n) \tilde{z}\).

  4. 4.

    A particular case of (4.20) is

    $$\begin{aligned} \dot{x}_i = f_i(t, x_i) + k B \sum _{j \in \mathscr {N}_i}\alpha _{ij}(x_j - x_i), \quad i \in \mathscr {N}, \end{aligned}$$

    where the matrix B is positive semi-definite, which can always be converted into (4.20) by a linear coordinate change.

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Acknowledgements

This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (Ministry of Science and ICT) under No. NRF-2017R1E1A1A03070342 and No. 2019R1A6A3A12032482.

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Authors and Affiliations

  1. Department of Engineering, University of Cambridge, Control Group, Trumpington Street, CB2 1PZ, Cambridge, United Kingdom

    Jin Gyu Lee

  2. ASRI, Department of Electrical and Computer Engineering, Seoul National University, Gwanak-ro 1, Gwanak-gu, 08826, Seoul, Korea

    Hyungbo Shim

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  1. Jin Gyu Lee
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Correspondence to Hyungbo Shim .

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Editors and Affiliations

  1. Department of Electrical and Computer Engineering, New York University, Brooklyn, NY, USA

    Zhong-Ping Jiang

  2. Automatic Control, CNRS, Saint Martin d’Heres, France

    Christophe Prieur

  3. Department of Electrical and Computer Engineering, Imperial College London, London, UK

    Alessandro Astolfi

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Lee, J.G., Shim, H. (2022). Design of Heterogeneous Multi-agent System for Distributed Computation. In: Jiang, ZP., Prieur, C., Astolfi, A. (eds) Trends in Nonlinear and Adaptive Control. Lecture Notes in Control and Information Sciences, vol 488. Springer, Cham. https://doi.org/10.1007/978-3-030-74628-5_4

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