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Volume 8 Issue 9
Sep.  2021

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2021  >  8(9): 1539-1548
M. S. Sarafraz, M. S. Tavazoei, "A Unified Optimization-Based Framework to Adjust Consensus Convergence Rate and Optimize the Network Topology in Uncertain Multi-Agent Systems," IEEE/CAA J. Autom. Sinica, vol. 8, no. 9, pp. 1539-1548, Sep. 2021. doi: 10.1109/JAS.2021.1004111
Citation: M. S. Sarafraz, M. S. Tavazoei, "A Unified Optimization-Based Framework to Adjust Consensus Convergence Rate and Optimize the Network Topology in Uncertain Multi-Agent Systems," IEEE/CAA J. Autom. Sinica, vol. 8, no. 9, pp. 1539-1548, Sep. 2021. doi: 10.1109/JAS.2021.1004111
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A Unified Optimization-Based Framework to Adjust Consensus Convergence Rate and Optimize the Network Topology in Uncertain Multi-Agent Systems

doi: 10.1109/JAS.2021.1004111

  • Department of Electrical Engineering, Sharif University of Technology, Tehran 11365-9363, Iran

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    Abstract
  • This paper deals with the consensus problem in an uncertain multi-agent system whose agents communicate with each other through a weighted undirected (primary) graph. The considered multi-agent system is described by an uncertain state-space model in which the involved matrices belong to some matrix boxes. As the main contribution of the paper, a unified optimization-based framework is proposed for simultaneously reducing the weights of the edges of the primary communication graph (optimizing the network topology) and synthesizing a controller such that the consensus in the considered uncertain multi-agent system is ensured with an adjustable convergence rate. Considering the NP-hardness nature of the optimization problem related to the aforementioned framework, this problem is relaxed such that it can be solved by regular LMI solvers. Numerical/practical-based examples are presented to verify the usefulness of the obtained results.

     

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    • 1 Formally speaking, there is a bilinear term in the constraint of the optimization (18) which can cause non-convexity. However, since the only source of non-convexity is the scalar variable $ \beta $, a straightforward approach is to adjust this variable through a grid-search or some other efficient methods like as that proposed in [52].
    2 http://www.complib.de/
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    Highlights

    • A unified optimization-based framework is introduced for simultaneously optimizing the network topology and synthesizing a controller such that the consensus in an uncertain multi-agent system ensured.
    • It us assumed that the considered multi-agent system is described by an uncertain state- space model in which the involved matrices belong to some matrix boxes.
    • A relaxation proposed such that the introduced optimization program can be solved using regular LMI solvers.

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