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Iterative LMI Approach to Robust Hierarchical Control of Homogenous Linear Multi-Agent Systems Subject to Polytopic Uncertainty and External Disturbance

IEEE access, 2021, Vol.9, p.151221-151234 [Peer Reviewed Journal]

Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2021 ;ISSN: 2169-3536 ;EISSN: 2169-3536 ;DOI: 10.1109/ACCESS.2021.3126424 ;CODEN: IAECCG

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  • Title:
    Iterative LMI Approach to Robust Hierarchical Control of Homogenous Linear Multi-Agent Systems Subject to Polytopic Uncertainty and External Disturbance
  • Author: Van Pham, Tuynh ; Nguyen, Dinh Hoa ; Banjerdpongchai, David
  • Subjects: Attenuation ; Control systems ; disturbance attenuation ; Dynamic models ; hierarchical control ; Iterative methods ; Liapunov functions ; Linear matrix inequalities ; Linear systems ; Lyapunov methods ; Multi-agent systems ; Multiagent systems ; Optimization ; parameter-dependent bilinear matrix inequality ; Parameterization ; polytopic uncertainty ; Robust control ; Symmetric matrices ; Uncertainty
  • Is Part Of: IEEE access, 2021, Vol.9, p.151221-151234
  • Description: This paper investigates design of robust hierarchical control for linear multi-agent systems (MAS) subject to polytopic uncertainty and external disturbance. Each agent of MAS is described by a homogeneous linear time-invariant dynamic model. The control structure has two layers, namely, an upper layer and a lower layer. Local actions are executed in the lower layer. Each agent shares information through an undirected graph with neighboring agents in the upper layer to achieve the global stabilization and disturbance attenuation. We employ a parameter-dependent Lyapunov function to formulate the robust control design of the local and global feedback in terms of bilinear matrix inequalities and incorporate constraints on disturbance attenuation. We propose the sufficient condition, where system matrices and Lyapunov variables are separated. The parameterization of the controller depends on a common slack variable instead of the Lyapunov matrices. We develop an iterative approach based on the coordinated optimization to solve sub-problems over linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness of the proposed robust control designs. It is shown that our proposed robust control designs outperform other robust control designs in terms of achievable disturbance attenuation and maximum admissible uncertainty bound.
  • Publisher: Piscataway: IEEE
  • Language: English
  • Identifier: ISSN: 2169-3536
    EISSN: 2169-3536
    DOI: 10.1109/ACCESS.2021.3126424
    CODEN: IAECCG
  • Source: IEEE Open Access Journals
    DOAJ Directory of Open Access Journals
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