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Volume 7 Issue 6
Oct.  2020

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2020  >  7(6): 1555-1564
Xinyi Yu, Fan Yang, Chao Zou and Linlin Ou, "Stabilization Parametric Region of Distributed PID Controllers for General First-Order Multi-Agent Systems With Time Delay," IEEE/CAA J. Autom. Sinica, vol. 7, no. 6, pp. 1555-1564, Nov. 2020. doi: 10.1109/JAS.2019.1911627
Citation: Xinyi Yu, Fan Yang, Chao Zou and Linlin Ou, "Stabilization Parametric Region of Distributed PID Controllers for General First-Order Multi-Agent Systems With Time Delay," IEEE/CAA J. Autom. Sinica, vol. 7, no. 6, pp. 1555-1564, Nov. 2020. doi: 10.1109/JAS.2019.1911627
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Stabilization Parametric Region of Distributed PID Controllers for General First-Order Multi-Agent Systems With Time Delay

doi: 10.1109/JAS.2019.1911627
Funds:  This work was partly supported by the National Key Research and Development Plan Intelligent Robot Key Project (2018YFB1308000) and the Key Research and Development Program of Zhejiang Province (2020C01109)
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    Abstract
  • The stabilization problem of distributed proportional-integral-derivative (PID) controllers for general first-order multi-agent systems with time delay is investigated in the paper. The closed-loop multi-input multi-output (MIMO) framework in frequency domain is firstly introduced for the multi-agent system. Based on the matrix theory, the whole system is decoupled into several subsystems with respect to the eigenvalues of the Laplacian matrix. Considering that the eigenvalues may be complex numbers, the consensus problem of the multi-agent system is transformed into the stabilizing problem of all the subsystems with complex coefficients. For each subsystem with complex coefficients, the range of admissible proportional gains is analytically determined. Then, the stabilizing region in the space of integral gain and derivative gain for a given proportional gain value is also obtained in an analytical form. The entire stabilizing set can be determined by sweeping proportional gain in the allowable range. The proposed method is conducted for general first-order multi-agent systems under arbitrary topology including undirected and directed graph topology. Besides, the results in the paper provide the basis for the design of distributed PID controllers satisfying different performance criteria. The simulation examples are presented to check the validity of the proposed control strategy.

     

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    Highlights

    • The stabilization parametric region of distributed PID controllers for general first-order multi-agent systems with time delay is acquired in this paper, and the proposed method is conducted for systems under arbitrary topology including undirected and directed graph topology. Moreover, we ensure that the parameters chosen in the resultant set can guarantee the consensus of the multi-agent system with time delay.
    • In the actual engineering application, the distributed PID controllers are generally required to meet several performance criteria simultaneously. For this phenomenon, the results in this paper solve the stabilization problem of the systems with complex coefficients, and provide the basis for the design of distributed PID controllers satisfying different performance criteria.
    • The multi-agent system can be decoupled into several subsystems with respect to the eigenvalues of the Laplacian matrix based on the matrix theory. For each subsystem, the range of admissible proportional gains is analytically determined. Then, the stabilizing region in the space of integral gain and derivative gain for a given value is obtained in an analytical form. Finally, the entire stabilizing set can be determined by sweeping in the allowable range.

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