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Stability Margin of Data-Driven LQR and Its Application to Consensus Problem

Author

Listed:
  • Abdul Aris Umar

    (Research Center for Electrical and Information Technology, Department of Electrical and Information Engineering, Seoul National University of Science and Technology, Seoul 01811, Republic of Korea
    These authors contributed equally to this work.)

  • Kunhee Ryu

    (Research Center for Electrical and Information Technology, Department of Electrical and Information Engineering, Seoul National University of Science and Technology, Seoul 01811, Republic of Korea
    These authors contributed equally to this work.)

  • Juhoon Back

    (School of Robotics, Kwangwoon University, Nowon-gu, Seoul 01897, Republic of Korea)

  • Jung-Su Kim

    (Research Center for Electrical and Information Technology, Department of Electrical and Information Engineering, Seoul National University of Science and Technology, Seoul 01811, Republic of Korea)

Abstract

In contrast with traditional control input design techniques based on mathematical models of the system, in data-driven control approaches, which have recently gained substantial attention, the controller is derived directly from the data that are collected from experiments or observations of the target system. In particular, several data-driven optimal control and model predictive control (MPC) techniques have been proposed. In this paper, it is shown that the recently proposed data-driven LQR (Linear Quadratic Regulator) has a stability margin that is the set of the uncertainties in the control input channels maintaining the closed-loop stability. As an application of the proposed stability margin of the data-driven LQR, the consensus problem is considered. Since the control design for the consensus of multi-agent systems can be reformulated into the robust stabilization of a linear system with uncertainty in the input channel, it is demonstrated that the derived stability margin can be used to design a controller for the consensus of multi-agent systems.

Suggested Citation

  • Abdul Aris Umar & Kunhee Ryu & Juhoon Back & Jung-Su Kim, 2024. "Stability Margin of Data-Driven LQR and Its Application to Consensus Problem," Mathematics, MDPI, vol. 12(2), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:199-:d:1314765
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    References listed on IDEAS

    as
    1. Peter Wieland & Jung-Su Kim & Frank Allgöwer, 2011. "On topology and dynamics of consensus among linear high-order agents," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(10), pages 1831-1842.
    2. Jinyoung Lee & Jung-Su Kim & Hyungbo Shim, 2012. "Disc margins of the discrete-time LQR and its application to consensus problem," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(10), pages 1891-1900.
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