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

Abdul Aris Umar, Kunhee Ryu, Juhoon Back and Jung-Su Kim ()
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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
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
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

Mathematics, 2024, vol. 12, issue 2, 1-16

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.

Keywords: LQR (Linear Quadratic Regulator); stability margin; gain margin; consensus problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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