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Model Reference Adaptive Control for Switched Linear Systems With Uncertain Parameters and Its Application in Electro-hydraulic Systems

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  • Control Theory and Applications
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Abstract

This paper studies the model reference adaptive control for a class of switched linear systems with uncertain parameters under the dwell time switching. Firstly, the sufficient conditions for the model reference adaptive control synthesis are derived by introducing the time-varying Lyapunov function with increase coefficient in the framework of dwell time technique, where the dwell time is an arbitrary prespecified constant. Secondly, an adaptive controller is proposed to ensure that the state of the switched system asymptotically track the state of the reference switched system. Thirdly, based on the Lyapunov function proposed, the lower bound of dwell time is restricted, the decrease of Lyapunov function between two consecutive switched times of the active subsystem is limited, the energy of the whole switched system is reduced, and the asymptotic stability of the error system is realized. Then, if the reference is persistently exciting, the closed-loop error system is asymptotically stable and the parameter estimation error asymptotically converges to zero. Finally, an electro-hydraulic system is taken as an example to verify the effectiveness of the proposed method.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Liaoning University, No.66 Chongshan Middle Road, Huanggu District, Shenyang, Liaoning Province, 110036, China

    Ruicheng Ma, Xuedong Xia & Yuanchao Qu

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  1. Ruicheng Ma
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  2. Xuedong Xia
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  3. Yuanchao Qu
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Correspondence to Ruicheng Ma.

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This work was partially supported by National Natural Science Foundation of China (62073157), Natural Science Foundation of Liaoning Province, China (2022-MS-173), and Scientific Research Fund of Educational Department of Liaoning Province, China (JYTMS20230773).

Ruicheng Ma received his M.S. degree in applied mathematics from Liaoning University, Shenyang, China, in 2008. He completed his Ph.D. degree in control theory and control engineering from Northeastern University, Shenyang, China, in 2012. He is currently a professor with the School of Mathematics and Statistics, Liaoning University, Shenyang, China. He won the 2020 National Natural Science Award of China. He is currently an Editor of Control Engineering of China. His research interests include switched systems, hybrid control, and nonlinear systems.

Xuedong Xia received her B.S. degree in Information and Computing Science from Liaoning University of Technology, Jin zhou, China, in 2021. Now she is currently pursuing an M.S. degree at the School of Mathematics and Statistics, Liaoning University, Shenyang, China. Her research interests include switched systems, nonlinear systems, and observers design.

Yuanchao Qu received her M.S. degree in applied mathematics from Shenyang Normal University, Shenyang, China, in 2012. She is currently a lecturer with the School of Mathematics and Statistics, Liaoning University, Shenyang, China. Her research interests include Kalman filtering, variational Bayesian, and switched systems.

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Ma, R., Xia, X. & Qu, Y. Model Reference Adaptive Control for Switched Linear Systems With Uncertain Parameters and Its Application in Electro-hydraulic Systems. Int. J. Control Autom. Syst. 22, 2990–2998 (2024). https://doi.org/10.1007/s12555-023-0753-4

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  • DOI: https://doi.org/10.1007/s12555-023-0753-4

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