Abstract
In this paper, an innovative sliding mode framework is used to propose an observer-based adaptive control scheme for uncertain switched systems with unknown time-varying delay. First, a state observer with no input information is built incorporating a new sliding manifold (SM) to rebuild the unmeasured state variables, which does not rely on accurate information of the time-delay. By picking a suitable Lyapunov function, using the average dwell time (ADT) approach and linear matrix inequality (LMI) tool, a novel stability criterion for the resultant sliding motion is devised. In addition, to meet the defined SM’s arrival condition, a new adaptive variable structure controller is constructed. Finally, two illustrative examples are given to demonstrate the efficacy of the control method.
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This work is supported by the Natural Science Foundation of Shandong Province under grant ZR2023MF029, the National Natural Science Foundation of China under grants 61803217 and 62003231, and the Team Plan for Youth Innovation of Universities in Shandong Province under grant 2022KJ142.
Zhongzheng Liu received his B.S. degree in automation from the University of Qingdao, China, in 2018. He is currently pursuing a master’s degree with the School of Automation, Qingdao University, Qingdao, China. His current research interests include sliding mode control, uncertain switched systems, and adaptive control.
Zhen Liu received his Ph.D. degree in control theory and applications from Ocean University of China, Qingdao, China, in 2017; and from 2015 to 2017, he was a joint Ph.D. candidate at the Department of Engineering, Design and Mathematics, University of the West of England, UK, and the College of Engineering, University of Kentucky, USA. He is currently a Distinguished Professor at the School of Automation, Qingdao University, China. His current research interests include intelligent control and robot, sliding mode control, hybrid systems, and cyber-physical systems.
Baoping Jiang received his Ph.D. degree in control theory from the Ocean University of China, Qingdao, China, in 2019. From 2017 to 2019, he was a joint training Ph.D. Candidate with the Department of Mechanical Engineering, Politecnico di Milano, Milan, Italy. He joined the Suzhou University of Science and Technology, Suzhou, China, in 2019, where he is an associate professor. His research interests include sliding mode control and stochastic systems.
Cunchen Gao received his Ph.D. degree in control theory from the South China University of Technology, Guangzhou, China, 1997. He is currently a Full Professor in control theory with the School of Mathematical Sciences, Ocean University of China, Qingdao, China. His research interests include variable structure control, distributed parameter systems, time-delay systems, and singular systems.
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Liu, Z., Liu, Z., Jiang, B. et al. Adaptive Variable Structure Controller Design for Uncertain Switched Systems With Unknown Time-varying Delay. Int. J. Control Autom. Syst. 21, 3850–3859 (2023). https://doi.org/10.1007/s12555-022-0425-9
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DOI: https://doi.org/10.1007/s12555-022-0425-9