Parameter-dependent functional observer-based finite-time adaptive memory ISMC for continuous LPV systems with unknown nonlinear functions

AbstractThis paper investigates a parameter-dependent (PD) functional observer-based finite-time adaptive memory integral sliding mode controller (ISMC) scheme for continuous linear parameter varying (LPV) systems with unknown nonlinear functions. First, a novel functional observer including parameters and parameter rates is proposed, and the observer gains can be directly designed. Different from the previous studies, a memory ISMC scheme with a time-varying delay through the functional observer is used for the first time in LPV systems to improve the performance. Moreover, to fully adopt the model characteristics of LPV systems and the functional observer, an integral PD surface function that contains PD input matrices and a memory parameter is established simultaneously. And then, an adaptive compensator is deduced for eliminating the influence of unknown nonlinear functions, so that the designed memory ISMC can make closed-loop LPV systems stable within a preset finite time. Furthermore, stability criteria with less conservatism for the LPV systems are proposed by memory Lyapunov–Krasovskii functional with measurable parameters. These criteria can guarantee LPV systems are finite-time boundedness with H∞ performance (FTB-H∞) on the sliding stage, arriving stage and entire finite-time region. Finally, a riderless bicycle is given to display the validity and superiority of the developed approach.Keywords: PD functional observerlinear parameter varying systemsadaptive memory integral sliding mode controlfinite-time boundedness Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementThe authors confirm that the data supporting the findings of this study are available within the article [and/or] its supplementary materials.Additional informationFundingThis work was supported in part by the National Natural Science Foundation of China [grant numbers 62273058 and U22A2045], and in part by the Youth Science and Technology Innovation and Entrepreneurship Outstanding Talents Project of Jilin Province [grant number 20230508043RC].Notes on contributorsWenchengyu JiWenchengyu Ji received the B.S. degree from Wuhan University, Wuhan, China, in 2016, and the M.S. degree from the College of Electrical and Electronic Engineering, Changchun University of Technology, Changchun, China, in 2019, where he is currently pursuing the Ph.D. degree. His current research interests include sampled-data control and stability for time-delay systems.Yulian JiangYulian Jiang received the Ph.D. degree in control science and engineering from Northeastern University, Shenyang, China, in 2014. She is currently an Associate Professor with the College of Electrical and Electronic Engineering, Changchun University of Technology, Changchun, China. Her research interest covers coordination control for multiagent systems, and intelligent control theory and application.Xiangpeng XieXiangpeng Xie received the B.S. degree and Ph.D. degree in engineering from Northeastern University, Shenyang, China, in 2004 and 2010, respectively. He is currently a full professor with the Institute of Advanced Technology, Nanjing University of Posts and Telecommunications, Nanjing, China. His research interests include fuzzy modeling and control synthesis, state estimations, optimization in process industries and intelligent optimization algorithms. Prof. Xie serves as Associate Editors of International Journal of Control, Automation, and Systems and International Journal of Fuzzy Systems.Shenquan WangShenquan Wang received the Ph.D. degree in control science and engineering from Northeastern University, Shenyang, China, in 2014. From November 2014 to July 2017, he was a Postdoctoral Research Associate with the State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China. From 2021 to 2022, he was an Academic Visitor with the Department of Automation, Tsinghua University, Beijing. He is currently a Professor with the College of Electrical and Electronic Engineering, Changchun University of Technology, Changchun, China. His main research interests include robust stability theory, adaptive/distributed control, and complex systems security and reliability.