Decentralised state-feedback prescribed performance control for a class of interconnected nonlinear full-state time-delay systems with strong interconnection

Abstract

This paper investigates the problem of the state-feedback control design for a class of interconnected nonlinear full-state time-delay systems with strong interconnection and prescribed performance. Based on the dynamic gain approach and Lyapunov-Krasovskii method, it overcomes the rigorous restriction that the interconnected time-delay functions should satisfy linear growth condition. Compared with the existing results, the main contribution is that the dynamic gain approach is extended to state-feedback control for interconnected time-delay systems, and it is strictly proved that the closed-loop system is globally bounded stable with the proposed decentralised control strategy. The problem of the strong interconnection terms is solved by combining the backstepping approach and graph theory. Furthermore, the expected transient and steady-state performance of the output can be guaranteed by considering prescribed performance control into such strongly interconnected systems. Finally, simulation is performed and the results show the effectiveness of the proposed method.

Keywords:

• Interconnected nonlinear systems
• full-state time-delay
• strong interconnection
• prescribed performance

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Key R&D Program of China under Grant 2018YFB1308300, in part by the National Natural Science Foundation of China (61803326, 61825304 and 6182500417), in part by the Innovative Research Groups of the Natural Science Foundation of Hebei Province (E2020203174).

Notes on contributors

Liuliu Zhang

Liuliu Zhang received the Ph.D. degree in electrical engineering from Yanshan University, Qinhuangdao, China, in 2018. She is currently an associate professor in Yanshan University. Her current research interests include nonlinear system control, intelligent control of networked interconnected system, multi-robot cooperative control.

Lingchen Zhu

Lingchen Zhu received the B.S. degree in automation from ShanDong JiaoTong University, Jinan, China, in 2019. He is currently working toward the M.S. degree in Yanshan University. His current research interest includes nonlinear system control.

Changchun Hua

Changchun Hua received the Ph.D. degree in electrical engineering from Yanshan University, Qinhuangdao, China, in 2005. He was a Research Fellow with the National University of Singapore, Singapore, from 2006 to 2007. From 2007 to 2009, he was with Carleton University, Ottawa, ON, Canada, funded by the Province of Ontario Ministry of Research and Innovation Program. From 2009 to 2010, he was with the University of Duisburg-Essen, Essen, Germany, funded by Alexander von Humboldt Foundation. He is currently a Full Professor with Yanshan University. He has authored or coauthored over 80 papers in mathematical, technical journals, and conferences. He has been involved in over 10 projects supported by the National Natural Science Foundation of China, the National Education Committee Foundation of China, and other important foundations. His current research interests include nonlinear control systems, control systems design over network, teleoperation systems, and intelligent control.

Cheng Qian

Cheng Qian received the Ph.D. degree in mechanical engineering from Yanshan University, Qinhuangdao, China, in 2020. His research interests are in dynamic modeling, and analysis and control of rolling process.