Safety and Stability of Nonlinear Systems With Multiple High-Relative-Degree Time-Varying State Constraints: Theory and Its Application to UAV Tracking

Fan Yang; Jiangping Hu; Qingrui Zhou; Xiaoming Hu

doi:10.1109/JAS.2025.125990

Volume 13 Issue 6

Jun. 2026

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2026 > 13(6): 1446-1458

F. Yang, J. Hu, Q. Zhou, and X. Hu, “Safety and stability of nonlinear systems with multiple high-relative-degree time-varying state constraints: Theory and its application to UAV tracking,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 6, pp. 1446–1458, Jun. 2026. doi: 10.1109/JAS.2025.125990

Citation:

F. Yang, J. Hu, Q. Zhou, and X. Hu, “Safety and stability of nonlinear systems with multiple high-relative-degree time-varying state constraints: Theory and its application to UAV tracking,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 6, pp. 1446–1458, Jun. 2026. doi: 10.1109/JAS.2025.125990

Citation:

F. Yang, J. Hu, Q. Zhou, and X. Hu, “Safety and stability of nonlinear systems with multiple high-relative-degree time-varying state constraints: Theory and its application to UAV tracking,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 6, pp. 1446–1458, Jun. 2026. doi: 10.1109/JAS.2025.125990

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Safety and Stability of Nonlinear Systems With Multiple High-Relative-Degree Time-Varying State Constraints: Theory and Its Application to UAV Tracking

doi: 10.1109/JAS.2025.125990

Funds: This work was partially supported by the National Key Research and Development Program of China (2022YFE0133100), the State Key Program of National Natural Science Foundation of China (U21B2008), and by the Sichuan Science and Technology Program (2024NSFSC0528)

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Author Bio:
Fan Yang received the B.S. degree and the M.S. degree from Wuhan Institute of Technology and the University of Electronic Science and Technology of China in 2019 and 2024. He is currently pursuing the Ph.D. degree in control science and engineering with the School of Automation Engineering, University of Electronic Science and Technology of China. His current research interests include state-constrained control, autonomous driving, and unmanned systems

Jiangping Hu (Senior Member, IEEE) received the B.S. degree in applied mathematics and the M.S. degree in computational mathematics from Lanzhou University in 2000 and 2004, respectively, and the Ph.D. degree in modelling and control of complex systems from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences in 2007. He has held various positions with the KTH Royal Institute of Technology, Stockholm, Sweden, The City University of Hong Kong, Hong Kong, China, Sophia University, Tokyo, Japan, and Western Sydney University, Sydney, Australia. He is currently a Professor with the School of Automation Engineering, University of Electronic Science and Technology of China. His current research interests include modeling and control of complex systems, and decision and optimization of unmanned systems. Dr. Hu has served as an Associate Editor of Journal of Systems Science and Complexity, Kybernetika, Mathematics, and PLOS Complex Systems

Qingrui Zhou received the B.S. degree in control science and the M.S. degree in operational research and cybernetics from Shandong University in 1994 and 2002, respectively, and the Ph.D. degree in control theory and control engineering from the Institute of Automation, Chinese Academy of Sciences in 2005. He is currently a Professor with the Qianxuesen Laboratory for Space Technology, China Academy of Space Technology. His current research interests include spacecraft formation flying, spacecraft navigation and control, and swarm intelligence

Xiaoming Hu (Senior Member, IEEE) received the M.S. and Ph.D. degrees in electrical engineering from the Arizona State University, Tempe, USA, in 1986 and 1989, respectively. He served as a Research Assistant with the Institute of Automaton, Chinese Academy of Sciences from 1983 to 1984. From 1989 to 1990, he was a Gustafsson Postdoctoral Fellow with KTH Royal Institute of Technology, Stockholm, Sweden, where he is currently a Professor of optimization and systems theory with the Department of Mathematics. His research interests include nonlinear dynamical systems, nonlinear observation and filtering, and multiagent systems
Corresponding author: Jiangping Hu, e-mail: hujp@uestc.edu.cn
Received Date: 2024-11-20
Revised Date: 2025-07-18
Accepted Date: 2025-10-17

Abstract

Abstract

It remains a challenge to stabilize a nonlinear system while satisfying time-varying state constraints for safety. In this study, we developed a time-varying nonlinear control barrier function (TVNCBF) approach to stabilize a nonlinear system with high-relative-degree state constraints. This approach mitigated potential conflicts among multiple control barrier function constraints, providing a theoretical foundation for safety control of affine nonlinear systems. We then proposed a safety control strategy for nonlinear systems and comprehensively analyzed its safety and feasibility. At the same time, considering a scenario where an unmanned aerial vehicle (UAV) avoids several dynamic obstacles during target tracking, we designed a direct safety control for the UAV system to ensure safe target tracking. Simulation results demonstrated the safety and stability of the UAV system under the proposed control strategy.

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References(34)

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