Temporal Formation Control for Multi-agent Systems Based on Reachable Sets

Yuhua Yao; Jitao Sun; Xiaoming Hu

doi:10.1109/JAS.2025.125960

Volume 13 Issue 5

May 2026

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 19.2, Top 1 (SCI Q1)

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2026 > 13(5): 1151-1165

Y. Yao, J. Sun, and X. Hu, “Temporal formation control for multi-agent systems based on reachable sets,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 5, pp. 1151–1165, May 2026. doi: 10.1109/JAS.2025.125960

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Y. Yao, J. Sun, and X. Hu, “Temporal formation control for multi-agent systems based on reachable sets,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 5, pp. 1151–1165, May 2026. doi: 10.1109/JAS.2025.125960

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Temporal Formation Control for Multi-agent Systems Based on Reachable Sets

doi: 10.1109/JAS.2025.125960

Funds: This work was supported by the National Natural Science Foundation of China (61673296), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0100), and the National Scholarship Fund

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Author Bio:
Yuhua Yao received the B.S. and Ph.D. degrees from the School of Mathematical Sciences, Tongji University, in 2018 and 2024, respectively. She is currently a Postdoctoral Researcher with Fudan University and the KTH Royal Institute of Technology, Stockholm, Sweden. Her current research interests include hybrid systems, temporal logic, and learning-based control

Jitao Sun received the B.Sc. degree in mathematics from Nanjing University in 1983, and the Ph.D. degree in control theory and control engineering from the South China University of Technology in 2002. He was with Anhui University of Technology from 1983 to 1997. From 1997 to 2000, he was with Shanghai Tiedao University. In 2000, he joined the School of Mathematical Sciences, Tongji University. He was a Professor with Anhui University of Technology and Shanghai Tiedao University from 1995 to 2000. He is currently a Professor with Tongji University. He has authored or coauthored more than 220 journals papers. His recent research interests include impulsive control, time delay systems, hybrid systems, and systems biology. Dr. Sun is a Member of Technical Committee on Nonlinear Circuits and Systems, IEEE Circuits and Systems Society, and a Reviewer of Mathematical Reviews of American Mathematical Society

Xiaoming Hu received the B.S. degree from University of Science and Technology of China in 1983, and the M.S. and Ph.D. degrees from the Arizona State University, USA, in 1986 and in 1989, respectively. He served as a Research Assistant at the Institute of Automaton, Chinese Academy of Sciences, from 1983 to 1984. From 1989 to 1990 he was a Gustafsson Postdoctoral Fellow at KTH Royal Institute of Technology, Stockholm, Sweden, where he is currently a Professor of optimization and systems theory in the Department of Mathematics. His research interests include nonlinear dynamical systems, nonlinear observation and filtering, and multiagent systems
Corresponding author: Xiaoming Hu, e-mail: hu@kth.se
Received Date: 2024-10-17
Revised Date: 2025-07-02
Accepted Date: 2025-10-03

Available Online: 2026-05-26

Abstract

Abstract

This paper explores formation control for multi-agent systems by reformulating desired formations using signal temporal logic (STL) specifications. To achieve flexibility and efficiency, we employ sparse polynomial zonotopes (SPZs) to represent several common formations and the system’s state sets. This representation allows us to frame the formation control problem as a series of transitions between different state sets within a specific time horizon, which can be solved using optimal transport theory. By combining the optimal transport matrix with shrinking horizon model predictive control (MPC), we have developed a feasible control strategy that gradually guides the system trajectories toward the target set. This innovative approach decomposes the formation control problem into multiple temporal logic subproblems, reducing computational complexity and mitigating the impact of sampling randomness introduced by optimal transport. The effectiveness of our proposed approach is demonstrated through its application to a multi-unicycle system.
- Formation control,
- optimal transport,
- reachable set,
- signal temporal logic (STL),
- sparse polynomial zonotope (SPZ)

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References(38)

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