中国物理B ›› 2026, Vol. 35 ›› Issue (3): 30502-030502.doi: 10.1088/1674-1056/adf31b

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Adaptive distributed optimization of high-order nonlinear multi-agent systems with predefined accuracy under state observer

Xiao-Wen Zhao(赵小文)1,†, Tong Shu(疏彤)1, Deng-Hao Pang(庞登浩)2, Tao Li(李涛)3, and Mei Yao(姚梅)1   

  1. 1 School of Mathematics, Hefei University of Technology, Hefei 230601, China;
    2 School of Internet, AnHui University, Hefei 230601, China;
    3 School of Electrical and Automation Engineering, Hubei Normal University, Huangshi 435002, China
  • 收稿日期:2025-06-03 修回日期:2025-07-14 接受日期:2025-07-23 出版日期:2026-02-11 发布日期:2026-03-12
  • 通讯作者: Xiao-Wen Zhao E-mail:zhaoxiaowen@hfut.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 62173121, 12301185, 62573173, and 62473135).

Adaptive distributed optimization of high-order nonlinear multi-agent systems with predefined accuracy under state observer

Xiao-Wen Zhao(赵小文)1,†, Tong Shu(疏彤)1, Deng-Hao Pang(庞登浩)2, Tao Li(李涛)3, and Mei Yao(姚梅)1   

  1. 1 School of Mathematics, Hefei University of Technology, Hefei 230601, China;
    2 School of Internet, AnHui University, Hefei 230601, China;
    3 School of Electrical and Automation Engineering, Hubei Normal University, Huangshi 435002, China
  • Received:2025-06-03 Revised:2025-07-14 Accepted:2025-07-23 Online:2026-02-11 Published:2026-03-12
  • Contact: Xiao-Wen Zhao E-mail:zhaoxiaowen@hfut.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 62173121, 12301185, 62573173, and 62473135).

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摘要： This paper discusses adaptive distributed optimization with predefined accuracy for high-order nonlinear multi-agent systems (MASs) that are subject to disturbances and nonlinear uncertainties. To estimate the global optimal solution in real-time, a distributed proportional-integral optimization technique is used to generate a virtual system for each agent. For the unknown control gain of the controller, the Nussbaum function is employed. Then, a fuzzy adaptive observer is designed to estimate the unmeasured state by leveraging the general approximation capabilities of fuzzy logic systems. Using the Lyapunov stability method and backstepping technique, we develop the adaptive law and a new distributed controller. This ensures that the outputs of multi-agent systems converge to optimal values. Finally, a simulation example is used to confirm the viability of the presented control mechanism.

关键词: distributed optimization, nonlinear multi-agent systems (MASs), fuzzy state observer, predefined accuracy control

Abstract: This paper discusses adaptive distributed optimization with predefined accuracy for high-order nonlinear multi-agent systems (MASs) that are subject to disturbances and nonlinear uncertainties. To estimate the global optimal solution in real-time, a distributed proportional-integral optimization technique is used to generate a virtual system for each agent. For the unknown control gain of the controller, the Nussbaum function is employed. Then, a fuzzy adaptive observer is designed to estimate the unmeasured state by leveraging the general approximation capabilities of fuzzy logic systems. Using the Lyapunov stability method and backstepping technique, we develop the adaptive law and a new distributed controller. This ensures that the outputs of multi-agent systems converge to optimal values. Finally, a simulation example is used to confirm the viability of the presented control mechanism.

Key words: distributed optimization, nonlinear multi-agent systems (MASs), fuzzy state observer, predefined accuracy control

中图分类号:  (High-dimensional chaos)

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