自适应分布式聚合博弈广义纳什均衡算法

时侠圣; 任璐; 孙长银

doi:10.16383/j.aas.c230584

自适应分布式聚合博弈广义纳什均衡算法

doi: 10.16383/j.aas.c230584

时侠圣^{1, 2, 3,},
任璐^{1, 2, 3,},
孙长银^{1, 2, 3,}

1.
安徽大学自主无人系统技术教育部工程研究中心合肥 230601
2.
安徽大学安徽省无人系统与智能技术工程研究中心合肥 230601
3.
安徽大学人工智能学院合肥 230601

基金项目: 国家自然科学基金创新研究群体科学基金(61921004), 国家自然科学基金重点项目(62236002, 62136008), 国家自然科学基金(62303009)资助

详细信息

作者简介:
时侠圣：安徽大学人工智能学院博士后. 2020年获得浙江大学控制科学与控制工程专业博士学位. 主要研究方向为分布式协同优化和网络化系统. E-mail: shixiasheng@zju.edu.cn

任璐：安徽大学人工智能学院讲师. 2021年获得东南大学控制科学与工程专业博士学位. 主要研究方向为多智能体系统一致性控制, 复杂动态网络的同步. E-mail: penny_lu@ahu.edu.cn

孙长银：安徽大学人工智能学院教授. 1996年获得四川大学应用数学专业学士学位. 分别于2001年, 2004年获得东南大学电子工程专业硕士和博士学位. 主要研究方向为智能控制, 飞行器控制, 模式识别和优化理论. 本文通信作者. E-mail: cysun@seu.edu.cn

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出版历程
- 收稿日期: 2023-09-19
- 录用日期: 2024-01-23
- 网络出版日期: 2024-03-12
- 刊出日期: 2024-06-27

Distributed Adaptive Generalized Nash Equilibrium Algorithm for Aggregative Games

SHI Xia-Sheng^{1, 2, 3
,},
REN Lu^{1, 2, 3
,},
SUN Chang-Yin^{1, 2, 3
,}

1.
Engineering Research Center of Autonomous Unmanned System Technology, Ministry of Education, Anhui University, Hefei 230601
2.
Anhui Provincial Engineering Research Center for Unmanned System and Intelligent Technology, Anhui University, Hefei 230601
3.
School of Artificial Intelligence, Anhui University, Hefei 230601

Funds: Supported by Foundation for Innovative Research Groups of National Natural Science Foundation of China (61921004), Key Projects of National Natural Science Foundation of China (62236002, 62136008), and National Natural Science Foundation of China (62303009)

More Information

Author Bio:
SHI Xia-Sheng　Postdoctor at the School of Artificial Intelligence, Anhui University. He received his Ph.D. degree in control science and control engineering from Zhejiang University in 2020. His research interest covers distributed cooperative optimization and network system

REN Lu　Lecturer at the School of Artificial Intelligence, Anhui University. She received her Ph.D. degree in control science and engineering from Southeast University in 2021. Her research interest covers consensus control of multi-agent systems and synchronization of complex dynamical networks

SUN Chang-Yin　Professor at the School of Artificial Intelligence, Anhui University. He received his bachelor degree in applied mathematics from Sichuan University in 1996, and his master and Ph.D. degrees in electrical engineering from Southeast University in 2001 and 2004, respectively. His research interest covers intelligent control, flight control, pattern recognition, and optimal theory. Corresponding author of this paper

摘要

摘要: 随着信息物理系统技术的发展, 面向多智能体系统的分布式协同优化问题得到广泛研究. 主要研究面向多智能体系统的受约束分布式聚合博弈问题, 其中局部智能体成本函数受到全局聚合项约束和全局等式耦合约束. 首先, 面向一阶积分型多智能体系统设计一种基于估计梯度下降的纳什均衡求解算法. 其中, 利用多智能体系统平均一致性方法设计一种自适应估计策略, 以实现全局聚合项约束分布式估计, 并据此计算出梯度函数估计值. 其次, 利用状态反馈策略和输出反馈策略将上述算法推广至状态信息可测和状态信息不可测一般线性异构多智能体系统. 最后, 利用拉萨尔不变性原理证实上述算法收敛性, 并提供多组案例仿真用以验证算法有效性.
- 聚合博弈 /
- 自适应 /
- 比例积分 /
- 梯度跟踪 /
- 一般线性多智能体系统
Abstract: With the development of cyber-physical system technology, the distributed cooperative optimization problem for multi-agent systems has been widely studied. This study focuses on the distributed constrained aggregative game for multi-agent systems, where the local cost function is subject to the global aggregative and global equality constraints. Firstly, a Nash equilibrium seeking algorithm based on estimation gradient descent is designed for the first-order integrator-based multi-agent systems. To this end, an adaptive estimation scheme is designed using the average consensus method of multi-agent systems to realize the distributed estimation of global aggregative function. Based on this, the estimation gradient function is calculated. Secondly, the above algorithm is extended to the state-accessible and state-inaccessible general heterogeneous linear multi-agent systems using the state and output feedback control scheme, respectively. Finally, the convergence proof is provided using the LaSalle＇s invariance principle and several simulation examples are provided for illustrating the effectiveness of our proposed algorithms.
- Aggregative game /
- adaptive /
- proportional-integral /
- gradient tracking /
- general linear multi-agent system

HTML全文

图 1 本文算法的状态$ x_i$轨迹

Fig. 1 The state trajectories $ x_i$in our algorithm

下载: 全尺寸图片幻灯片

图 2 本文算法的自适应权重$ \alpha_{ij}$轨迹

Fig. 2 The trajectories of the adaptive weight $ \alpha_{ij}$ in our algorithm

下载: 全尺寸图片幻灯片

图 3 不同算法的输出收敛误差轨迹

Fig. 3 The output convergence error trajectories of different algorithms

下载: 全尺寸图片幻灯片

图 4 不同控制参数值下本文算法的输出收敛误差轨迹

Fig. 4 The output convergence error trajectories of our algorithm under different control parameters

下载: 全尺寸图片幻灯片

图 5 本文算法的输出$ y_i$轨迹

Fig. 5 The output trajectories $ y_i$ in our algorithm

下载: 全尺寸图片幻灯片

图 6 本文算法的状态观测误差轨迹

Fig. 6 The trajectories of state observer error in our algorithm

下载: 全尺寸图片幻灯片

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