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              自適應分布式聚合博弈廣義納什均衡算法

              時俠圣 任璐 孫長銀

              時俠圣, 任璐, 孫長銀. 自適應分布式聚合博弈廣義納什均衡算法. 自動化學報, 2024, 50(6): 1?11 doi: 10.16383/j.aas.c230584
              引用本文: 時俠圣, 任璐, 孫長銀. 自適應分布式聚合博弈廣義納什均衡算法. 自動化學報, 2024, 50(6): 1?11 doi: 10.16383/j.aas.c230584
              Shi Xia-Sheng, Ren Lu, Sun Chang-Yin. Distributed adaptive generalized Nash equilibrium algorithm for aggregative games. Acta Automatica Sinica, 2024, 50(6): 1?11 doi: 10.16383/j.aas.c230584
              Citation: Shi Xia-Sheng, Ren Lu, Sun Chang-Yin. Distributed adaptive generalized Nash equilibrium algorithm for aggregative games. Acta Automatica Sinica, 2024, 50(6): 1?11 doi: 10.16383/j.aas.c230584

              自適應分布式聚合博弈廣義納什均衡算法

              doi: 10.16383/j.aas.c230584
              基金項目: 國家自然科學基金創新研究群體科學基金(61921004), 國家自然科學基金重點項目(62236002, 62136008), 國家自然科學基金(62303009)資助
              詳細信息
                作者簡介:

                時俠圣:安徽大學人工智能學院博士后. 2020年獲得浙江大學控制科學與控制工程博士學位. 主要研究方向為分布式協同優化和網絡化系統. E-mail: shixiasheng@zju.edu.cn

                任璐:安徽大學人工智能學院講師. 2021年獲得東南大學控制科學與工程博士學位. 主要研究方向為多智能體系統一致性控制, 復雜動態網絡的同步. E-mail: penny_lu@ahu.edu.cn

                孫長銀:安徽大學人工智能學院教授. 1996年獲得四川大學應用數學專業理學學士學位. 分別于2001年, 2004年獲得東南大學電子工程專業碩士和博士學位. 主要研究方向為智能控制, 飛行器控制, 模式識別和優化理論. 本文通信作者. E-mail: cysun@seu.edu.cn

              Distributed Adaptive Generalized Nash Equilibrium Algorithm for Aggregative Games

              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: 隨著信息物理系統技術的發展, 面向多智能體系統的分布式協同優化問題得到廣泛研究. 主要研究面向多智能體系統的受約束分布式聚合博弈問題, 其中局部智能體成本函數受到全局聚合項約束和全局等式耦合約束. 首先, 面向一階積分型多智能體系統設計一種基于估計梯度下降的納什均衡求解算法. 其中, 利用多智能體系統平均一致性方法設計一種自適應估計策略, 以實現全局聚合項約束分布式估計. 并據此計算出梯度函數估計值. 其次, 利用狀態反饋策略和輸出反饋策略將上述算法推廣至狀態信息可測和狀態信息不可測一般異構線性多智能體系統. 最后, 利用拉薩爾不變性原理證實上述算法收斂性, 并提供多組案例仿真用以驗證算法有效性.
              • 圖  1  算法(9)的狀態$ x_i$軌跡

                Fig.  1  The state trajectories $ x_i$in algorithm (9)

                圖  2  算法(9)的自適應權重$ \alpha_{ij}$軌跡

                Fig.  2  The trajectories of the adaptive weight $ \alpha_{ij}$ in algorithm (9)

                圖  3  不同算法的收斂速度軌跡

                Fig.  3  The convergence rate trajectories of different algorithms

                圖  4  不同控制參數值下算法(9)的收斂速度軌跡

                Fig.  4  The convergence rate trajectories of algorithm (9) under different control parameters

                圖  5  算法(26)的輸出$ y_i$軌跡

                Fig.  5  The output trajectories $ y_i$ in algorithm (26)

                圖  6  算法(26)的狀態觀測誤差軌跡

                Fig.  6  The trajectories of state observer error in algorithm (26)

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                        • 收稿日期:  2023-09-19
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