自適應分布式聚合博弈廣義納什均衡算法

時(shí)俠圣; 任璐; 孫長(cháng)銀

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

時(shí)俠圣^{1, 2, 3,},
任璐^{1, 2, 3,},
孫長(cháng)銀^{1, 2, 3,}

1.
安徽大學(xué)自主無(wú)人系統技術(shù)教育部工程研究中心合肥 230601
2.
安徽大學(xué)安徽省無(wú)人系統與智能技術(shù)工程研究中心合肥 230601
3.
安徽大學(xué)人工智能學(xué)院合肥 230601

基金項目: 國家自然科學(xué)基金創(chuàng )新研究群體科學(xué)基金(61921004), 國家自然科學(xué)基金重點(diǎn)項目(62236002, 62136008), 國家自然科學(xué)基金(62303009)資助

詳細信息

作者簡(jiǎn)介:
時(shí)俠圣：安徽大學(xué)人工智能學(xué)院博士后. 2020年獲得浙江大學(xué)控制科學(xué)與控制工程專(zhuān)業(yè)博士學(xué)位. 主要研究方向為分布式協(xié)同優(yōu)化和網(wǎng)絡(luò )化系統. E-mail: shixiasheng@zju.edu.cn

任璐：安徽大學(xué)人工智能學(xué)院講師. 2021年獲得東南大學(xué)控制科學(xué)與工程專(zhuān)業(yè)博士學(xué)位. 主要研究方向為多智能體系統一致性控制, 復雜動(dòng)態(tài)網(wǎng)絡(luò )的同步. E-mail: penny_lu@ahu.edu.cn

孫長(cháng)銀：安徽大學(xué)人工智能學(xué)院教授. 1996年獲得四川大學(xué)應用數學(xué)專(zhuān)業(yè)學(xué)士學(xué)位. 分別于2001年, 2004年獲得東南大學(xué)電子工程專(zhuān)業(yè)碩士和博士學(xué)位. 主要研究方向為智能控制, 飛行器控制, 模式識別和優(yōu)化理論. 本文通信作者. E-mail: cysun@seu.edu.cn

計量
- 文章訪(fǎng)問(wèn)數: 657
- HTML全文瀏覽量: 252
- PDF下載量: 158
- 被引次數: 0
出版歷程
- 收稿日期: 2023-09-19
- 錄用日期: 2024-01-23
- 網(wǎng)絡(luò )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: 隨著(zhù)信息物理系統技術(shù)的發(fā)展, 面向多智能體系統的分布式協(xié)同優(yōu)化問(wèn)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(wèn)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(shí)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(tài)反饋策略和輸出反饋策略將上述算法推廣至狀態(tài)信息可測和狀態(tài)信息不可測一般線(xiàn)性異構多智能體系統. 最后, 利用拉薩爾不變性原理證實(shí)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.
- 聚合博弈 /
- 自適應 /
- 比例積分 /
- 梯度跟蹤 /
- 一般線(xiàn)性多智能體系統
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

圖 1 本文算法的狀態(tài)$ x_i$軌跡

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

下載: 全尺寸圖片幻燈片

圖 2 本文算法的自適應權重$ \alpha_{ij}$軌跡

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

下載: 全尺寸圖片幻燈片

圖 3 不同算法的輸出收斂誤差軌跡

Fig. 3 The output convergence error trajectories of different algorithms

下載: 全尺寸圖片幻燈片

圖 4 不同控制參數值下本文算法的輸出收斂誤差軌跡

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

下載: 全尺寸圖片幻燈片

圖 5 本文算法的輸出$ y_i$軌跡

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

下載: 全尺寸圖片幻燈片

圖 6 本文算法的狀態(tài)觀(guān)測誤差軌跡

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

下載: 全尺寸圖片幻燈片

<button id="qm3rj"><thead id="qm3rj"></thead></button>

亚洲第一网址_国产国产人精品视频69_久久久久精品视频_国产精品第九页

參考文獻(51)

[1]	Cornes R. Aggregative environmental games. Environmental and Resource Economics, 2016, 63(2): 339?365 doi: 10.1007/s10640-015-9900-6
[2]	Barrera J, Garcia A. Dynamic incentives for congestion control. IEEE Transactions on Automatic Control, 2015, 60(2): 299?310 doi: 10.1109/TAC.2014.2348197
[3]	耿遠卓, 袁利, 黃煌, 湯亮. 基于終端誘導強化學(xué)習的航天器軌道追逃博弈. 自動(dòng)化學(xué)報, 2023, 49(5): 974?984 Geng Yuan-Zhuo, Yuan Li, Huang Huang, Tang Liang. Terminal-guidance based reinforcement-learning for orbital pursuit-evasion game of the spacecraft. Acta Automatica Sinica, 2023, 49(5): 974?984
[4]	Ye M J, Han Q L, Ding L, Xu S Y. Distributed Nash equilibrium seeking in games with partial decision information: A survey. Proceedings of the IEEE, 2023, 111(2): 140?157 doi: 10.1109/JPROC.2023.3234687
[5]	王龍, 黃鋒. 多智能體博弈、學(xué)習與控制. 自動(dòng)化學(xué)報, 2023, 49(3): 580?613 Wang Long, Huang Feng. An interdisciplinary survey of multi-agent games, learning, and control. Acta Automatica Sinica, 2023, 49(3): 580?613
[6]	陳靈敏, 馮宇, 李永強. 基于距離信息的追逃策略: 信念狀態(tài)連續隨機博弈. 自動(dòng)化學(xué)報, 2024, 50(4): 828?840 Chen Ling-Min, Feng Yu, Li Yong-Qiang. Distance information based pursuit-evasion strategy: Continuous stochastic game with belief state. Acta Automatica Sinica, 2024, 50(4): 828?840
[7]	Koshal J, Nedi? A, Shanbhag U V. Distributed algorithms for aggregative games on graphs. Operations Research, 2016, 64(3): 680?704 doi: 10.1287/opre.2016.1501
[8]	Grammatico S. Dynamic control of agents playing aggregative games with coupling constraints. IEEE Transactions on Automatic Control, 2017, 62(9): 4537?4548 doi: 10.1109/TAC.2017.2672902
[9]	Huang S J, Lei J L, Hong Y G. A linearly convergent distributed Nash equilibrium seeking algorithm for aggregative games. IEEE Transactions on Automatic Control, 2023, 68(3): 1753?1759 doi: 10.1109/TAC.2022.3154356
[10]	Ye M J, Hu G Q, Xie L H, Xu S Y. Differentially private distributed Nash equilibrium seeking for aggregative games. IEEE Transactions on Automatic Control, 2022, 67(5): 2451?2458 doi: 10.1109/TAC.2021.3075183
[11]	Shi C X, Yang G H. Distributed Nash equilibrium computation in aggregative games: An event-triggered algorithm. Information Sciences, 2019, 489: 289?302 doi: 10.1016/j.ins.2019.03.047
[12]	Parise F, Gentile B, Lygeros J. A distributed algorithm for almost-Nash equilibria of average aggregative games with coupling constraints. IEEE Transactions on Control of Network Systems, 2020, 7(2): 770?782 doi: 10.1109/TCNS.2019.2944300
[13]	Sun C, Hu G Q. Nash equilibrium seeking with prescribed performance. Control Theory and Technology, 2023, 21(3): 437?447 doi: 10.1007/s11768-023-00169-4
[14]	Belgioioso G, Nedic A, Grammatico S. Distributed generalized Nash equilibrium seeking in aggregative games on time-varying networks. IEEE Transactions on Automatic Control, 2021, 66(5): 2061?2075 doi: 10.1109/TAC.2020.3005922
[15]	Pan W, Xu X L, Lu Y, Zhang W D. Distributed Nash equilibrium learning for average aggregative games: Harnessing smoothness to accelerate the algorithm. IEEE Systems Journal, 2023, 17(3): 4855?4865 doi: 10.1109/JSYST.2023.3264791
[16]	Zhang P, Yuan Y, Liu H P, Gao Z. Nash equilibrium seeking for graphic games with dynamic event-triggered mechanism. IEEE Transactions on Cybernetics, 2022, 52(11): 12604?12611 doi: 10.1109/TCYB.2021.3071746
[17]	Fang X, Wen G H, Zhou J L, Lv J H, Chen G R. Distributed Nash equilibrium seeking for aggregative games with directed communication graphs. IEEE Transactions on Circuits and Systems I: Regular Papers, 2022, 69(8): 3339?3352 doi: 10.1109/TCSI.2022.3168770
[18]	Shi X L, Wen G H, Yu X H. Finite-time convergent algorithms for time-varying distributed optimization. IEEE Control Systems Letters, 2023, 7: 3223?3228 doi: 10.1109/LCSYS.2023.3312297
[19]	時(shí)俠圣, 楊濤, 林志赟, 王雪松. 基于連續時(shí)間的二階多智能體分布式資源分配算法. 自動(dòng)化學(xué)報, 2021, 47(8): 2050?2060 Shi Xia-Sheng, Yang Tao, Lin Zhi-Yun, Wang Xue-Song. Distributed resource allocation algorithm for second-order multi-agent systems in continuous-time. Acta Automatica Sinica, 2021, 47(8): 2050?2060
[20]	An L W, Yang G H. Distributed optimal coordination for heterogeneous linear multiagent systems. IEEE Transactions on Automatic Control, 2022, 67(12): 6850?6857 doi: 10.1109/TAC.2021.3133269
[21]	Shi J, Ye M J. Distributed optimal formation control for unmanned surface vessels by a regularized game-based approach. IEEE/CAA Journal of Automatica Sinica, 2024, 11(1): 276?278 doi: 10.1109/JAS.2023.123930
[22]	王鼎. 一類(lèi)離散動(dòng)態(tài)系統基于事件的迭代神經(jīng)控制. 工程科學(xué)學(xué)報, 2022, 44(3): 411?419 Wang Ding. Event-based iterative neural control for a type of discrete dynamic plant. Chinese Journal of Engineering, 2022, 44(3): 411?419
[23]	王鼎. 基于學(xué)習的魯棒自適應評判控制研究進(jìn)展. 自動(dòng)化學(xué)報, 2019, 45(6): 1031?1043 Wang Ding. Research progress on learning-based robust adaptive critic control. Acta Automatica Sinica, 2019, 45(6): 1031?1043
[24]	Ye M J, Hu G Q. Adaptive approaches for fully distributed Nash equilibrium seeking in networked games. Automatica, 2021, 129: Article No. 109661 doi: 10.1016/j.automatica.2021.109661
[25]	Ye M J. Distributed Nash equilibrium seeking for games in systems with bounded control inputs. IEEE Transactions on Automatic Control, 2021, 66(8): 3833?3839 doi: 10.1109/TAC.2020.3027795
[26]	Zhang K J, Fang X, Wang D D, Lv Y Z, Yu X H. Distributed Nash equilibrium seeking under event-triggered mechanism. IEEE Transactions on Circuits and Systems II: Express Briefs, 2021, 68(11): 3441?3445
[27]	Liu P, Xiao F, Wei B, Yu M. Nash equilibrium seeking for individual linear dynamics subject to limited communication resource. Systems and Control Letters, 2022, 161: Article No. 105162
[28]	張苗苗, 葉茂嬌, 鄭元世. 預設時(shí)間下的分布式優(yōu)化和納什均衡點(diǎn)求解. 控制理論與應用, 2022, 39(8): 1397?1406 doi: 10.7641/CTA.2022.10604 Zhang Miao-Miao, Ye Mao-Jiao, Zheng Yuan-Shi. Prescribed-time distributed optimization and Nash equilibrium seeking. Control Theory and Applications, 2022, 39(8): 1397?1406 doi: 10.7641/CTA.2022.10604
[29]	Zou Y, Huang B M, Meng Z Y, Ren W. Continuous-time distributed Nash equilibrium seeking algorithms for non-cooperative constrained games. Automatica, 2021, 127: Article No. 109535 doi: 10.1016/j.automatica.2021.109535
[30]	Zhu Y N, Yu W W, Ren W, Wen G H, Gu J P. Generalized Nash equilibrium seeking via continuous-time coordination dynamics over digraph. IEEE Transactions on Control of Network Systems, 2021, 8(2): 1023?1033 doi: 10.1109/TCNS.2021.3056034
[31]	Deng Z H, Liu Y Y, Chen T. Generalized Nash equilibrium seeking algorithm design for distributed constrained noncooperative games with second-order players. Automatica, 2022, 141: Article No. 110317 doi: 10.1016/j.automatica.2022.110317
[32]	Shi X S, Su Y X, Huang D R, Sun C Y. Distributed aggregative game for multi-agent systems with heterogeneous integrator dynamics. IEEE Transactions on Circuits and Systems II: Express Briefs, 2024, 71(4): 2169?2173
[33]	Liang S, Yi P, Hong Y G, Peng K X. Exponentially convergent distributed Nash equilibrium seeking for constrained aggregative games. Autonomous Intelligent Systems, 2022, 2(1): Article No. 6 doi: 10.1007/s43684-022-00024-4
[34]	Zhu Y N, Yu W W, Wen G H, Chen G R. Distributed Nash equilibrium seeking in an aggregative game on a directed graph. IEEE Transactions on Automatic Control, 2021, 66(6): 2746?2753 doi: 10.1109/TAC.2020.3008113
[35]	Cheng M F, Wang D, Wang X D, Wu Z G, Wang W. Distributed aggregative optimization via finite-time dynamic average consensus. IEEE Transactions on Network Science and Engineering, 2023, 10(6): 3223?3231
[36]	Wang X F, Teel A R, Sun X M, Liu K Z, Shao G R. A distributed robust two-time-scale switched algorithm for constrained aggregative games. IEEE Transactions on Automatic Control, 2023, 68(11): 6525?6540 doi: 10.1109/TAC.2023.3240981
[37]	梁銀山, 梁舒, 洪奕光. 非光滑聚合博弈納什均衡的分布式連續時(shí)間算法. 控制理論與應用, 2018, 35(5): 593?600 doi: 10.7641/CTA.2017.70617 Liang Yin-Shan, Liang Shu, Hong Yi-Guang. Distributed continuous-time algorithm for Nash equilibrium seeking of nonsmooth aggregative games. Control Theory & Applications, 2018, 35(5): 593?600 doi: 10.7641/CTA.2017.70617
[38]	Deng Z H, Nian X H. Distributed algorithm design for aggregative games of disturbed multiagent systems over weight-balanced digraphs. International Journal of Robust and Nonlinear Control, 2018, 28(17): 5344?5357 doi: 10.1002/rnc.4316
[39]	Lin W T, Chen G, Li C J, Huang T W. Distributed generalized Nash equilibrium seeking: A singular perturbation-based approach. Neurocomputing, 2022, 482: 278?286 doi: 10.1016/j.neucom.2021.11.073
[40]	Deng Z H, Nian X H. Distributed generalized Nash equilibrium seeking algorithm design for aggregative games over weight-balanced digraphs. IEEE Transactions on Neural Networks and Learning Systems, 2019, 30(3): 695?706 doi: 10.1109/TNNLS.2018.2850763
[41]	Liang S, Yi P, Hong Y G. Distributed Nash equilibrium seeking for aggregative games with coupled constraints. Automatica, 2017, 85: 179?185 doi: 10.1016/j.automatica.2017.07.064
[42]	Deng Z H. Distributed generalized Nash equilibrium seeking algorithm for nonsmooth aggregative games. Automatica, 2021, 132: Article No. 109794 doi: 10.1016/j.automatica.2021.109794
[43]	Zhang Y W, Liang S, Wang X H, Ji H B. Distributed Nash equilibrium seeking for aggregative games with nonlinear dynamics under external disturbances. IEEE Transactions on Cybernetics, 2020, 50(12): 4876?4885 doi: 10.1109/TCYB.2019.2929394
[44]	Wang X F, Sun X M, Teel A R, Liu K Z. Distributed robust Nash equilibrium seeking for aggregative games under persistent attacks: A hybrid systems approach. Automatica, 2020, 122: Article No. 109255 doi: 10.1016/j.automatica.2020.109255
[45]	Deng Z H. Distributed Nash equilibrium seeking for aggregative games with second-order nonlinear players. Automatica, 2022, 135: Article No. 109980 doi: 10.1016/j.automatica.2021.109980
[46]	Deng Z H, Liang S. Distributed algorithms for aggregative games of multiple heterogeneous Euler-Lagrange systems. Automatica, 2019, 99: 246?252 doi: 10.1016/j.automatica.2018.10.041
[47]	Deng Z H. Distributed algorithm design for aggregative games of Euler-Lagrange systems and its application to smart grids. IEEE Transactions on Cybernetics, 2022, 52(8): 8315?8325 doi: 10.1109/TCYB.2021.3049462
[48]	Liu X Y, Zhang Y W, Wang X H, Ji H B. Distributed Nash equilibrium seeking design in network of uncertain linear multi-agent systems. In: Proceedings of the 16th IEEE International Conference on Control & Automation. Sapporo, Japan: IEEE, 2020. 147?152
[49]	Li L, Yu Y, Li X X, Xie L H. Exponential convergence of distributed optimization for heterogeneous linear multi-agent systems over unbalanced digraphs. Automatica, 2022, 141: Article No. 110259 doi: 10.1016/j.automatica.2022.110259
[50]	Liu Y, Yang G H. Distributed robust adaptive optimization for nonlinear multiagent systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(2): 1046?1053 doi: 10.1109/TSMC.2019.2894948
[51]	Li S L, Nian X H, Deng Z H, Chen Z, Meng Q. Distributed resource allocation of second-order nonlinear multiagent systems. International Journal of Robust and Nonlinear Control, 2021, 31(11): 5330?5342 doi: 10.1002/rnc.5543