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                    基于連續時間的二階多智能體分布式資源分配算法

                    時俠圣 楊濤 林志赟 王雪松

                    時俠圣,  楊濤,  林志赟,  王雪松.  基于連續時間的二階多智能體分布式資源分配算法.  自動化學報,  2021,  47(8): 2050?2060 doi: 10.16383/j.aas.c200968
                    引用本文: 時俠圣,  楊濤,  林志赟,  王雪松.  基于連續時間的二階多智能體分布式資源分配算法.  自動化學報,  2021,  47(8): 2050?2060 doi: 10.16383/j.aas.c200968
                    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 doi: 10.16383/j.aas.c200968
                    Citation: 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 doi: 10.16383/j.aas.c200968

                    基于連續時間的二階多智能體分布式資源分配算法

                    doi: 10.16383/j.aas.c200968
                    基金項目: 國家自然科學基金重大項目(61991403, 61991400), 國家自然科學基金(61976215, 61673344)資助
                    詳細信息
                      作者簡介:

                      時俠圣:中國礦業大學信息與控制工程學院講師. 主要研究方向為分布式協同優化和網絡化系統. E-mail: shixiasheng@cumt.edu.cn

                      楊濤:東北大學流程工業自動化國家重點實驗室教授. 主要研究方向為工業人工智能, 信息物理系統, 分布式協同控制和優化. 本文通信作者. E-mail: yangtao@email.neu.edu.cn

                      林志赟:杭州電子科技大學自動化學院人工智能研究院教授. 主要研究方向為多智能體系統, 機器人與無人系統和網絡化系統. E-mail: linz@hdu.edu.cn

                      王雪松:中國礦業大學信息與控制工程學院教授. 主要研究方向為機器學習, 人工智能, 復雜系統優化及控制. E-mail: wangxuesongcumt@163.com

                    Distributed Resource Allocation Algorithm for Second-order Multi-agent Systems in Continuous-time

                    Funds: Supported by Major Program of the National Natural Science Foundation of China (61991403, 61991400), National Natural Science Foundation of China (61976215, 61673344)
                    More Information
                      Author Bio:

                      SHI Xia-Sheng Lecturer at the School of Information and Control Engineering, China University of Mining and Technology. His research interest covers distributed cooperative optimization and network system

                      YANG Tao Professor at the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. His research interest covers industrial artificial intelligence, cyber physical system, distributed collaborative control and optimization. Corresponding author of this paper

                      LIN Zhi-Yun Professor at the Intelligence, Automation School, Hangzhou Dianzi University. His research interest covers multi-agent systems, unmanned robotic systems, and network systems

                      WANG Xue-Song Professor at the School of Information and Control Engineering, China University of Mining and Technology. His research interest covers machine learning, artificial intelligence, and complex system optimization and control

                    • 摘要:

                      針對二階多智能體系統中的分布式資源分配問題, 本文設計兩種連續時間算法. 基于KKT (Karush?Kuhn?Tucker, 卡羅需?庫恩?塔克)優化條件, 第一種控制算法利用節點局部不等式及其梯度信息來約束節點狀態. 與上述梯度方法不同, 第二種控制算法包括一致性梯度下降法和固定時間收斂映射算子, 其中固定時間收斂映射算子確保算法的節點狀態在固定時間收斂到局部約束集, 一致性梯度下降法目的是確保節點迭代到資源分配問題最優解. 兩種控制算法都對狀態無初始值約束, 且控制參數都是常數. 利用凸優化理論和固定時間李雅普諾夫方法, 分別分析了上述控制策略在有向平衡網絡條件下的漸近和指數收斂性. 最后通過數值仿真驗證了所設計算法在一維和高維資源分配問題的有效性.

                    • 圖  1  案例1中算法(8)的各發電機曲線圖

                      Fig.  1  The trajectories of each generator by algorithm (8) in case 1

                      圖  2  案例1中算法(9)的各發電機曲線圖

                      Fig.  2  The trajectories of each generator by algorithm (9) in case 1

                      圖  3  基于案例1數據的算法性能對比

                      Fig.  3  The comparison between the existence algorithms and ours based on case 1

                      圖  4  案例2中算法 (8)的各節點仿真結果軌跡

                      Fig.  4  The trajectories of each agent by algorithm (8) in case 2

                      圖  5  案例2中算法 (9)各節點仿真結果軌跡

                      Fig.  5  The trajectories of each agent by algorithm (9) in case 2

                      圖  6  基于案例2數據的算法性能對比

                      Fig.  6  The comparison between the existence algorithms and ours based on case 2

                      圖  7  案例3中各發電單元的通信鏈路

                      Fig.  7  The communication links of each generator in case 3

                      圖  8  案例3中算法 (8)的各節點仿真結果軌跡

                      Fig.  8  The trajectories of each agent by algorithm (8) in case 3

                      圖  9  案例3中算法 (9)各節點仿真結果軌跡

                      Fig.  9  The trajectories of each agent by algorithm (9) in case 3

                      圖  10  案例3中算法 (8)和 (9)的收斂速度比較

                      Fig.  10  The convergence rate comparison between algorithms (8) and (9) in case 3

                      表  1  案例1各節點參數

                      Table  1  System parameters in case 1

                      Agent $a_{i1}$ $a_{i2}$ $a_{i3}$ 功率約束 $d_i$ $x_i(0)$
                      1 2 3 0.5 $[20,40]$ 45 40
                      2 1 4 1.5 $[25,35]$ 40 24
                      3 0.5 5 3 $[35,50]$ $25$ 35
                      4 1.5 2 1 $[25,45]$ 35 45
                      5 1 3.5 2.5 $[30,47]$ 30 28
                      6 1.5 4.5 2 $[28,42]$ 40 50
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                    • 收稿日期:  2020-11-22
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