多智能体系统的自适应群集分布式优化（英文）
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摘要
本文对具有非线性函数群集行为的连续时间多智能体系统的分布式优化问题进行了研究.这篇文章旨在说明所有智能体的速度和位置可以渐近一致,并且速度达到最优,从而使局部代价函数之和最小.在这个研究中,每个智能体只知道与其对应的代价函数.首先,文章对局部代价函数作了一些假设;第二,设计了一个分布式控制法则和更新律,该控制法则仅仅依赖于自己和邻居的速度.然后证明了多智能体系统的稳定性以及在最小化局部代价函数之和的同时所有智能体可以避免碰撞.最后,使用一个仿真案例来说明所获得的分析结果.
A distributed optimization problem is investigated for continuous-time multi-agent systems with flocking behavior of a nonlinear continuous function. This paper aims at showing that the velocities and positions of all agents can be the same asymptotically and the velocity is optimal, thus minimizing the sum of local cost functions. In this study, each cost function can only be known to its corresponding agent. Firstly, the paper makes some assumptions about the local cost function; Secondly, a distributed control rule and updating laws are designed, in which each agent depends only on its own velocity and neighbor's velocity. Then, the stability of the multi-agent systems is proved and the agents can avoid inter-agent collision while minimizing the sum of local cost functions. Finally, using a simulation case to illustrate the obtained analytical results.
A distributed optimization problem is investigated for continuous-time multi-agent systems with flocking behavior of a nonlinear continuous function. This paper aims at showing that the velocities and positions of all agents can be the same asymptotically and the velocity is optimal, thus minimizing the sum of local cost functions. In this study, each cost function can only be known to its corresponding agent. Firstly, the paper makes some assumptions about the local cost function; Secondly, a distributed control rule and updating laws are designed, in which each agent depends only on its own velocity and neighbor's velocity. Then, the stability of the multi-agent systems is proved and the agents can avoid inter-agent collision while minimizing the sum of local cost functions. Finally, using a simulation case to illustrate the obtained analytical results.
引文
[1]HONG Y,CHEN G,BUSHNELL L.Distributed observers design for leader-follower control of multi-agent networks.Automatica,2008,44(3):846-850.
[2]SONG Q,CAO J,YU W.Second-order leader-following consensus of nonlinear multi-agent systems via pinning control.Systems&Control Letters,2010,59(9):553-562.
[3]ZHAO Y,DUAN Z,WEN G,et al.Distributed finite-time tracking of multiple non-identical second-order nonlinear systems with settling time estimation.Automatica,2016,64:86-93.
[4]SU H,CHEN G,WANG X,et al.Adaptive second-order consensus of networked mobile agents with nonlinear dynam.Automatica,2011,47(2):368-375.
[5]ZHAO Y,LIU Y,LI Z,et al.Distributed average tracking for multiple signals generated by linear dynamical systems:An edge-based framework.Automatica,2017,75:158-166.
[6]NEDIC A,OZDAGLAR A.Distributed subgradient methods for multi-agent optimization.IEEE Transactions on Automatic Control,2009,54(1):48-61.
[7]NEDIC A,OLSHEVSKY A.Distributed optimization over timevarying directed graphs.IEEE Transactions on Automatic Control,2014,60(3):601-615.
[8]NEDIC A,OZDAGLAR A,PARRILO P.Constrained consensus and optimization in multi-agent networks.IEEE Transactions on Automatic Control,2010,55(4):922-938.
[9]JOHANSSON B,KEVICZKY T,JOHANSSON M,et al.Subgradient methods and consensus algorithms for solving convex optimization problems.Proceedings of the 47th IEEE Conference on Decision and Control.Cancun,Mexico:IEEE,2008:4185-4190.
[10]LU J,TANG C,REGIER P,et al.Gossip algorithms for convex consensus optimization over networks.IEEE Transactions on Automatic Control,2012,56(12):2917-2923.
[11]WANG J,ELIA N.A control perspective for centralized and distributed convex optimization.Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference.Orlando,FL,USA:IEEE,2011:3800-3805.
[12]GHARESIFARD B,CORTES J.Distributed continuous-time convex optimization on weight-balanced digraphs.IEEE Transactions on Automatic Control,2012,59(3):781-786.
[13]KIA S,CORTES J,MARTINEZ S.Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication.Automatica,2015,55:254-264.
[14]LIN P,REN W,FARRELL J.Distributed continuous-time optimization:nonuniform gradient gains,finite-time convergence,and convex constraint set.IEEE Transactions on Automatic Control,2016,62(5):2239?-2253.
[15]ZHAO Y,LIU Y,WEN G,et al.Distributed optimization of linear multi-agent systems:edge-and node-based adaptive designs.IEEETransactions on Automatic Control,2017,62(7):3602-3609.
[16]WANG X,HONG Y.Finite-time consensus for multi-agent networks with second-order agent dynamics.IFAC Proceedings Volumes,2008,41(2):15185-15190.
[17]GEORGE K,SUBRAMANIAN K.Adaptive control of a class of nonlinear time-varying systems with multiple models.Control Theory and Technology,2016,14(4):323-334.
[18]ZHANG Y,HONG Y.Distributed optimization design for secondorder multi-agent systems.Proceedings of the 33rd IEEE Control Conference.Nanjing,China:IEEE,2014:1755-1760.
[19]ZHANG Q,LI P,YANG Z,et al.Adaptive flocking of non-linear multi-agents systems with uncertain parameters.IET Control Theory and Applications,2015,9(3):351-357.
[20]YU P,DING L,LIU Z,et al.Leader-follower flocking based on distributed event-triggered hybrid control.International Journal of Robust and Nonlinear Control,2016,26(1):143-153.
[21]YANG Zhengquan,ZHANG Qing,CHEN Zengqiang.Distributed velocity optimization of time-varying functions with flocking behavior.Control Theory&Applications,2017,34(2):1648-1653.(杨正全,张青,陈增强.具有群集行为的时变函数分布式优化.控制理论与应用,2017,34(2):1648-1653.)
[22]CHUNG F.Spectral graph theory.Conference Board of the mathematical sciences by the American Mathematical Society.California,USA:American Mathematical Society,1997.
[23]BOYD,VANDENBERGHE,FAYBUSOVICH.Convex optimization.IEEE Transactions on Automatic Control,2006,51(11):1859-1865.
[24]OLFATISABER R,MURRAY R.Consensus problems in networks of agents with switching topology and time-delays.IEEE Transactions on Automatic Control,2004,49(9):1520-1533.
[25]ZAVLANOS M,JADBABAIE A,PAPPAS G.Flocking while preserving network connectivity.Proceedings of the 46th IEEE conference on Decision and Control.New Orleans,LA,USA:IEEE,2007:2919-2924.
[2]SONG Q,CAO J,YU W.Second-order leader-following consensus of nonlinear multi-agent systems via pinning control.Systems&Control Letters,2010,59(9):553-562.
[3]ZHAO Y,DUAN Z,WEN G,et al.Distributed finite-time tracking of multiple non-identical second-order nonlinear systems with settling time estimation.Automatica,2016,64:86-93.
[4]SU H,CHEN G,WANG X,et al.Adaptive second-order consensus of networked mobile agents with nonlinear dynam.Automatica,2011,47(2):368-375.
[5]ZHAO Y,LIU Y,LI Z,et al.Distributed average tracking for multiple signals generated by linear dynamical systems:An edge-based framework.Automatica,2017,75:158-166.
[6]NEDIC A,OZDAGLAR A.Distributed subgradient methods for multi-agent optimization.IEEE Transactions on Automatic Control,2009,54(1):48-61.
[7]NEDIC A,OLSHEVSKY A.Distributed optimization over timevarying directed graphs.IEEE Transactions on Automatic Control,2014,60(3):601-615.
[8]NEDIC A,OZDAGLAR A,PARRILO P.Constrained consensus and optimization in multi-agent networks.IEEE Transactions on Automatic Control,2010,55(4):922-938.
[9]JOHANSSON B,KEVICZKY T,JOHANSSON M,et al.Subgradient methods and consensus algorithms for solving convex optimization problems.Proceedings of the 47th IEEE Conference on Decision and Control.Cancun,Mexico:IEEE,2008:4185-4190.
[10]LU J,TANG C,REGIER P,et al.Gossip algorithms for convex consensus optimization over networks.IEEE Transactions on Automatic Control,2012,56(12):2917-2923.
[11]WANG J,ELIA N.A control perspective for centralized and distributed convex optimization.Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference.Orlando,FL,USA:IEEE,2011:3800-3805.
[12]GHARESIFARD B,CORTES J.Distributed continuous-time convex optimization on weight-balanced digraphs.IEEE Transactions on Automatic Control,2012,59(3):781-786.
[13]KIA S,CORTES J,MARTINEZ S.Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication.Automatica,2015,55:254-264.
[14]LIN P,REN W,FARRELL J.Distributed continuous-time optimization:nonuniform gradient gains,finite-time convergence,and convex constraint set.IEEE Transactions on Automatic Control,2016,62(5):2239?-2253.
[15]ZHAO Y,LIU Y,WEN G,et al.Distributed optimization of linear multi-agent systems:edge-and node-based adaptive designs.IEEETransactions on Automatic Control,2017,62(7):3602-3609.
[16]WANG X,HONG Y.Finite-time consensus for multi-agent networks with second-order agent dynamics.IFAC Proceedings Volumes,2008,41(2):15185-15190.
[17]GEORGE K,SUBRAMANIAN K.Adaptive control of a class of nonlinear time-varying systems with multiple models.Control Theory and Technology,2016,14(4):323-334.
[18]ZHANG Y,HONG Y.Distributed optimization design for secondorder multi-agent systems.Proceedings of the 33rd IEEE Control Conference.Nanjing,China:IEEE,2014:1755-1760.
[19]ZHANG Q,LI P,YANG Z,et al.Adaptive flocking of non-linear multi-agents systems with uncertain parameters.IET Control Theory and Applications,2015,9(3):351-357.
[20]YU P,DING L,LIU Z,et al.Leader-follower flocking based on distributed event-triggered hybrid control.International Journal of Robust and Nonlinear Control,2016,26(1):143-153.
[21]YANG Zhengquan,ZHANG Qing,CHEN Zengqiang.Distributed velocity optimization of time-varying functions with flocking behavior.Control Theory&Applications,2017,34(2):1648-1653.(杨正全,张青,陈增强.具有群集行为的时变函数分布式优化.控制理论与应用,2017,34(2):1648-1653.)
[22]CHUNG F.Spectral graph theory.Conference Board of the mathematical sciences by the American Mathematical Society.California,USA:American Mathematical Society,1997.
[23]BOYD,VANDENBERGHE,FAYBUSOVICH.Convex optimization.IEEE Transactions on Automatic Control,2006,51(11):1859-1865.
[24]OLFATISABER R,MURRAY R.Consensus problems in networks of agents with switching topology and time-delays.IEEE Transactions on Automatic Control,2004,49(9):1520-1533.
[25]ZAVLANOS M,JADBABAIE A,PAPPAS G.Flocking while preserving network connectivity.Proceedings of the 46th IEEE conference on Decision and Control.New Orleans,LA,USA:IEEE,2007:2919-2924.