多个体系统的聚集行为建模和仿真研究
摘要
本文研究多个体系统的聚集问题。近年来,多个体系统的研究工作已成为一个研究热点。这主要是由于多个体系统的广泛应用,如多个无人驾驶飞行器协调运动、鸟群的飞行、水下航行器的群体行为、分散式传感网络、卫星簇的姿态协调、通讯网络的拥塞控制等。尽管应用背景是不同的,但是它们的基本原理是相似的,即利用个体的局部信息通过简单的控制律使系统达到全局的控制目标。主要研究内容如下：
1、第一章对群体聚集问题的当前研究状况进行了综述。针对于聚集问题,前人提出了哪些一阶模型、二阶模型,并做了哪些方面的工作,得到了什么结果,同时也指出我们接下去所要做的工作。
2、第二章介绍群体聚集问题的一阶模型。关于具有营养面的一阶模型,我们对一类具有常吸引力项与无界排斥力项作用的群体研究了聚集的范围,对系统的稳定性也做了分析。关于具有营养面的一阶加权模型,我们对一类具有线性吸引力项与无界排斥力项作用的群体做了聚集范围的估计。仿真例子证明了理论结果的正确性。
3、为了更加合理描述生物的聚集行为,在第三章中引入了基于牛顿动力学的二阶聚集模型。对于基于位置的二阶模型,我们对一类有线性吸引力项和有界排斥力项作用的群体,研究了群体的聚集范围、最终速度、稳定性等,仿真例子表明给出的群集模型能较好的描述群集现象。对于基于位置和速度的二阶模型,我们对线性吸引力项与有界排斥力项、线性吸引力项与无界排斥力项、常吸引力项与无界排斥力项作用的群体我们也给了理论证明与实验模拟。
Major:Applied mathematics
Speciality:Control theory
Supervisor:Lixin Gao
Author:Dan Jin
This paper investigates the swarm problems of multi-agent systems. In recent years, the problem of coordination and control of multiple agents is becoming one of the hotspots. This is partly due to broad applications of multi-agent systems in many areas including cooperative control of unmanned air vehicles, flocking of birds, schooling for underwater vehicles, distributed sensor net-works, gestural coordination of clustered satellite, crowded control of communicating network, etc. Although the application back-grounds are different, the fundamental principles are very simi-lar, that is, using the local information makes the system arrive a whole object through a simple control-law. The main researching contents are as following:
1. Chapter One summarizes the current researching condition of swarm problems. Concerning the swarm problems, we introduce that which integrator models and double integrator models the former scientists had brought forward, what work they had done, and what results they had got, meanwhile, we point out what work we will go on to do.
2. Chapter Two introduces integrator models of swarm prob-lems. About an integrator model basing on nutrient profiles we study the aggregating bound for constant attraction and un-bounded repulsion, also we analyze the stability for the system. About an weighted model basing on nutrient profiles, we estimated the aggregating bound for linear attraction and unbounded repul-sion. Simulating examples prove the correctness of our results.
3. In order to describe the aggregating behavior of critters more reasonably, we introduce the double integrator swarm model basing on the Newton's law. About the double model only related to the position, we present stability analysis for the case of lin-ear attraction and bounded repulsion considered to characterize swarm cohesiveness. size and ultimate motions, simulations prove that our model could describe the behavior of cohesion efficiently. Concerning the double model related to the position and velocity, we also get the expecting results by academic proofs and simu-lating examples for three cases:linear attraction and bounded repulsion, linear attraction and unbounded repulsion, constant at-traction and unbounded repulsion.
1、第一章对群体聚集问题的当前研究状况进行了综述。针对于聚集问题,前人提出了哪些一阶模型、二阶模型,并做了哪些方面的工作,得到了什么结果,同时也指出我们接下去所要做的工作。
2、第二章介绍群体聚集问题的一阶模型。关于具有营养面的一阶模型,我们对一类具有常吸引力项与无界排斥力项作用的群体研究了聚集的范围,对系统的稳定性也做了分析。关于具有营养面的一阶加权模型,我们对一类具有线性吸引力项与无界排斥力项作用的群体做了聚集范围的估计。仿真例子证明了理论结果的正确性。
3、为了更加合理描述生物的聚集行为,在第三章中引入了基于牛顿动力学的二阶聚集模型。对于基于位置的二阶模型,我们对一类有线性吸引力项和有界排斥力项作用的群体,研究了群体的聚集范围、最终速度、稳定性等,仿真例子表明给出的群集模型能较好的描述群集现象。对于基于位置和速度的二阶模型,我们对线性吸引力项与有界排斥力项、线性吸引力项与无界排斥力项、常吸引力项与无界排斥力项作用的群体我们也给了理论证明与实验模拟。
Major:Applied mathematics
Speciality:Control theory
Supervisor:Lixin Gao
Author:Dan Jin
This paper investigates the swarm problems of multi-agent systems. In recent years, the problem of coordination and control of multiple agents is becoming one of the hotspots. This is partly due to broad applications of multi-agent systems in many areas including cooperative control of unmanned air vehicles, flocking of birds, schooling for underwater vehicles, distributed sensor net-works, gestural coordination of clustered satellite, crowded control of communicating network, etc. Although the application back-grounds are different, the fundamental principles are very simi-lar, that is, using the local information makes the system arrive a whole object through a simple control-law. The main researching contents are as following:
1. Chapter One summarizes the current researching condition of swarm problems. Concerning the swarm problems, we introduce that which integrator models and double integrator models the former scientists had brought forward, what work they had done, and what results they had got, meanwhile, we point out what work we will go on to do.
2. Chapter Two introduces integrator models of swarm prob-lems. About an integrator model basing on nutrient profiles we study the aggregating bound for constant attraction and un-bounded repulsion, also we analyze the stability for the system. About an weighted model basing on nutrient profiles, we estimated the aggregating bound for linear attraction and unbounded repul-sion. Simulating examples prove the correctness of our results.
3. In order to describe the aggregating behavior of critters more reasonably, we introduce the double integrator swarm model basing on the Newton's law. About the double model only related to the position, we present stability analysis for the case of lin-ear attraction and bounded repulsion considered to characterize swarm cohesiveness. size and ultimate motions, simulations prove that our model could describe the behavior of cohesion efficiently. Concerning the double model related to the position and velocity, we also get the expecting results by academic proofs and simu-lating examples for three cases:linear attraction and bounded repulsion, linear attraction and unbounded repulsion, constant at-traction and unbounded repulsion.
引文
[1]A. Fax and R. M. Murray, Information flow and cooperative control of vehicle formation, IEEE Transactions on Automatic Control 49(9):1453-1464,2004
[2]A. Jadbabaie, J. Lin, and A. Stephen Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transaction on Automatic Control,48(6):988-1001,2003
[3]A. Mogilner, L. Edelstein-Keshet, L. Bent, A. Spiros, Mutual interactions, potentials, and individual distance in a social aggregation, J. Math. Boil., 47:353-389,2003
[4]C. M.Breder, Equations descriptive of fish schools and other animal aggre-gations, Ecology,35(3):361-370,1954
[5]C. W. Reynolds, Flocks, herds, and schools:a distributed behavioral model, Computer Graphics, ACM SIGGRAPH'87 Conference Proceedings, 21(4):25-34,1987
[6]Herbert G.Tanner, Ali Jadbabaie, and Geroge J.Pappas, Flocking in fixed and switching networks, Automation and computing,3(1):8-16,2006
[7]H.-S. Niwa, Mathematical model for the size distribution of fish schools, Computers Math. Applic.,32(11):79-88,1996
[8]H. S. Niwa, Newtonian dynamical approach to fish schooling, J. theor. Biol.,181:47-63,1996
[9]H.-S. Niwa, Self-organizing approach to fish schooling, J.Theor. Biol., 171:123-136,1996
[10]J. Bender and R. Fenton, On the flow capacity of antomated highways, Transport. Sci.,4:52-63,1970
[11]K. M. Passino, Biomimicry of bacterial foraging for distributed optimiza-tion and control, IEEE control syst. Mag,22:52-67,2002
[12]K. Warbuton and J. Lazarus, Tendency-distance models of social cohesion in animal groups, J.Theoret. Biolo.,150:473-488,1991
[13]L. Chen and L. Xu, Collective behavior of an anisotropic swarm model based on unbounded repulsion in social potential fields, Computational Intelligence and Bioinformatics,4115:164-173,2006
[14]L. Gao, D. Cheng and Y. Hong, On local control strategies for groups of mobile autonomous agents, Proceeding of the 24th Chinese Control Con-ference,2005
[15]L. Wang, H. Shi, T. Chu, etal, Aggregation of foraging swarms, Computer Science,3339/2004(0302-9743):766-777,2004
[16]Reza Olfati-Saber, Flocking for multi-agent dynamic systems:Algorithms and theory, IEEE Transactions on Automatic Control,51(3),2006
[17]Reza Olfati-Saber and Richard M. Murray, Consensus problems in networks of agents with switching topology and time-delays, IEEE Transaction on Automatic Control 49(9),2004
[18]R. Horn and C. R. Johnson, Matrix Analysis. New York:Cambridge Univ. Press,1985
[19]S. M. Chen and H. J. Fang, An improved cooperative tracking model used for large-scale social foraging swarm, ACTA AUTOMATIC SINICA.32(1), 2006
[20]T. Chu. L. Wang and S. Mu, Collective behavior of an anisotropic swarm model. The 16th International Symposium on Mathematical Theory of Net-works and Systems, Leuven, Belgium.2004
[21]V. Gazi and K. M. Passino, Stability analysis of swarms, IEEE Transac-tions on Automatic Control,48:692-697.2003
[22]V. Gazi and K. M. Passino, A class of attractions/repulsion functions for stable swarm aggregations, Int. J. Control,77(18):1567-1579,2004
[23]Veysel Gazi and Kevin M. Passino, Stability analysis of social foraging swarms, IEEE Transactions on Systems, Man, and Cybernetics-part B: Cybernetics,34(1),2004
[24]Veysal Gazi, Swarm aggregations using artificial potentials and sliding mode control. Proceedings of the 42th IEEE Conference on Decision and Control,2(9-12):2041-2046,2003
W. Ren and Randal. W. Beard, Consensus of information under dynami-cally changing interaction topologies, American control conference,2004
[26]X. Tu, Artificial animals for computer animation:biomechanics, locomo-tion, percerption and behavior, Lecture notes in computer science,1635, Springer-Verlag,1999
[27]Y. Hong, L. X. Gao and D. Cheng, Lyapunov-based approach to multi-agent systems with switching jointly-connected interconnection, IEEE Transactions on Automatic Control,52(5),2007
[28]Y. Hong, J. Hu and L. Gao, Tracking control for multi-agent consensus with an active leader and variable topology, Automatica,42:1177-1182,2006
[29]Y. Liu and K. M. Passino, Stable social foraging swarms in a noisy envi-ronment, IEEE Transactions on Automatic Control,49(1):1453-1464,2004
[30]陈世名,方华京,大规模智能群体的建模及稳定性分析,Control and De-cision,20(5),2005
[31]戴华,矩阵论,北京：科学出版社,2004
[32]郑大钟,线性系统理论,北京：清华大学出版社,2002
[2]A. Jadbabaie, J. Lin, and A. Stephen Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transaction on Automatic Control,48(6):988-1001,2003
[3]A. Mogilner, L. Edelstein-Keshet, L. Bent, A. Spiros, Mutual interactions, potentials, and individual distance in a social aggregation, J. Math. Boil., 47:353-389,2003
[4]C. M.Breder, Equations descriptive of fish schools and other animal aggre-gations, Ecology,35(3):361-370,1954
[5]C. W. Reynolds, Flocks, herds, and schools:a distributed behavioral model, Computer Graphics, ACM SIGGRAPH'87 Conference Proceedings, 21(4):25-34,1987
[6]Herbert G.Tanner, Ali Jadbabaie, and Geroge J.Pappas, Flocking in fixed and switching networks, Automation and computing,3(1):8-16,2006
[7]H.-S. Niwa, Mathematical model for the size distribution of fish schools, Computers Math. Applic.,32(11):79-88,1996
[8]H. S. Niwa, Newtonian dynamical approach to fish schooling, J. theor. Biol.,181:47-63,1996
[9]H.-S. Niwa, Self-organizing approach to fish schooling, J.Theor. Biol., 171:123-136,1996
[10]J. Bender and R. Fenton, On the flow capacity of antomated highways, Transport. Sci.,4:52-63,1970
[11]K. M. Passino, Biomimicry of bacterial foraging for distributed optimiza-tion and control, IEEE control syst. Mag,22:52-67,2002
[12]K. Warbuton and J. Lazarus, Tendency-distance models of social cohesion in animal groups, J.Theoret. Biolo.,150:473-488,1991
[13]L. Chen and L. Xu, Collective behavior of an anisotropic swarm model based on unbounded repulsion in social potential fields, Computational Intelligence and Bioinformatics,4115:164-173,2006
[14]L. Gao, D. Cheng and Y. Hong, On local control strategies for groups of mobile autonomous agents, Proceeding of the 24th Chinese Control Con-ference,2005
[15]L. Wang, H. Shi, T. Chu, etal, Aggregation of foraging swarms, Computer Science,3339/2004(0302-9743):766-777,2004
[16]Reza Olfati-Saber, Flocking for multi-agent dynamic systems:Algorithms and theory, IEEE Transactions on Automatic Control,51(3),2006
[17]Reza Olfati-Saber and Richard M. Murray, Consensus problems in networks of agents with switching topology and time-delays, IEEE Transaction on Automatic Control 49(9),2004
[18]R. Horn and C. R. Johnson, Matrix Analysis. New York:Cambridge Univ. Press,1985
[19]S. M. Chen and H. J. Fang, An improved cooperative tracking model used for large-scale social foraging swarm, ACTA AUTOMATIC SINICA.32(1), 2006
[20]T. Chu. L. Wang and S. Mu, Collective behavior of an anisotropic swarm model. The 16th International Symposium on Mathematical Theory of Net-works and Systems, Leuven, Belgium.2004
[21]V. Gazi and K. M. Passino, Stability analysis of swarms, IEEE Transac-tions on Automatic Control,48:692-697.2003
[22]V. Gazi and K. M. Passino, A class of attractions/repulsion functions for stable swarm aggregations, Int. J. Control,77(18):1567-1579,2004
[23]Veysel Gazi and Kevin M. Passino, Stability analysis of social foraging swarms, IEEE Transactions on Systems, Man, and Cybernetics-part B: Cybernetics,34(1),2004
[24]Veysal Gazi, Swarm aggregations using artificial potentials and sliding mode control. Proceedings of the 42th IEEE Conference on Decision and Control,2(9-12):2041-2046,2003
W. Ren and Randal. W. Beard, Consensus of information under dynami-cally changing interaction topologies, American control conference,2004
[26]X. Tu, Artificial animals for computer animation:biomechanics, locomo-tion, percerption and behavior, Lecture notes in computer science,1635, Springer-Verlag,1999
[27]Y. Hong, L. X. Gao and D. Cheng, Lyapunov-based approach to multi-agent systems with switching jointly-connected interconnection, IEEE Transactions on Automatic Control,52(5),2007
[28]Y. Hong, J. Hu and L. Gao, Tracking control for multi-agent consensus with an active leader and variable topology, Automatica,42:1177-1182,2006
[29]Y. Liu and K. M. Passino, Stable social foraging swarms in a noisy envi-ronment, IEEE Transactions on Automatic Control,49(1):1453-1464,2004
[30]陈世名,方华京,大规模智能群体的建模及稳定性分析,Control and De-cision,20(5),2005
[31]戴华,矩阵论,北京：科学出版社,2004
[32]郑大钟,线性系统理论,北京：清华大学出版社,2002