Problems in swarm dynamics and coordinated control

Transcription

1 : (2010) Control Theory & Applications Vol. 27 No. 1 Jan. 2010,,,, (, ) :,.,,.,. : ; ; ; ; ; ; : TP13; TP18; O23; N941 : A Problems in swarm dynamics and coordinated control CHU Tian-guang, YANG Zheng-dong, DENG Kui-ying, WANG Long, XIE Guang-ming (College of Engineering, Key Laboratory of Machine Perception(Ministry of Education), Peking University, Beijing , China) Abstract: Swarming behavior is ubiquitous in nature and society. It is of both theoretical and practical importance to investigate the underlying principles and mechanisms of coordination and cooperation emerging in swarms. This paper discusses some basic issues in swarm dynamics and coordinated control from the perspective of systems and control. Specifically, we review some typical swarm models proposed in the literature, and discuss the roles and effects of connection topology on swarm dynamics, as well as the effects of variable topologies, communication delays, and exogenous influences, etc. We also give some numerical simulation results to demonstrate the complex aggregation-oscillation behavior of swarms in the cases of asymmetric coupling and delayed communication. Key words: swarming behavior; coordinated control; connection topology; communication delay; controllability; convergence; collective oscillation 1 (Introduction) (swarming behavior),.,.,.,.., ( ),, [1, 2]. [3 58]., /,. :.,,.,,., : ; : : ( , , , ); ( ); 863 (2006AA04Z247)

2 1 : 87.,..,.,. 2 (Basic problems),,., +. ( )., ;..,,.,,.,..,., ( ).,., ( )...,.,,,.,,, (, leaderfollowing ).,,,.,.,.,.,,. 3 (Swarm dynamics models), Boid Swarm.,.., Boid (Boid model) 1987 Reynolds Boid [6],. 3 : (collision avoidance), ; (velocity matching), ; (flock centering),., (separation, alignment and cohesion).

3 Boid,. 3.2 (Particle swarm model) Vicsek [7],,.,,., Toner Tu, Navier-Stokes ( ) [8].,., Jadbabaie [9] Vicsek. [10, 11]. Vicsek, Reynolds., Vicsek., Vicsek.,,, (Models based on attractive-repulsive rules).,. Boid,..,., [5],.,.,.,. ẋ i = w ij [ V a ( r ij ) V r ( r ij )]. (1) x i R n i, i = 1,, N; w ij 0 i, j ; V a, V r : R R, ;, r ij = x i x j. [13 18]. (1), w ij = 0 i, j, w ii = 0. w ij = w ji, i, j. W = [w ij ] /. (1),, (1) : ẋ i = f i (x i ) w ij [ V a ( r ij ) V r ( r ij )]. f i (x i ) i.,, ( [13] ).,. [17],,. 3.4 (Models with exogenous effects),.,.,,.., (1) ẋ i = w ij [ V a ( r ij ) V r ( r ij )] + w i0 u i. : u i ; i w i0 = 1, w i0 = 0. u i,, (leader-follower) leader.,, multi-leader

4 1 : 89. [9 29]. 3.5 (Networked systems and graph description),., G = (V, E, A), V ( ), ; E,, ; A,, ( ).., i j, i j.,., leader-following,., ( [35 40] ). 3.6 (Modeling with nonaveraging update rules), [7, 9].,.,,.,..,, ( )...,,.,,.. 4 (Swarm dynamics analysis).,. 4.1 (Roles and effects of coupling topology),,, (, ). (1),, /Lyapunov,,. V a V b,.,.,.,, /Lyapunov,.,,.,,, 1. [18, 51]. (a) 2D

5 90 27 (b) 3D 1 Fig. 1 Swarm trajectories,., /,. [52].,,. [52]., (leader-follower), leader follower, follower,.,, leader.,.,. [53, 54]. 4.2 (Variable topology and dynamic graph),,., [33 47].,., (joint connectivity), [9].,, [35] [40].,.,,.,..,, [53 56] (Effects of communication),., [57].,,.,,,. /, Lyapunov,.,. 2, (a) ( ), (b)., s, [51]. (a) 2 Fig. 2 Swarm with time delay (b) 4.4 (Effects of exogenous actions) ( leader(s)),

6 1 : 91.,. [20 30] leader(s),. [50] leader : leader, ;. leader-follower,. 4.5 (Co-evolution of dynamics and topologies),,.,., [58].,,...,.,.,, ( ),.,.. 5 (Concluding remarks),.,., ( ).,.,,.,,.,. (References): [1] BOABEAU E, DORIGO M, THERAULAZ G. Swarm Intelligence: From Natural to Artificial Systems[M]. Oxford: Oxford University Press, [2] KENNEDY J, EBERHART R C, SHI Y. Swarm Intelligence[M]. San Francisco: Morgan Kaufmann Publishers, [3],. [J]., 2004, 8: 4 7. (CHENG Daizhan, CHEN Hanfu. From swarm to social behavior control[j]. Science & Technology Review, 2004, 8: 4 7.) [4] GUO L, LIU Z, HAN J. Multi-agent systems with local rules: towards a theory of analysis and control[c] //Proceedings of the 25th Chinese Control Conference. Beijing: Beijing Uinversity of Aeronautics & Astronautics Press, 2006, 43. [5] BREDER C M. Equations descriptive of fish schools and other animal aggregations[j]. Ecology, 1954, 35(3): [6] REYNOLDS C. Flocks, birds and schools: a distributed behavioral model[j]. Computer Graphics, 1987, 21: [7] VICSEK T, CZIROK A, BEN-JACOB E, et al. Novel type of phase transition in a system of self-driven particles[j]. Physical Review E, 1995, 75(6): [8] TONER J, TU Y. Flocks, herds and schools: a quantitative theory of flocking[j]. Physical Review E, 1998, 58: [9] JADBABAIE A, LIN J, MORSE A S. Coordination of groups of mobile autonomous agents using nearest neighbor rules[j]. IEEE Transactions on Automatic Control, 2003, 48(6): [10] SAVKIN A V. Coordinated collective motion of groups of autonomous mobile robots: analysis of Vicsek s model[j]. IEEE Transactions on Automatic Control, 2004, 49(6): [11],. Vicsek [C] //. :, 2006: (TANG Gongguo, GUO Lei. Synchronization analysis of linearized Vicsek model[c] //Proceedings of the 25th Chinese Control Conference. Harbin: Beijing Uinversity of Aeronautics & Astronautics Press, 2006: ) [12] LIN Z, BROUCKE M, FRANCIS B. Local control strategies for groups of mobile autonomous agents[j]. IEEE Transactions on Automatic Control, 2004, 49(4): [13] GAZI V, PASSINO K M. Stability analysis of swarms[j]. IEEE Transactions on Automatic Control, 2003, 48(4): [14] CHU T, WANG L, CHEN T. Self-organized motion in anisotropic swarms[j]. Journal of Control Theory & Applications, 2003, 1(1): [15] WANG L, SHI H, CHU T, et al. Aggregation of foraging swarm[c] //Lecture Notes in Artificial Intelligence. Berlin: Springer, 2004, 3339: [16] SHI H, WANG L, CHU T. Swarming behavior of multi-agent systems[j]. Journal of Control Theory & Applications, 2004, 2(4): [17] LIU B, CHU T, WANG L, et al. Swarm dynamics of a group of mobile autonomous agents[j]. Chinese Physics Letters, 2005, 22(1):

7 92 27 [18] CHU T, WANG L, CHEN T, et al. Self-organized motion in a class of anisotropic swarms: convergence vs oscillation[j]. Chaos, Solitons & Fractals, 2006, 30(4): [19] LIU Y, KEVIN M, PASSINO. Stable social foraging swarms in a noisy environment[j]. IEEE Transactions on Automatic Control, 2004, 49(1): [20] TANNER H G, PAPPAS G J, KUMAR V. Leader-to-formation stability[j]. IEEE Transactions on Robotics & Automation, 2004, 20(3): [21] MU S, CHU T, WANG L. Coordinated collective motion in a motile particle group with a leader[j]. Physica A, 2005, 351(2): [22] SHI H, WANG L, CHU T. Virtual leader approach to coordinated control of multiple mobile agents with asymmetric interactions[j]. Physica D, 2006, 213(1): [23] LIU B, CHU T, WANG L, et al. Collective motion of a class of social foraging swarms[j]. Chaos, Solitons & Fractals, 2008, 38(1): [24] LIU B, CHU T, WANG L. Collective motion in non-reciprocal swarms[j]. Journal of Control Theory & Appications, 2009, 7(2): [25] SHI H, WANG L, CHU T. Flocking of multi-agent systems with a dynamic virtual leader[j]. International Journal of Control, 2009, 82(1): [26],. Leader [J]., 2006, 2(1): (LI Zonggang, JIA Yingmin. Aggreagtion behavior of a type of multiagent system with a leader[j]. CAAI Transactions on Intelligent Systems, 2006, 2(1): ) [27] HONG Y, GAO L, CHENG D, et al. Lyapunov-based approach to multi-agent systems with switching jointly connected interconnection[j]. IEEE Transactions on Automatic Control, 2007, 52(5): [28] HONG Y, HUA J, GAO L. Tracking control for multi-agent consensus with an active leader and variable topology[j]. Automatica, 2006, 42(7): [29] HU J, HONG Y. Leader-following coordination of multi-agent systems with coupling time delays[j]. Physica A, 2007, 374(2), [30] HONG Y, CHEN G, Bushnell L. Distributed observers design for leader-following control of multi-agent networks[j]. Automatica, 2008, 44(3): [31],. [C] //. :, 2006, (LI Tao, ZHANG Jifeng. Asymptotically optiomal decentralized control of a type of multi-agent system[c] //Proceedings of the 25th Chinese Control Conference. Beijing: Beijing University of Aeronautics & Astronautics Press, 2006, ) [32] SABER R O. Flocking for multi-agent dynamic systems: algorithms and theory[j]. IEEE Transactions on Automatic Control, 2006, 51: [33] OLFATI-SABER R, MURRAY R M. Consensus problems in networks of agents with switching topology and time-delays[j]. IEEE Transactions on Automatic Control, 2004, 49: [34] MOREAU L. Stability of multiagent systems with time-dependent communication links[j]. IEEE Transactions on Automatic Control, 2005, 50(2): [35] REN W, BEARD R W. Consensus seeking in multiagent systems under dynamically changing interaction topologies[j]. IEEE Transactions on Automatic Control, 2005, 50(5): [36] XIE G, WANG L. Consensus control for networks of dynamic agents via active switching topology[c] //Lecture Notes in Computer Science. Berlin: Springer-Verlag, 2005, 3612: [37] XIAO F, WANG L, WANG A. Consensus problems in discrete-time multiagent systems with fixed topology[j]. Journal of Mathematical Analysis & Applications, 2006, 322(2): [38] XIAO F, WANG L. State consensus for multi-agent systems with switching topologies and time-varying delays[j]. International Journal of Control, 2006, 79(10): [39] XIAO F, WANG L. Dynamic behavior of discrete-time multiagent systems with general communication structures[j]. Physica A, 2006, 370(2): [40] XIAO F, WANG L. Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays[j]. IEEE Transactions on Automatic Control, 2008, 53(9): [41] XIE G, WANG L. Consensus control for a class of networks of dynamic agents[j]. International Journal of Robust & Nonlinear Control, 2007, 17(10/11): [42] OLFATI-SABER R, FAX J A, MURRAY R M. Consensus and cooperation in networked multi-agent systems[j]. Proceedings of the IEEE, 2007, 95(1): [43] REN W, BEARD R W, ATKINS E M. Information consensus in multivehicle cooperative control[j]. IEEE Control Systems Magazine, 2007, 27(2): [44] LIN P, JIA Y. Average consensus in networks of multi-agents with both switching topology and coupling time-delay[j]. Physica A, 2008, 387(1): [45] LIN P, JIA Y, LI L. Distributed robust H-infinity consensus control in directed networks of agents with time-delay[j]. Systems & Control Letters, 2008, 57(8): [46] CAO M, MORSE A S, ANDERSON B D O. Agreeing asynchronously[j]. IEEE Transactions on Automatic Control, 2008, 53(8): [47] TIAN Y P, LIU C L. Consensus of multi-agent systems with diverse input and communication delays[j]. IEEE Transactions on Automatic Control, 2008, 53(9): [48] LIU B, CHU T, WANG L. Collective behavior analysis of a class of social foraging swarms[c] //Lecture Notes in Artificial Intelligence. Berlin: Springer-Verlag, 2005, 3630: [49] SHI H, WANG L, CHU T, XU M. Flocking control of multiple interactive dynamical agents with switching topology via local feedback[c] //Lecture Notes in Artificial Intelligence. Berlin: Springer- Verlag, 2005, 3630: [50] WANG W, SLOTINE J E. A theoretical study of different leader roles in networks[j]. IEEE Transactions on Automatic Control, 2006, 51(7): [51] YANG M, CHU T. Multi-frequency Oscillations in Swarms with Delay: Numerical Results[R]. Technical Report, COE, Peking University, [52] TANNER H G. On the controllability of nearest neighbor interconnections[c] //Proceedings of the 43rd IEEE Conference on Decision & Control. Paradise Island, the Bahamas: Springer Press, 2004:

8 1 : 93 [53] LIU B, XIE G, CHU T, et al. Controllability of interconnected systems via switching networks with a leader[c] //IEEE International Conference on Systems, Man & Cybernetics. Taipei: IEEE Press, 2006: [54] LIU B, CHU T, WANG L, et al. Controllability of a leader-follower dynamic network with switching topology[j]. IEEE Transactions on Automatic Control, 2008, 53(4): [55] JI Z, LIN H, LEE T H. Controllability of multi-agent systems with switching topology[c] //Proceedings of the 43rd IEEE Conference on Cybernetics, Intelligent Systems, Robotics, Automation and Mechatronics. Chengdu, China: IEEE Press, 2008: [56] JI Z, LIN H, LEE T H. A graph theory based characterization of controllability for multi-agent systems with fixed topology[c] //Proceedings of the 47th IEEE Conference on Decision & Control. Cancun, Mexico: IEEE Press, 2008: [57] YU M, WANG L, CHU T, et al. Stabilization of networked control systems with data packet dropout and transmission delays: continuous-time case[j]. European Journal of Control, 2005, 11(1): [58] OLFATI-SABER R. Ultrafast consensus in small-world networks[c] //Proceedings of the American Control Conference. Portland, Oregon: IEEE Press, 2005, 4: : (1964 ),, 1993,, chutg@pku.edu.cn; ; ; (1980 ),,, (1979 ),,, (1964 ),, 1992,,,, ; (1972 ),, 2001,,..