Group Formation Tracking Control of Nonlinear Coupled Multi-agent Systems
DU Xiangyang1, LI Weixun1, CHEN Zengqiang2, ZHANG Limin3
1. School of Science, Tianjin University of Technology and Education, Tianjin 300222, China; 2. College of Artificial Intelligence, Nankai University, Tianjin 300350, China; 3. School of Electronic and Information Engineering, Zhongyuan University of Technology, Zhengzhou 451191, China
Abstract：This paper studies the group formation control problem of nonlinear and two-integrator coupling leading the following multi-agent systems. In dealing with the grouping of multi-agent systems, a new control protocol is designed, which does not based on the conventional conservative assumption that the sum of adjacent weights of all nodes from each node in one group to all nodes in the other group is zero or another constant. Then, based on Lyapunov stability theory and algebraic graph theory, sufficient conditions for formation control problems of nonlinear and double integrator second-order multi-agent systems are given respectively. So that the agents in the multi-agent system can reach and maintain the designed formation over time. Finally, two numerical simulations are presented to verify the effectiveness of the results.
杜向阳, 李伟勋, 陈增强, 张利民. 非线性耦合多智能体系统组编队跟踪控制[J]. 复杂系统与复杂性科学, 2022, 19(4): 72-79.
DU Xiangyang, LI Weixun, CHEN Zengqiang, ZHANG Limin. Group Formation Tracking Control of Nonlinear Coupled Multi-agent Systems. Complex Systems and Complexity Science, 2022, 19(4): 72-79.
[1] REN W, BEARD R W. Consensus seeking in multi-agent systems under dynamically changing interactional topologies[J]. IEEE Transactional on Automatic Control, 2005, 50(5): 655661. [2] 仉伟, 纪志坚, 渠继军. 基于领导者对称的多智能体系统可控性研究[J]. 复杂系统与复杂性科学, 2019, 16(2): 5259. ZHANG W, JI Z J, QU J J. Controllability of multi-agent systems based on leader symmetry[J]. Complex Systems and Complexity Science, 2019, 16 (2): 5259. [3] 李勃, 陈增强, 刘忠信, 等. 含时延的多智能体系统的多静态领导者包容控制[J]. 复杂系统与复杂性科学, 2016, 13(2):105110. LI B, CHEN Z Q, LIU Z X, et al. Containment control for multi-agent system with multiple stationary leaders and time-delays [J]. Complex Systems and Complexity Science, 2016, 13(2):105110. [4] HONG Y G, HU J P, GAO L X. Tracking control for multi-agent consensus with an active leader and variable topology[J]. IEEE Trans on Automatic Control, 2006, 42(7): 11771182. [5] 孙玉娇,杨洪勇,于美妍. 基于领航跟随的 多机器人系统有限时间一致性控制研究[J]. 复杂系统与复杂性科学,2020,17(4):6672. SUN Y J, YANG H Y, YU M Y. The finite time consistency control of multi-robot systems based on leader-following[J]. Complex Systems and Complexity Science, 2020, 17(4):6672. [6] HU Q L, DONG H Y, ZHANG Y M, et al. Tracking control of spacecraft formation flying with collision avoidance[J]. Aerospace Science and Technology, 2015, 42: 353364. [7] LI W X, CHEN Z Q, LIU Z X. Leader-following formation control for second-order multi-agent systems with time-varying delay and nonlinear dynamics[J]. Nonlinear Dynamics, 2013, 72(4):803812. [8] LIN Z Y, DING W, YAN G F, et al. Leader-follower formation via complex Laplacian[J]. Automatica, 2013, 49(6): 19001916. [9] BEARD R W, LAWTON J, HADAEGH F Y. A coordination architecture for spacecraft formation control[J]. IEEE Transactions of Control System Technology, 2001, 9(6): 777790. [10] YU J Y, WANG L. Group consensus in multi-agent systems with switching topologies and communication delays[J]. Systems and Control Letters, 2010, 59(6): 340348. [11] HU H X, YU L, ZHANG W A, et al. Group consensus in multi-agent systems with hybrid protocol[J]. Journal of the Franklin Institute, 2013, 350: 575597. [12] TAN C, LIU G P, DUAN G R. Group consensus of networked multi-agent systems with directed topology[J]. IFAC Proceeding Volumes, 2011, 44(1): 88788883. [13] XIE D M, LIU Q L, LÜ L F, et al. Necessary and sufficient condition for the group consensus of multi-agent systems[J]. Applied Mathematics and Computation, 2014, 243: 870878. [14] JI L H, LIU Q, LIAO X F. On reaching group consensus for linearly coupled multi-agent networks[J]. Information Sciences, 2014, 287: 112. [15] YAO C, LU J H, HAN F L, et al. On the cluster consensus of discrete-time multi-agent systems[J]. Systems & Control Letters, 2011, 60(7): 517523. [16] LUO X Y, LI S B, GUAN X P. Flocking algorithm with multi-target tracking for multi-agent systems[J]. Pattern Recognition Letters, 2010, 31(9): 800805. [17] HAN T, GUAN Z H, CHI M, et al. Multi-formation control of nonlinear leader-following multi-agent systems[J]. ISA Transactions, 2017, 69: 140147. [18] SONG Q, CAO J D, YU W W. Second-order leader-following consensus of nonlinear multi-agent systems via pinning control [J]. Systems & Control Letters, 2010, 59(9): 553562. [19] YU W W, CHEN G R, CAO M. Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems[J]. Automatica, 2010, 46(6):10891095. [20] DU H B, CHENG Y Y, He Y G, et al. Second-order consensus for nonlinear leader-following multi-agent systems via dynamic output feedback control[J]. International Journal of Robust Nonlinear Control, 2016, 26(2): 329344. [21] WANG Y, MA Z J. Lag consensus of the second-order leader-following multi-agent systems with nonlinear dynamics[J]. Neurocomputing, 2016, 171:8288. [22] WILKINSON J H. The Algebraic Eigenvalue Problem [M]. London: Oxford University Press, 1965. [23] WANG Y Y, XIE L H, SOUZA C E. Robust control of a class of uncertain nonlinear systems[J]. Systems & Control Letters, 1992, 19(2): 139149.
