Abstract
This paper studies the preset time consensus problem of sing-integrator multi-agent systems for reaching the desired state in both undirected and directed communication networks. Two linear consensus protocols with time-varying gain are proposed. In fixed undirected networks, if the undirected topology is connected, the proposed protocol can achieve the consensus at the preset time even if only a portion of agents can obtain the desired state. In fixed directed networks, if the directed topology has a directed spanning tree, the proposed protocol can solve the consensus problem at a given preset time. Finally, numerical simulation results are presented to demonstrate the effectiveness of the theoretical results.
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References
Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules. IEEE T. Automat. Contr. 48, 988–1001 (2003)
Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel Type of Phase Transition in a System of Self-Driven Particles. Phys. Rev. Lett. 75, 122–1229 (1995)
Olfati-Saber, R., Murray, R.M.: Consensus Problems in Networks of Agents with Switching Topology and Time-Delays. IEEE T. Automat. Contr. 49, 1520–1533 (2004)
Sun, Y.G., Wang, L., Xie, G.: Average Consensus in Networks of Dynamic Agents with Switching Topologies and Multiple Time-Varying Delays. Syst. Control Lett. 57, 175–183 (2008)
Munz, U., Papachristodoulou, A., Allgower, F.: Consensus in Multi-agent Systems with Coupling Delays and Switching Topology. IEEE T. Automat. Contr. 56, 2976–2982 (2011)
Nian, X.-H., Su, S.-J., Pan, H.: Consensus Tracking Protocol and Formation Control of Multi-agent Systems with Switching Topology. J. Cent. South. Univ. T. 18, 1178–1183 (2011)
Chun-Xi, Z., Hui, L., Peng, L.: Agreement Coordination for Second-Order Multi-agent Systems with Disturbances. Chin. Phy. B 17, 4458–4465 (2008)
Lin, P., Jia, Y., Du, J., Yuan, S.: Distributed Control of Multi-agent Systems with Second-Order Agent Dynamics and Delay-Dependent Communications. Asian J. Control 10, 254–259 (2008)
Yu, W., Chen, G., Cao, M.: Some Necessary and Sufficient Conditions for Second-Order Consensus in Multi-agent Dynamical Systems. Automatica 46, 1089–1095 (2010)
Yang, H., Zhang, Z., Zhang, S.: Consensus of Second-Order Multi-agent Systems with Exogenous Disturbances. Int. J. Robust Nonlin. 21, 945–956 (2011)
Seo, J.H., Shim, H., Back, J.: Consensus of High-Order Linear Systems Using Dynamic Output Feedback Compensator: Low Gain Approach. Automatica 45, 2659–2664 (2009)
Jiang, F., Wang, L., Xie, G.: Consensus of High-Order Dynamic Multi-agent Systems with Switching Topology and Time-Varying Delays. Journal of Control Theory and Applications 8, 52–60 (2010)
Tan, Y., Yue-Hui, J., Wei, W., Ying-Jing, S.: Consensus of High-Order Continuous-Time Multi-agent Systems with Time-Delays and Switching Topologies. Chin. Phy. B 20, 20511–20516 (2011)
Zhang, Q., Niu, Y., Wang, L., Shen, L., Zhu, H.: Average Consensus Seeking of High-Order Continuous-Time Multi-agent Systems with Multiple Time-Varying Communication Delays. Int. J. Control Autom. 9, 1209–1218 (2011)
Cortés, J.: Finite-Time Convergent Gradient Flows with Applications to Network Consensus. Automatica 42, 1993–2000 (2006)
Chen, G., Lewis, F.L., Xie, L.: Finite-Time Distributed Consensus via Binary Control Protocols. Automatica 47, 1962–1968 (2011)
Li, S., Du, H., Lin, X.: Finite-Time Consensus Algorithm for Multi-agent Systems with Double-Integrator Dynamics. Automatica 47, 1706–1712 (2011)
Lu, X., Chen, S., Lü, J.: Finite-Time Tracking for Double-Integrator Multi-agent Systems with Bounded Control Input. IET Control Theory. A. 7, 1562–1573 (2013)
Zhao, Y., Duan, Z., Wen, G., Zhang, Y.: Distributed Finite-Time Tracking Control for Multi-agent Systems: An Observer-Based Approach. Syst. Control Lett. 62, 22–28 (2013)
Zuo, Z., Tie, L.: A new class of finite-time nonlinear consensus protocols for multi-agent systems. Int. J. Control 87, 363–370 (2014)
Cai, Y., Xie, G.M., Liu, H.Y.: Reaching Consensus at a Preset Time: Single-Integrator Dynamics Case. In: Proceedings of the 31st Chinese Control Conference, pp. 6220–6225. IEEE Computer Society, Washington, DC (2012)
Biggs, N.: Algebraic Graph Theory. Cambridge University Press, Cambridge (1993)
Hong, Y., Hu, J., Gao, L.: Tracking Control for Multi-agent Consensus with an Active Leader and Variable Topology. Automatica 42, 1177–1182 (2006)
Ren, W., Beard, R.W.: Consensus Seeking in Multi-agent Systems under Dynamically Changing Interaction Topologies. IEEE T. Automat. Contr., 655–661 (2005)
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Liu, C., Zhou, Q., Liu, Y. (2014). Consensus of Single-Integrator Multi-Agent Systems at a Preset Time. In: Tan, Y., Shi, Y., Coello, C.A.C. (eds) Advances in Swarm Intelligence. ICSI 2014. Lecture Notes in Computer Science, vol 8794. Springer, Cham. https://doi.org/10.1007/978-3-319-11857-4_49
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DOI: https://doi.org/10.1007/978-3-319-11857-4_49
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11856-7
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