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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-11857-4_49
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11856-7
Online ISBN: 978-3-319-11857-4
eBook Packages: Computer ScienceComputer Science (R0)