Abstract
This article mainly studies the distributed fixed-time (FT) consensus and optimization of second-order multi-agent systems (SOMASs). Firstly, a power-law algorithm is developed by virtue of the gradients of local cost functions and agent neighbor information. Under the algorithm, it is proved that all agents’ velocities approach to zero, while the position state of each agent achieves consensus within a fixed time. In addition, it is further revealed that the problem of unconstrained convex optimization can be solved by this algorithm. An example is provided at last to illustrate the derived results.
This work was supported by National Natural Science Foundation of China (61963033), by the Key Project of Natural Science Foundation of Xinjiang (2021D01D10), by the Special Project for Local Science and Technology Development Guided by the Central Government (ZYYD2022A05) and by Xinjiang Key Laboratory of Applied Mathematics (XJDX1401).
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
References
Chu, T., Wang, L., Chen, T., Mu, S.: Complex emergent dynamics of anisotropic swarms: convergence vs oscillation. Chaos Solitons Fractals 30(4), 875–885 (2006)
Jadbabaie, A., Jie, L., Morse, A.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Autom. Control 48(6), 988–1001 (2003)
Fang, H., Shang, C., Chen, J.: An optimization-based shared control framework with applications in multi-robot systems. Science China Inf. Sci. 61(1), 261–263 (2018)
DeGroot, M.: Reaching a consensus. J. Am. Stat. Assoc. 69(345), 118–121 (1974)
Zhao, J., Cui, H., Li, Z.: Distributed reset control for leader-following consensus of nonlinear multi-agent systems. Int. J. Control Autom. Syst. 20, 983–991 (2022)
Zou, W., Xiang, Z., Ahn, C.: Mean-square leader-following consensus of second-order nonlinear multiagent systems with noises and unmodeled dynamics. IEEE Trans. Syst. Man Cybern. Syst. 49(12), 2478–2486 (2019)
Zhao, G., Cui, H.: A novel reset control approach to leader-following consensus of second-order nonlinear multi-agent systems. J. Franklin Inst. 358(18), 9678–9697 (2021)
Meng, D., Jia, Y., Du, J.: Finite-time consensus for multiagent systems with cooperative and antagonistic interactions. IEEE Trans. Neural Netw. Learn. Syst. 27(4), 762–770 (2016)
He, X., Hao, Y., Wang, Q.: Leaderless finite-time consensus for second-order Lipschitz nonlinear multi-agent systems with settling time estimation. Physica A 514, 280–289 (2019)
Polyakov, A.: Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans. Autom. Control 57(8), 2106–2110 (2012)
Hu, C., He, H., Jiang, H.: Fixed/preassigned-time synchronization of complex networks via improving fixed-time stability. IEEE Trans. Cybern. 51(6), 2882–2892 (2021)
Feng, L., Hu, C., Yu, J.: Fixed-time synchronization of coupled memristive complex-valued neural networks. J. Xinjiang Univ. 38(2), 129–143 (2021)
Ni, J., Liu, L., Liu, C., Liu, J.: Fixed-time leader-following consensus for second-order multiagent systems with input delay. IEEE Trans. Industr. Electron. 64(11), 8635–8646 (2017)
Ni, J., Tang, Y., Shi, P.: A new fixed-time consensus tracking approach for second-order multiagent systems under directed communication topology. IEEE Trans. Syst. Man Cybern. Syst. 51(4), 2488–2500 (2021)
Liu, Y., Zhang, F., Huang, P., Lu, Y.: Fixed-time consensus tracking for second-order multiagent systems under disturbance. IEEE Trans. Syst. Man Cybern. Syst. 51(8), 4883–4894 (2021)
Ning, B., Han, Q., Zuo, Z.: Distributed optimization for multiagent systems: an edge-based fixed-time consensus approach. IEEE Trans. Cybern. 49(1), 122–132 (2019)
Yu, Z., Yu, S., Jiang, H., Mei, X.: Distributed fixed-time optimization for multi-agent systems over a directed network. Nonlinear Dyn. 103(1), 775–789 (2021). https://doi.org/10.1007/s11071-020-06116-1
Hardy, G., Littlewood, J., Polya, G.: Inequalities. Cambridge University Press, Cambridge (1952)
Qin, J., Gao, H., Zheng, W.: Exponential synchronization of complex networks of linear systems and nonlinear oscillators: a unified analysis. IEEE Trans. Neural Netw. Learn. Syst. 26(3), 510–521 (2015)
Lin, P., Ren, W., Farrell, J.: Distributed continuous-time optimization: nonuniform gradient gains, finite-time convergence, and convex constraint set. IEEE Trans. Autom. Control 62(5), 2239–2253 (2017)
Mo, L., Liu, X., Cao, X., Yu, Y.: Distributed second-order continuous-time optimization via adaptive algorithm with nonuniform gradient gains. J. Syst. Sci. Complex. 33, 1914–1932 (2020)
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, New York (2004)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Cao, X., Hu, C., Yu, J., Jiang, H. (2022). Distributed Fixed-Time Consensus and Optimization for Second-Order Multi-Agent Systems. In: Zhang, L., Yu, W., Jiang, H., Laili, Y. (eds) Intelligent Networked Things. CINT 2022. Communications in Computer and Information Science, vol 1714. Springer, Singapore. https://doi.org/10.1007/978-981-19-8915-5_40
Download citation
DOI: https://doi.org/10.1007/978-981-19-8915-5_40
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-19-8914-8
Online ISBN: 978-981-19-8915-5
eBook Packages: Computer ScienceComputer Science (R0)