Abstract
We will study the adaptive fast finite-time consensus (FTC) control problem of second-order multi-agent systems (MASs) with unknown dynamics and external disturbances in this paper. Based on the basis of radial basis function neural networks theories, we use it to approximate the unknown functions. According to the consensus protocols and adaptive laws, we will prove that velocity errors of arbitrary two agents reach a small region of zero in finite time as well as position errors. Ultimately, the effectiveness of the designed method is tested through a numerical example.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Lewis, M., Tan, K.: High precision formation control of mobile robots using virtual structures. Auton. Robots 4(4), 387–403 (1997)
Zhang, Z., Chow, M.Y.: Convergence analysis of the incremental cost consensus algorithm under different communication network topologies in a smart grid. IEEE Trans. Power Syst. 27(4), 1761–1768 (2012)
Fax, J., Murray, R.: Information flow and cooperative control of vehicle formations. IEEE Trans. Autom. Control 49(9), 1465–1476 (2004)
Cai, M., Xiang, R.: Adaptive finite-time consensus protocols for multi-agent systems by using neural networks. IET Control Theory Appl. 10(4), 371–380 (2016)
Bhat, S.P., Bernstein, D.S.: Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751–766 (2000)
Bhat, S.P., Bernstein, D.S.: Geometric homogeneity with applications to finite-time stability. Math. Control Sign. Syst. 17(2), 101–127 (2005)
Wang, L., Xiao, F.: Finite-time consensus problems for networks of dynamic agents. IEEE Trans. Autom. Control 55(4), 950–955 (2010)
Wang, X., Hong, Y.: Finite-time consensus for multi-agent networks with second-order agent dynamics. In: Proceedings of the IFAC World Congress, pp. 15185–15190 (2008)
Liu, J., Wang, C., Li, L., et al.: Finite-time consensus control for second-order multi-agent systems with output constraint. In: Proceedings of the 37th Chinese Control Conference, pp. 7171–7176. Wuhan (2018)
Ranjbar, M.A., Ghasemi, R., Akramizadeh, A.: Time-varying leader-following consensus of high order multi-agent systems. Int. J. Model. Ident. Control 30, 333–341 (2018)
Onyeka, A.E., Yan, X., Mao, Z., et al.: Stabilisation of time delay systems with nonlinear disturbances using sliding mode control. Int. J. Model. Ident. Control 31, 259–267 (2019)
Zhang, B., Gao, S., Yang, X., et al.: A chattering-free adaptive second-order non-singular fast terminal sliding mode control scheme for a class of nonlinear uncertain systems. Int. J. Model. Ident. Control 29, 255–265 (2018)
Liu, H., Cheng, L., Tan, M., et al.: Exponential finite-time consensus of fractional-order multiagent systems. IEEE Trans. Syst. Man Cybern.: Syst. 2816060 (2018) https://doi.org/10.1109/TSM-C
Li, R., Shi, Y., Sheldon, X.D.: The fast convergence analysis of finite-time consensus for multi-agent systems with switching topology. In: Proceedings of the 31st Chinese Control Conference, pp. 2296–2300. Hefei (2012)
Qian, C., Lin, W.: A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans. Autom. Control 46(7), 1061–1079 (2001)
Qian, C., Lin, W.: Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Syst. Control Lett. 42(3), 185–200 (2015)
Yu, J., Shi, P., Zhao, L.: Finite-time command filtered backstepping control for a class of nonlinear systems. Automatica 92, 173–180 (2018)
Li, S., Du, H., Lin, X.: Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics. Automatica 47(8), 1706–1712 (2011)
Olfatisaber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)
Acknowledgements
This work is supported by the National Natural Science Foundation (NNSF) of China (61803215), the Natural Science Foundation of Shandong Province (ZR2019BF038), and Qingdao Application Basic Research Project (18-2-2-40-jch).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Ren, J., Wang, B., Cai, M. (2020). Adaptive Fast Finite-Time Consensus for Second-Order Multi-agent Systems. In: Wang, R., Chen, Z., Zhang, W., Zhu, Q. (eds) Proceedings of the 11th International Conference on Modelling, Identification and Control (ICMIC2019). Lecture Notes in Electrical Engineering, vol 582. Springer, Singapore. https://doi.org/10.1007/978-981-15-0474-7_100
Download citation
DOI: https://doi.org/10.1007/978-981-15-0474-7_100
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-0473-0
Online ISBN: 978-981-15-0474-7
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)