Abstract
A novel control algorithm based on Nussbaum function is proposed to settle the adaptive consensus tracking for first-order multi-agent systems with completely non-identical unknown control directions (UCDs) and uncertainties under connected undirected graphs or balanced and weakly connected digraphs in this paper. The Nussbaum function is introduced in the distributed control law to settle the UCDs of multi-agent systems. Then, it is proven that multi-agent systems with UCDs and uncertainties can achieve asymptotic consensus and reach the target state under the assumption that the underlying topology is undirected graphs or balanced and weakly connected graphs. Finally, theoretical and simulation results has verified the validity of our proposed algorithm.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Olfati-Saber, R., Fax, J.A., Murray, R.M.: Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95(1), 215–233 (2007)
Li, H., Liao, X., Huang, T., Zhu, W.: Event-triggering sampling based leader-following consensus in second-order multi-agent systems. IEEE Trans. Autom. Control 60(7), 1998–2003 (2015)
Wenwu, Y., Chen, G., Cao, M.: Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. Automatica 46(6), 1089–1095 (2010)
Wen, G., Duan, Z., Ren, W., Chen, G.: Distributed consensus of multi-agent systems with general linear node dynamics and intermittent communications. Int. J. Robust Nonlinear Control 24(16), 2438–2457 (2014)
Wenwu, Y., Ren, W., Zheng, W.X., Chen, G., Lü, J.: Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics. Automatica 49(7), 2107–2115 (2013)
Chen, W., Li, X., Ren, W., Wen, C.: Adaptive consensus of multi-agent systems with unknown identical control directions based on a novel Nussbaum-type function. IEEE Trans. Autom. Control 59(7), 1887–1892 (2014)
Du, J., Guo, C., Yu, S., Zhao, Y.: Adaptive autopilot design of time-varying uncertain ships with completely unknown control coefficient. IEEE J. Ocean. Eng. 32(2), 346–352 (2007)
Astolfi, A., Hsu, L., Netto, M.S., Ortega, R.: Two solutions to the adaptive visual servoing problem. IEEE Trans. Robotics Autom. 18(3), 387–392 (2002)
Yang, C., Ge, S.S., Lee, T.H.: Output feedback adaptive control of a class of nonlinear discrete-time systems with unknown control directions. Automatica 45(1), 270–276 (2009)
Peng, J., Ye, X.: Cooperative control of multiple heterogeneous agents with unknown high-frequency-gain signs. Syst. Control Lett. 68, 51–56 (2014)
Nussbaum, R.D.: Some remarks on a conjecture in parameter adaptive control. Syst. Control Lett. 3(5), 243–246 (1983)
Ren, W., Beard, R.W.: Distributed Consensus in Multi-vehicle Cooperative Control. Springer, London (2008). https://doi.org/10.1007/978-1-84800-015-5
Slotine, J.J.E., Li, W.: Applied Nonlinear Control. Prentice Hall, Englewood Cliffs (1991)
Xudong, Y., Jingping, J.: Adaptive nonlinear design without a priori knowledge of control directions. IEEE Trans. Autom. Control 43(11), 1617–1621 (1998)
Zhang, H., Lewis, F.L., Qu, Z.: Lyapunov, adaptive, and optimal design techniques for cooperative systems on directed communication graphs. IEEE Trans. Ind. Electron. 59(7), 3026–3041 (2012)
Hong, Y., Jiangping, H., Gao, L.: Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42(7), 1177–1182 (2006)
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Zheng, Y., Wang, Q., Sun, C. (2018). Adaptive Consensus Tracking of First-Order Multi-agent Systems with Unknown Control Directions. In: Huang, T., Lv, J., Sun, C., Tuzikov, A. (eds) Advances in Neural Networks – ISNN 2018. ISNN 2018. Lecture Notes in Computer Science(), vol 10878. Springer, Cham. https://doi.org/10.1007/978-3-319-92537-0_47
Download citation
DOI: https://doi.org/10.1007/978-3-319-92537-0_47
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-92536-3
Online ISBN: 978-3-319-92537-0
eBook Packages: Computer ScienceComputer Science (R0)