Abstract
In this paper, the adaptive finite-time consensus (FTC) control problem of second-order nonlinear multi-agent systems (MASs) with input quantization and external disturbances is studied. With the help of finite time control technology, a novel distributed adaptive control protocol is constructed to achieve FTC performance for second-order nonlinear MASs by using the recursive method. The control input is quantized through a hysteresis quantizer, which reduces the communication rate of arbitrary two agents. The unknown functions are approximated by adopting the radial basis function neural networks. Under the consensus protocols and adaptive laws, it can be proved that velocity errors of arbitrary two agents reach a small region of zero in finite time as well as position errors. Finally, the effectiveness of the proposed method is illustrated via a simulation example.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Y. Liu and Y. Jia, “Formation control of discrete-time multi-agent systems by iterative learning approach,” International Journal of Control, Automation, and Systems, vol. 10, pp. 913–919, September 2012.
H. L. Trentelman, K. Takaba, and N. Monshizadeh, “Robust synchronization of uncertain linear multi-agent systems,” IEEE Transactions on Automatic Control, vol. 58, no. 6, pp. 1511–1523, June 2013.
R. Olfati-Saber, “Flocking for multi-agent dynamic systems: algorithms and theory,” IEEE Transactions on Automatic Control, vol. 51, no. 3, pp. 401–420, April 2004.
B. Li, H. Yang, Z. Chen, and Z. Liu, “Containment control of multi-agent systems with time-delays over heterogeneous networks,” International Journal of Control, Automation, and Systems, vol. 17, pp. 2521–2530, July 2019.
W. Zhang, Y. Tang, T. Huang, and J. Kurths, “Sampleddata consensus of linear multi-agent systems with packet losses,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, pp. 2516–2527, August 2017.
L. Ding, Q. L. Han, and G. Guo, “Network-based leader-following consensus for distributed multi-agent systems,” Automatica, vol. 49, pp. 2281–2286, July 2013.
X. Wang and Y. Hong, “Finite-time consensus for multi-agent networks with second-order agent dynamics,” IFAC Proceedings Volumes, vol. 41, no. 2, pp. 15185–15190, July 2008.
L. W. Zhao and C. C. Hua, “Finite-time consensus tracking of second-order multi-agent systems via nonsingular TSM,” Nonlinear Dynamics, vol. 75, no. 1–2, pp. 311–318, September 2014.
S. Li, H. Du and X. Lin, “Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics,” Automatica, vol. 47, no. 8, pp. 1706–1712, August 2011.
H. Liu, L. Cheng, M. Tan, and Z. G. Hou, “Exponential finite-Time consensus of fractional-order multiagent systems,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 50, no. 4, pp. 1549–1558, May 2018.
L. Wang and F. Xiao, “Finite-time consensus problems for networks of dynamic agents,” IEEE Transactions on Automatic Control, vol. 55, no. 4, pp. 950–955, May 2010.
C. Hua, X. Sun, Xi. You, and X. Guan, “Finite-time consensus control for second-order multi-agent systems without velocity measurements,” International Journal of Systems Science, vol. 48, no. 2, pp. 337–346, May 2017.
H. Du, S. Li, Y. He, and Y. Cheng, “Distributed high-order finite-time consensus algorithm for multi-agent systems,” Proc. of the 32nd Chinese Control Conference, pp. 603–608, October 2013.
F. Jiang and L. Wang, “Finite-timein formation consensusfor multi-agent systems with fixed and switching topologies,” Physica D: Nonlinear Phenomena, vol. 238, no. 16, pp. 1550–1560, August 2009.
J. Liu, C. Wang, X. Li, and X. Cai, “Adaptive finite-time practical consensus protocols for second-order multiagent systems with nonsymmetric input dead zone and uncertain dynamics,” Journal of the Franklin Institute, vol. 356, no. 6, pp. 3217–3244, February 2019.
Y. Yang, C. Hua, and X. Guan, “Adaptive fuzzy finite-time coordination control for networked nonlinear bilateral teleoperation system,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 3, pp. 631–641, June 2014.
J. Na, S. Wang, Y. J. Liu, Y. Huang, and X. Ren, “Finite-time convergence adaptive neural network control for nonlinear servo systems,” IEEE Transactions on Cybernetics, vol. 50, no. 6, pp. 2568–2579, June 2020.
W. Zou, C. K. Ahn, and Z. Xiang, “Leader-following consensus of second-order nonlinear multi-agent systems with unmodeled dynamics,” Neurocomputing, vol. 322, pp. 120–129, December 2018.
X. He and Q. Wang, “Distributed finite-time leaderless consensus control for double-integrator multi-agent systems with external disturbances,” Applied Mathematics and Computation, vol. 295, pp. 65–76, February 2017.
W. Liu, Q. Ma, Q. Wang, and H. Feng, “Finite-time consensus control of heterogeneous nonlinear MASs with uncertainties bounded by positive functions,” Neurocomputing, vol. 330, pp. 29–38, October 2019.
M. Cai and Z. Xiang, “Adaptive finite-time consensus protocols for multi-agent systems by using neural networks,” IET Control Theory and Applications, vol. 10, pp. 371–380, February 2016.
H. Ishii and B. A. Francis, Limited Data Rate in Control Systems with Network, Berlin, Germany: Springer, 2002.
S. Tatikonda and S. Mitter, “Control under communication constraints,” IEEE Transactions on Automatic Control, vol. 49, no. 7, pp. 1056–1068, April 2004.
M. Yu, S. Bai, T. Yang, and J. Zhang, “Quantized output feedback control of networked control systems with packet dropout,” International Journal of Control, Automation, and Systems, vol. 16, pp. 2559–2568, September 2018.
F. Ceragioli, C. D. Persis, and P. Frasca, “Discontinuities and hysteresis in quantized average consensus,” Automatica, vol. 47, pp. 1916–1928, January 2011.
J. Zhou, C. Wen, and G. H. Yang, “Adaptive backstepping stabilization of nonlinear uncertain systems with quantized input signal,” IEEE Transactions on Automatic Control, vol. 59, no. 2, pp. 460–464, February 2014.
L. Xing, C. Wen, Y. Zhu, H. Su, and Z. Liu, “Output feedback control for uncertain nonlinear systems with input quantization,” Automatica, vol. 65, pp. 191–202, March 2016.
D. V. Dimarogonas and K. H. Johansson, “Stability analysis for multi-agent systems using the incidence matrix: Quantized communication and formation control,” Automatica, vol. 46, pp. 695–700, April 2010.
T. Furusaka, T. Sato, N. Araki, and Y. Konishi, “On consensus in multiagent systems with quantized signal communication,” IEEE Transactions on Electronics, Information and Systems, vol. 139, no. 4, pp. 300–304, June 2019.
C. Wang, C. Wen, Q. Hu, W. Wang, and X. Zhang, “Containment control of multi-agent systems with uniform quantization,” Circuits Systems and Signal Processing, vol. 38, pp. 3952–3970, January 2019.
Z. Q. Zhang, L. Zhang, F. Hao, and L. Wang, “Leader-following consensus for linear and Lipschitz nonlinear multiagent systems with quantized communication,” IEEE Transactions on Cybernetics, vol. 47, no. 8, pp. 1970–1982, June 2017.
Z. Qiu, Y. Hong, and L. Xie, “Quantized leaderless and leader-following consensus of high-order multi-agent systems with limited data rate,” Proc. of the IEEE Conference on Decision and Control, December 2013.
Z. Wang, J. Yuan, Y. Pan, and J. Wei, “Neural network-based adaptive fault tolerant consensus control for a class of high order multiagent systems with input quantization and time-varying parameters,” Neurocomputing, vol. 266, pp. 315–324, May 2017.
Y. Li, C. Wang, X. Cai, L. Li, and G. Wang, “Neural-network-based distributed adaptive asymptotically consensus tracking control for nonlinear multiagent systems with input quantization and actuator faults,” Neurocomputing, vol. 349, pp. 64–76, April 2019.
Y. Zhang, J. Sun, W. He, and H. Li, “Cooperative adaptive finite-time control for stochastic multi-agent systems with input quantisation,” IET Control Theory Applications, vol. 13, pp. 746–754, January 2019.
J. Liu, C. Wang, and X. Cai, “Global finite-time event-triggered consensus for a class of second-order multi-agent systems with the power of positive odd rational number and quantized control inputs,” Neurocomputing, vol. 360, pp. 254–264, May 2019.
Z. Zhu, Y. Xia, and M. Fu, “Attitude stabilization of rigid spacecraft with finite-time convergence,” International Journal of Robust and Nonlinear Control, vol. 21, no. 6, pp. 686–702, April 2011.
R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520–1533 September 2004.
C. Qian and W. Lin, “A continuous feedback approach to global strong stabilization of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 46, no. 7, pp. 1061–1079, August 2001.
G. Hardy, J. Littlewood, and G. Polya, Inequalities, Cambridge: Cambridge University Press, 1952.
C. Qian and W. Lin, “Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization,” Systems & Control Letters, vol. 42, no. 3, pp. 185–200, March 2001.
G. Lai, Z. Liu, Y. Zhang, and C. Chen, “Asymmetric actuator backlash compensation in quantized adaptive control of uncertain networked nonlinear systems,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 2, pp. 294–307, March 2017.
Funding
This work is supported by the National Natural Science Foundation of China (61803215, 62103212), the Natural Science Foundation of Shandong Province (ZR2019BF038), the Science and Technology Support Plan for Youth Innovation of Universities in Shandong Province (2019KJN033), China Postdoctoral Science Foundation (2019M652323) and Qingdao Application Basic Research Project (18-2-2-40-jch).
Author information
Authors and Affiliations
Corresponding author
Additional information
Jiabo Ren received his B.Sc. degree from the Faculty of Electronic Information Engineering, Huaiyin Institute of Technology, Huaian, China, in 2018. He is currently pursuing an M.S. degree with the School of Automation, Qingdao University, Qingdao, China. His current research interests include distributed control of multi-agent systems and nonlinear system control.
Baofang Wang received his B.Sc. degree in Automation from Nanjing University of Science and Technology, Nanjing, China, in 2012, and a Ph.D. degree in Control Theory and Control Engineering from Nanjing University of Science and Technology, Nanjing, China, in 2018. He is currently a Lecturer in the School of Automation, Qingdao University. His current research interests include robot intelligent control, servo system and nonlinear system control.
Mingjie Cai received her B.Sc. degree in Automation from Nanjing University of Science and Technology, Nanjing, China, in 2012, and a Ph.D. degree in Control Theory and Control Engineering from Nanjing University of Science and Technology, Nanjing, China, in 2017. She is currently an Assistant Professor in the School of Automation, Qingdao University. Her current research interests include distributed control of multi-agent systems and nonlinear system control.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ren, J., Wang, B. & Cai, M. Adaptive Finite-time Consensus for Second-order Nonlinear Multi-agent Systems with Input Quantization. Int. J. Control Autom. Syst. 20, 769–779 (2022). https://doi.org/10.1007/s12555-020-0283-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-020-0283-2