Abstract
In this paper, we consider a containment control problem for a class of uncertain multi-agent systems (MASs). The systems contain unknown parameters and virtual control gain functions. By introducing lower bounds of virtual control gain functions into the Lyapunov functions, a novel controller design scheme is proposed based on adaptive control design approach and bound estimation method. The designed controller is simpler in comparison with other controllers. The simulation results show that three followers converge into the convex hull rapidly following the sinusoidal leaders, and the effectiveness of the designed controller is verified.
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Y. M. Shao, X. L. Jia, W. H. Liu, and G. B. Liu, “Adaptive stabilization of feedforward time-delay systems with uncertain output equation,” International Journal of Control, Automation, and Systems, vol. 20, no. 4, pp. 1194–1204, April 2022.
J. B. Ren, B. F. Wang, and M. J. Cai, “Adaptive finite-time consensus for second-order nonlinear multi-agent systems with input quantization,” International Journal of Control, Automation, and Systems, vol. 20, no. 3, pp. 769–779, March 2022.
M. Yu, M. Chen, and L.B. Wu, “Fast finite-time attitude tracking control of rigid spacecraft with quantized input signals,” International Journal of Control, Automation, and Systems, vol. 20, no. 6, pp. 1926–1934, April 2022.
M. V. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design, John Wiley and Sons, New York, 1995.
Z. P. Zhang and D. J. Hill, “A robust adaptive backstepping scheme for nonlinear systems with unmodeled dynamics,” IEEE Transactions on Automatic Control, vol. 44, no. 9, pp. 1705–1711, September 1999.
C. Hua, X. Guan, and S. Peng, “Robust backstepping control for a class of time delayed systems,” IEEE Transactions on Automatic Control, vol. 50, no. 6, pp. 894–899, June 2005.
X. Zheng and X. Yang, “Command filter and universal approximator based backstepping control design for strict-feedback nonlinear systems with uncertainty,” IEEE Transactions on Automatic Control, vol. 65, no. 3, pp. 1310–1317, March 2020.
Z. Jing, C. Wen, and W. Wei, “Adaptive backstepping control of uncertain systems with unknown input time-delay,” Automatica, vol. 45, no. 6, pp. 1415–1422, June 2009.
C. Wen, Z. Jing, Z. Liu, and H. Su, “Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance,” IEEE Transactions on Automatic Control, vol. 56, no. 7, pp. 1672–1678, 2011.
M. L. Chiang and L. C. Fu, “Adaptive stabilization of a class of uncertain switched nonlinear systems with back-stepping control,” Automatica, vol. 50, no. 8, pp. 2128–2135, May 2014.
J. Zhou, C. Wen, and G. 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.
Y. X. Li, “Finite time command filtered adaptive fault tolerant control for a class of uncertain nonlinear systems,” Automatica, vol. 106, pp. 117–123, August 2019.
S. S. Ge, H. Fang, and H. L. Tong, “Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients,” IEEE IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 34, no. 1, pp. 499–516, February 2004.
M. Wang, B. Chen, K.F. Liu, X.P. Liu and S.Y. Zhang, “Adaptive fuzzy control of nonlinear time-delay systems with unknown virtual control coefficients,” Information Sciences, vol. 178, no. 22, pp. 4326–4340, 2008.
Y. Wang and H. Wu, “A class of adaptive robust controllers for uncertain dynamical systems with unknown virtual control coefficients,” International Journal of Advanced Mechatronic Systems vol. 6, no. 2/3, pp. 65–74, 2015.
Y. X. Li, “Barrier Lyapunov function-based adaptive asymptotic tracking of nonlinear systems with unknown virtual control coefficients,” Automatica vol. 121, pp. 109181, November 2020.
C. Liu, C. Gao, X. Liu, H. Wang, and Y. Zhou, “Adaptive finite-time prescribed performance control for stochastic nonlinear systems with unknown virtual control coefficients,” Nonlinear Dynamics vol. 104, pp. 3655–3670, 2021.
W. Wang, C. Wen, and J. Huang, “Distributed adaptive asymptotically consensus tracking control of nonlinear multi-agent systems with unknown parameters and uncertain disturbances,” Automatica, vol. 77, pp. 133–142, 2017.
F. Wang, H. Yang, Z. Liu, and Z. Chen, “Containment control of leader-following multi-agent systems with jointly-connected topologies and time-varying delays,” Neurocomputing, vol. 260, pp. 341–348, May 2017.
M. F. Ge, Z. H. Guan, C. Yang, T. Li, and Y. W. Wang, “Time-varying formation tracking of multiple manipulators via distributed finite-time control,” Neurocomputing, vol. 202, pp. 20–26, August 2016.
J. Li, W. Ren, and S. Xu, “Distributed containment control with multiple dynamic leaders for double-integrator dynamics using only position measurements,” IEEE Transactions on Automatic Control, vol. 57, no. 6, pp. 1553–1559, June 2012.
J. S. Yoo, “Distributed adaptive containment control of uncertain nonlinear multi-agent systems in strict-feedback form,” Automatica, vol. 49, no. 7, pp. 2145–2153, 2013.
J. Q. Hu, J. Yu, and J.D. Cao, “Distributed containment control for nonlinear multi-Agent systems with time-delayed protocol,” Asian Journal of Control, vol. 18 no. 2, pp. 747–756, March 2015.
X. X. Zhang, X. P. Liu, and Z. G. Feng, “Distributed containment control of singular heterogeneous multi-agent systems,” Journal of the Franklin Institute vol. 357, no. 3, pp. 1378–1399, November 2019.
J. Zhang, H. Zhang, Y. Cai, and W. Li, “Containment control of general linear multi-agent systems by event-triggered control mechanisms,” Neurocomputing, vol. 433, pp. 263–274, April 2021.
Z. Y. Gao, H. G. Zhang, Y. C. Wang, and Y. F. Mu, “Time-varying output formation-containment control for homogeneous/heterogeneous descriptor fractional-order multiagent systems,” Information Sciences, vol. 567, pp. 146–166, August 2021.
M. Parsa and M. Danesh, “Robust containment control of uncertain multi-agent systems with time-delay and heterogeneous lipschitz nonlinearity,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 51, no. 4, pp. 2312–2321, April 2021.
S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, March 2004.
Z. Y. Meng, W. Ren, and Z. You, “Distributed finite-time attitude containment control for multiple rigid bodies,” Automatica, vol. 46, no. 12, pp. 2092–2099, December 2010.
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This work is financially sponsored by the National Natural Science Foundation of China (71771112 and 21978123).
Meng-Yi Jiang received her B.S. degree in mathematics and an M.S. degree in education from Liaoning Normal University, Dalian, China, in 2005 and 2011, respectively. She is currently a Ph.D. candidate in control science and engineering from University of Science and Technology Liaoning, Anshan, China. Her research interests include nonlinear system control and intelligent control.
Yong-Hui Yang received his B.Sc. degree in communication engineering, from Northeastern University, Shenyang, China, an M.Sc. degree in control engineering, and a Ph.D. degree in chemical process from University of Science and Technology Liaoning, Anshan, China, in 1995, 2010, and 2018, respectively. He is currently a Professor and Doctoral Supervisor at the School of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan, China. His research interests include nonlinear control, intelligent process control, robot communication and control, and machine learning.
Li-Bing Wu was born in Chaoyang, Liaoning, China, in 1980, received his B.S. degree from the Department of Mathematics from Jinzhou Normal College, Jinzhou, China, an M.S. degree in basic mathematics from Northeastern University, Shenyang, China, and a Ph.D. degree in control theory and control engineering from Northeastern University, Shenyang, China, in 2004, 2007, and 2016, respectively. He was a Postdoctoral Fellow with Yeungnam University, Kyongsan, Korea, from 2018 to 2019. He is currently an Associate Professor with the School of Science, University of Science and Technology Liaoning. His research interests include adaptive control, fault-tolerant control, nonlinear control, and fault estimation.
Qi Li received his B.S. degree in automation from Dalian University of Technology, Dalian, China, an M.S. degree in control theory and control engineering from University of Science and Technology Liaoning, Anshan, China, in 1997 and 2003, respectively. He is currently an Associate Professor with the School of Electronic and Information Engineering, University of Science and Technology Liaoning. His research interests include nonlinear system control, machine learning, and intelligent control.
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Jiang, MY., Yang, YH., Wu, LB. et al. Adaptive Containment Control for a Class of Uncertain Multi-agent Systems With Unknown Virtual Control Gain Functions. Int. J. Control Autom. Syst. 21, 2835–2843 (2023). https://doi.org/10.1007/s12555-022-0331-1
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DOI: https://doi.org/10.1007/s12555-022-0331-1