Document Type: Original Research Paper

Authors

1 Control Engineering Department, School of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, Iran

2 Department of Control Engineering, School of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, Iran.

3 The school of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran

Abstract

This article discusses a finite-time fault-tolerant consensus control for stochastic Euler-Lagrange multi-agent systems. First, the finite-time consensus controller of Euler-Lagrange multi-agent systems with stochastic disturbances is presented. Then, the proposed controller is extended as a fault-tolerant controller in the presence of faults in the actuators. In these two cases, the sliding-mode distributed consensus controllers are designed. The results guarantee that by using these controllers, the consensus tracking errors converge to a desired area near the origin in finite-time with the mean-square sense and also remain bounded in probability. In the simulation section, a robotic manipulator model with actuator faults and stochastic disturbances is discussed and the suggested consensus controller has been used for this case study.

Graphical Abstract

Keywords

Main Subjects

[1] Y. Tang, X. Xing, H. R. Karimi, L. Kocarev, and J. Kurths, “Tracking control of networked multi-agent systems under new characterizations of impulses and its applications in robotic systems,” IEEE Transactions on Industrial Electronics, vol. 63, no. 2, pp. 1299-1307, 2016.
[2] J. Ansari, A. Gholami, and A. Kazemi, “Multi-agent systems for reactive power control in smart grids,” International Journal of Electrical Power & Energy Systems, vol. 83, pp. 411-425, 2016.
[3] S. Shams Shamsabad Farahani, “Congestion control approaches applied to wireless sensor networks: A survey,” Journal of Electrical and Computer Engineering Innovations, vol. 6, no. 2, pp.125-144, 2018.
[4] M. Siavash. “Asynchronous control and stabilization of linear switched systems with unstabilizable subsystems by average dwell time approach,” Journal of Control, vol. 9, no. 2, pp. 59-69, 2015.
[5] T. Balch, and R.C. Arkin, “Behaviour-based formation control for multirobot teams,” IEEE Transactions on Robotics and Automation, vol. 14, no. 6, pp. 926-939, 1998.
[6] 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, Dec. 2018.
[7] T. A. Jesus, L. C. Pimenta, L.A. Tôrres, and E. M. Mendes, “Consensus for double-integrator dynamics with velocity constraints,” International Journal of Control, Automation and Systems, vol. 12, no. 5, pp. 930-938, 2014.
[8] M. Keshavarz and M. H. Shafiei, “Design of a novel framework to control nonlinear affine systems based on fast terminal sliding-mode controller,” Journal of Electrical and Computer Engineering Innovations, vol. 5, no. 2, pp. 101-108, 2017.
[9] C. E. Ren and C. P. Chen, “Sliding mode leader-following consensus controllers for second-order non-linear multi-agent systems,” IET Control Theory & Applications, vol. 9, no. 10, pp. 1544-1552, 2015.
[10] S. Wang and J. Huang, “Adaptive leader-following consensus for multiple Euler–Lagrange systems with an uncertain leader system,” IEEE Trans. Neural Netw. Learn. Syst., vol. 30, no. 7, pp. 2188–2196, 2019.
[11] Y. Liu, “Leaderless consensus for multiple Euler-Lagrange systems with event-triggered communication,” presented at the 2018 IEEE International Conference on Systems, Man, and Cybernetics (SMC) Miyazaki, Japan, 2018.
[12] Y. Wang, L. Cheng, W. Ren, Z. G. Hou, and M. Tan, “Seeking consensus in networks of linear agents: communication noises and Markovian switching topologies,” IEEE Transactions on Automatic Control, vol. 60, no. 5, pp. 1374-1379, 2015.
[13] K. Deng, Y. Chen, and C. Belta, “An approximate dynamic programming approach to multiagent persistent monitoring in stochastic environments with temporal logic constraints,” IEEE Transactions on Automatic Control, vol. 62, no. 9, pp. 4549-4563, 2017.

[14] S. H. Crandall and W.D. Mark, Random vibration in mechanical systems. Massachusetts: Academic Press, 2014.
[15] M. Y. Cui, X.J. Xie, and Z. J. Wu, “Dynamics modeling and tracking control of robot manipulators in random vibration environment,” IEEE Transactions on Automatic Control, vol. 58, no.6, pp.1540-1545, 2013.
[16] R. Zárate-Minano, F. M. Mele, and F. Milano, “SDE-based wind speed models with Weibull distribution and exponential autocorrelation,” presented at the Power and Energy Society General Meeting (PESGM), Boston, USA, IEEE, pp. 1-5, 2016.
[17] M. Shahvali and K. Shojaei, “Distributed control of networked uncertain Euler–Lagrange systems in the presence of stochastic disturbances: a prescribed performance approach,” Nonlinear Dynamics, vol. 90, no. 1, pp. 697-715, 2017.
[18] H. Ji, H.T. Zhang, Z. Ye, H., Zhang, B. Xu, and G. Chen, “Stochastic consensus control of second-order nonlinear multiagent systems with external disturbances,” IEEE Transactions on Control of Network Systems, vol. 5, no. 4, pp. 1585-1596, 2017.
[19] G. R. Rezaei, T. Binazadeh, and B. Safarinejadian, “Optimal finite-time control of positive linear discrete-time systems,” Journal of Electrical and Computer Engineering Innovations, vol. 4, no. 2, pp. 177-184 , 2016.
[20] W. He, C. Xu, Q. Han, F. Qian, and Z. Lang, “Finite-time leader–follower consensus of networked Euler–Lagrange systems with external disturbances,” IEEE Trans. Syst. Man Cybern. Syst., vol. 48, no. 11, pp. 1920–1928, 2018.
[21] L. Chen, C. Li, Y. Sun, and G. Ma, “Distributed finite-time tracking control for multiple uncertain Euler-Lagrange systems with error constraints,” International Journal of Control, https://doi.org/10.1080/00207179.2019.1613560, 2019.
[22] M. Siavash, V.J. Majd, and M. Tahmasebi, “A practical finite-time back-stepping sliding-mode formation controller design for stochastic nonlinear multi-agent systems with time-varying weighted topology,” International Journal of Systems Science, vol. 51, no. 3, pp. 488-506, 2020.
[23] J. Qin, G. Zhang, W.X. Zheng, and Y. Kang, “Adaptive sliding mode consensus tracking for second-order nonlinear multiagent systems with actuator faults,” IEEE Transactions on Cybernetics, vol. 49, no. 5, pp. 1605-1615, 2018.
[24] G. Chen, Y. Song, and F. L. Lewis, “Distributed fault-tolerant control of networked uncertain Euler–Lagrange systems under actuator faults,” IEEE Trans. Cybern., vol. 47, no. 7, pp. 1706–1718, 2017.
[25] B. Xiao, S. Yin, and H. Gao, “Reconfigurable tolerant control of uncertain mechanical systems with actuator faults: A sliding mode observer-based approach,” IEEE Transactions on Control Systems Technology, vol. 26, no. 4, pp. 1249-1258, 2017.
[26] G. Chen and Y.-D. Song, “Robust fault-tolerant cooperative control of multi-agent systems: A constructive design method,” Journal of the Franklin Institute, vol. 352, no. 10, pp. 4045–4066, 2015.
[27] K. Yan, M. Chen, Q. Wu, and K. Lu, “Robust attitude fault-tolerant control for unmanned autonomous helicopter with flapping dynamics and actuator faults,” Transactions of the Institute of Measurement and Control, vol. 41, no. 5, pp. 1266–1277, 2019.
[28] A. Tariverdi, H. A. Talebi, and M. Shafiee, “Fault-tolerant consensus of nonlinear multi-agent systems with directed link failures, communication noise and actuator faults,” International Journal of Control, https://doi.org/10.1080/00207179.2019.1583376, 2019.
[29] M. Siavash, V. J. Majd, and M. Tahmasebi, “Fault-tolerant formation control of stochastic nonlinear multi-agent systems with time-varying weighted topology,” Transactions of the Institute of Measurement and Control, https://doi.org/10.1177/0142331219891588, 2020.
[30] W. He, C. Yuhao, and Z. Yin, “Adaptive neural network control of an uncertain robot with full-state constraints,” IEEE Transactions on cybernetics, vol. 46, no. 3, pp. 620-629, 2015.
[31] F. Wang, B. Chen, Y. Sun, and C. Lin, “Finite time control of switched stochastic nonlinear systems,” Fuzzy Sets and Systems, vol. 365, pp. 140-152, 2018.