Document Type: Original Research Paper


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

2 School of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran


Background and Objectives: This article discusses a finite-time fault-tolerant consensus control for stochastic Euler-Lagrange multi-agent systems.
Methods: 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.
Results: The results section is the most important part of the abstract and nothing should compromise its range and quality. This is because readers who peruse an abstract do so to learn about the findings of the study. The results section should therefore be the longest part of the abstract and should contain as much detail about the findings as the journal word count permits.
Conclusion: The proposed theorems in this paper guarantee that the consensus tracking errors are bounded in probability and after a finite-time remain in a desired area close to the origin in the mean-square senses. The obtained theorems were applied to consensus control of the robotic manipulators to indicate the performance of the proposed controllers.


Main Subjects

[1] Y. Tang, X. Xing, H. R. Karimi, L. Kocarev, 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, 63(2): 1299-1307, 2016.

[2] J. Ansari, A. Gholami, A. Kazemi, “Multi-agent systems for reactive power control in smart grids,” International Journal of Electrical Power & Energy Systems, 83: 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, 6(2):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, 9(2): 59-69, 2015.

[5] T. Balch, R.C. Arkin, “Behaviour-based formation control for multirobot teams,” IEEE Transactions on Robotics and Automation, 14(6): 926-939, 1998.

[6] W. Zou, C. K. Ahn, Z. Xiang, “Leader-following consensus of second-order nonlinear multi-agent systems with unmodeled dynamics,” Neurocomputing, 322: 120–129, 2018.

[7] T. A. Jesus, L. C. Pimenta, L.A. Tôrres, E. M. Mendes, “Consensus for double-integrator dynamics with velocity constraints,” International Journal of Control, Automation and Systems, 12(5): 930-938, 2014.

[8] M. Keshavarz, 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, 5(2): 101-108, 2017.

[9] C. E. Ren, C. P. Chen, “Sliding mode leader-following consensus controllers for second-order non-linear multi-agent systems,” IET Control Theory & Applications, 9(10): 1544-1552, 2015.

[10] S. Wang, J. Huang, “Adaptive leader-following consensus for multiple Euler–Lagrange systems with an uncertain leader system,” IEEE Trans. Neural Netw. Learn. Syst., 30(7): 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, M. Tan, “Seeking consensus in networks of linear agents: communication noises and Markovian switching topologies,” IEEE Transactions on Automatic Control, 60(5): 1374-1379, 2015.

[13] K. Deng, Y. Chen, C. Belta, “An approximate dynamic programming approach to multiagent persistent monitoring in stochastic environments with temporal logic constraints,” IEEE Transactions on Automatic Control, 62(9): 4549-4563, 2017.

[14] S. H. Crandall, W.D. Mark, Random vibration in mechanical systems. Massachusetts:  Academic Press, 2014.

[15] M. Y. Cui, X.J. Xie, Z. J. Wu, “Dynamics modeling and tracking control of robot manipulators in random vibration environment,” IEEE Transactions on Automatic Control, 58, no.6):1540-1545, 2013.

[16] R. Zárate-Minano, F. M. Mele, 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: 1-5, 2016.

[17] M. Shahvali, K. Shojaei, “Distributed control of networked uncertain Euler–Lagrange systems in the presence of stochastic disturbances: a prescribed performance approach,” Nonlinear Dynamics, 90(1): 697-715, 2017.

[18] H. Ji, H.T. Zhang, Z. Ye, H., Zhang, B. Xu, G. Chen, “Stochastic consensus control of second-order nonlinear multiagent systems with external disturbances,” IEEE Transactions on Control of Network Systems, 5(4): 1585-1596, 2017.

[19] G. R. Rezaei, T. Binazadeh, B. Safarinejadian, “Optimal finite-time control of positive linear discrete-time systems,” Journal of Electrical and Computer Engineering Innovations, 4(2): 177-184 , 2016.

[20] W. He, C. Xu, Q. Han, F. Qian, Z. Lang, “Finite-time leader–follower consensus of networked Euler–Lagrange systems with external disturbances,” IEEE Trans. Syst. Man Cybern. Syst., 48(11): 1920–1928, 2018.

[21] L. Chen, C. Li, Y. Sun, G. Ma, “Distributed finite-time tracking control for multiple uncertain Euler-Lagrange systems with error constraints,” International Journal of Control, 2019.

[22] M. Siavash, V.J. Majd, 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, 51(3): 488-506, 2020.

[23] J. Qin, G. Zhang, W.X. Zheng, Y. Kang, “Adaptive sliding mode consensus tracking for second-order nonlinear multiagent systems with actuator faults,” IEEE Transactions on Cybernetics, 49(5): 1605-1615, 2018.

[24] G. Chen, Y. Song, F. L. Lewis, “Distributed fault-tolerant control of networked uncertain Euler–Lagrange systems under actuator faults,” IEEE Trans. Cybern., 47(7): 1706–1718, 2017.

[25] B. Xiao, S. Yin, H. Gao, “Reconfigurable tolerant control of uncertain mechanical systems with actuator faults: A sliding mode observer-based approach,” IEEE Transactions on Control Systems Technology, 26(4): 1249-1258, 2017.

[26] G. Chen, Y.-D. Song, “Robust fault-tolerant cooperative control of multi-agent systems: A constructive design method,” Journal of the Franklin Institute, 352(10): 4045–4066, 2015.

[27] K. Yan, M. Chen, Q. Wu, 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, 41(5): 1266–1277, 2019.

[28] A. Tariverdi, H. A. Talebi, M. Shafiee, “Fault-tolerant consensus of nonlinear multi-agent systems with directed link failures, communication noise and actuator faults,” International Journal of Control, 2019.

[29] M. Siavash, V. J. Majd, 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, 42(8): 1461-1474, 2020.

[30] W. He, C. Yuhao, Z. Yin, “Adaptive neural network control of an uncertain robot with full-state constraints,” IEEE Transactions on cybernetics, 46(3): 620-629, 2015.

[31] F. Wang, B. Chen, Y. Sun, C. Lin, “Finite time control of switched stochastic nonlinear systems,” Fuzzy Sets and Systems, 365): 140-152, 2018.