عنوان مقاله [English]
In this paper, the compensation controller approach is investigated for uncertain nonlinear multi agent systems. The dynamics of each of the agents includes uncertainties. Meanwhile, the exchange of the information between the agents is done under directed and fixed graphs. In this design, nonlinear control method is used to design nonlinear backstepping controller. The systems uncertainties are approximated by using the adaptive control method. To overcome the unpredictable effects of faults occurrence in the considered system actuators, Defective adaptive compensation method is used without any knowing about the fault time, fault type and fault structure. Finally, with the introduction of the new Lyapunov functions and by using the graph theory, the stability of the closed loop system is proved. By presenting a simulated example, the efficiency of the control view presented for nonlinear multi agent systems is shown in the presence of unknown faults in actuators and unknown external disturbances.
 C.P. Chen, G.X. Wen, Y.J. Liu, F.Y. Wang, "Adaptive consensus control for a class of nonlinear multiagent time-delay systems using neural networks", IEEE Trans. Neural Networks Learning Systems, Vol. 25, No. 6, pp. 1217-1226, June 2014 (doi:10.1109/TNNLS.2014.2302477).
 Y. Wang, L. Cheng, Z.-G. Hou, M. Tan, M. Wang, " Containment control of multi-agent systems in a noisy communication environment", Automatica, Vol. 50, No. 7, pp. 1922-1928, July 2014 (doi:10.1016/j.automatica. 2014.05.018).
 J. Hu, Y. Wu, L. Liu, G. Feng, "Adaptive bipartite consensus control of high‐order multiagent systems on coopetition networks," Int. J. Robust Nonlinear Control, Vol. 28, No. 7, pp. 2868-2886, May 2018 (doi: 10.1002/rnc.4054).
 X. Niu, Y. Liu, F. Li, "Consensus via Time-Varying Feedback for Uncertain Stochastic Nonlinear Multiagent Systems," IEEE Trans. Cybernetics, Vol. 49, No. 4, pp. 1536 - 1544, April 2019 (doi: 10.1109/TCYB.2018.2808336).
 S. Jiang, X. Lu, G. Cai, S. Cai, "Adaptive fixed-time control for cluster synchronisation of coupled complex networks with uncertain disturbances," Int. J. Syst. Science, Vol. 48, pp. 3382-3390, 2017 (doi: 10.1080/00207721.2017.1384962).
 S. Kong, M. Saif, B. Liu, "Observer design for a class of nonlinear fractional-order systems with unknown input," J. Franklin Institute, Vol. 354, No. 13, pp. 5503-5518, September 2017 (doi: 10.1016/j.jfranklin.2017.06.011).
 R. Cui, B. Ren, S. S. Ge, "Synchronised tracking control of multi-agent system with high order dynamics," IET Control Theory Appl., Vol. 6, No. 5, pp. 603-614, March 2012 (doi: 10.1049/iet-cta.2011.0011)
 D. Wang, H. Ma, D. Liu, "Distributed control algorithm for bipartite consensus of the nonlinear time-delayed multi-agent systems with neural networks," Neurocomputing, Vol. 174, pp. 928-936, January 2016 (doi: 10.1016/j.neucom.2015.10.013).
 C.-E. Ren, L. Chen, C. P. Chen, "Adaptive fuzzy leader-following consensus control for stochastic multiagent systems with heterogeneous nonlinear dynamics,"IEEE Trans. Fuzzy Systems, Vol. 25, No. 1, pp. 181-190, February 2017 (doi: 10.1109/TFUZZ.2016.2554151).
 Z. Li, H. Ji, "Finite-Time Consensus and Tracking Control of A Class of Nonlinear Multiagent Systems," IEEE Trans. Automatic Control, Vol. 63, No. 12, pp. 4413-4420, December 2018 (doi: 10.1109/TAC.2018.2845677).
 W. Xiong, D. W. Ho, J. Cao, W. X. Zheng, "Backstepping approach to a class of hierarchical multi-agent systems with communication disturbance," IET Control Theory Applications, Vol. 10, No. 9, pp. 981-988, May 2016 (doi: 10.1049/iet-cta.2015.1066).
 H. Du, Y. He, Y. Cheng, "Finite-time synchronization of a class of second-order nonlinear multi-agent systems using output feedback control," IEEE Trans. Circuits Systems I: Regular Papers, Vol. 61, No. 6, pp. 1778-1788, June 2014 (doi: 10.1109/TCSI.2013.2295012).
 S. Zheng, P. Shi, S. Wang, Y. Shi, "Event triggered adaptive fuzzy consensus for interconnected switched multi-agent systems," IEEE Trans. Fuzzy Systems, Vol. 27, No. 1, January 2018 (doi: 10.1109/TFUZZ.2018.2873968).
 S. El-Ferik, H. A. Hashim, F. L. Lewis, "Neuro-adaptive distributed control with prescribed performance for the synchronization of unknown nonlinear networked systems," IEEE Trans. Systems Man Cybernetics: Systems, Vol. 48, No. 12, pp. 2135-2144, December 2018 (doi: 10.1109/TSMC.2017.2702705).
 J. Li, D. Zhang, "Backstepping and Sliding‐Mode Techniques Applied to Distributed Secondary Control of Islanded Microgrids," AsianJ. Control, vol. 20, No. 3, pp. 1288-1295, May 2018 (doi: 10.1002/asjc.1629).
 J. Liu, Y. Yu, Q. Wang, C. Sun, "Fixed-time event-triggered consensus control for multi-agent systems with nonlinear uncertainties," Neurocomputing, Vol. 260, pp. 497-504, October 2017 (doi: 10.1016/j.neucom.2017.04.061).
 W. Zhang, Y.Tang, Y. Liu, J. Kurths, "Event-Triggering Containment Control for a Class of Multi-Agent Networks With Fixed and Switching Topologies," IEEE Trans. Circuits Systems, Vol. 64, No.3, pp. 619-629, March 2017 (doi: 10.1109/TCSI.2016.2618944)
 Y. Shang, B. Chen, C. Lin, "Consensus tracking control for distributed nonlinear multiagent systems via adaptive neural backstepping approach," IEEE Trans. Systems Man Cybernetics: Systems, pp. 1-9, In Press (doi: 10.1109/TSMC.2018.2816928)
 M. Lingya, J. Bin, "Backstepping-based active fault-tolerant control for a class of uncertain SISO nonlinear systems," J.Systems Engineering Electronics, Vol. 20, No. 6, pp. 1263-1270, December 2009.
 D. Zhai, C. Xi, J. Dong, Q. Zhang, "Adaptive Fuzzy Fault-Tolerant Tracking Control of Uncertain Nonlinear Time-Varying Delay Systems," IEEE Trans. Systems Man Cybernetics: Systems, In Press, (doi: 10.1109/TSMC.2018.2789441).
 A. Baldini, L. Ciabattoni, R. Felicetti, F. Ferracuti, A. Freddi, A. Monteriù, "Dynamic surface fault tolerant control for underwater remotely operated vehicles," ISA transactions, Vol. 78, pp. 10-20, July 2018 (doi: 10.1016/j.isatra.2018.02.021).
 Y. Zhang, S. J. Qin, "Sensor fault compensation for nonlinear systems using fuzzy adaptive sliding control," 17th IFAC World Cong, pp. 13217-13222, July 2008.
 J. Cai, M. Zhang, L. Xing, L. Shen, "Adaptive Failure Compensation for Uncertain Systems with Unknown Utility Decrement of Actuators," Asian J. Control, Vol. 20, No.2, pp. 893-905, March 2018 (doi: 10.1002/asjc.1613).
 G. Lai, C. Wen, Z. Liu, Y. Zhang, C. P. Chen, S. Xie, "Adaptive compensation for infinite number of actuator failures based on tuning function approach," Automatica, Vol. 87, pp. 365-374, January 2018 (doi: 10.1016/j.automatica.2017.07.014).
 J. Qin, G. Zhang, W. X. Zheng, Y. Kang, "Adaptive Sliding Mode Consensus Tracking for Second-Order Nonlinear Multiagent Systems With Actuator Faults," IEEE Trans. Cybernetics, Vo. 49, No. 5, pp. 1605-1615, May 2018 (doi: 10.1109/TCYB.2018.2805167).
 A. Wu, B. Zhao, J. Mao, B. Wu, F. Yu, "Adaptive active fault-tolerant MPPT control for wind power generation system under partial loss of actuator effectiveness," Int. J. Electrical Power Energy Systems, Vol. 105, pp. 660-670, February 2019 (doi: 10.1016/j.ijepes.2018.09.015).
 Y. Hua, X. Dong, Q. Li, Z. Ren, "Distributed fault-tolerant time-varying formation control for second-order multi-agent systems with actuator failures and directed topologies," IEEE Trans. Circuits Systems II: Express Briefs, Vol. 65, No. 6, pp. 774-778, June 2018 (doi: 10.1109/TCSII.2017.2748967).
 G. Zhang, J. Qin, W. X. Zheng, Y. Kang, "Fault-tolerant coordination control for second-order multi-agent systems with partial actuator effectiveness," Information Sciences, Vol. 423, pp. 115-127, January 2018 (doi: 10.1016/j.ins.2017.09.043).
 Q. Shen, B. Jiang, P. Shi, J. Zhao, "Cooperative adaptive fuzzy tracking control for networked unknown nonlinear multiagent systems with time-varying actuator faults," IEEE Trans. Fuzzy Systems, Vol. 22, No.3, pp. 494-504, June 2014 (doi: 10.1109/TFUZZ.2013.2260757).
 S. Fu, J. Qiu, L. Chen, S. Mou, "Adaptive Fuzzy Observer Design for a Class of Switched Nonlinear Systems With Actuator and Sensor Faults," IEEE Trans. Fuzzy Systems, Vol. 26, No.6, pp. 3730-3742, December 2018 (doi: 10.1109/TFUZZ.2018.2848253).