In collaboration with Payame Noor University and the Iranian Society of Instrumentation and Control Engineers

Document Type : Research Article

Authors

Department of Mathematics‎, ‎Faculty of Sciences‎, ‎University of Zanjan‎, P. O. Box 45371-38791, Zanjan, Iran

10.30473/coam.2023.64817.1209

Abstract

In this paper‎, ‎we present a new approach for achieving leader-follower consensus in a network of nonlinear dynamic agents with an undirected graph topology‎, ‎using a fuzzy sliding mode controller (FSMC) for Multi-Agent Systems (MASs)‎. ‎Our proposed sliding mode controller is based on a separating hyperplane that effectively addresses the consensus problem in MASs‎. ‎Additionally‎, ‎we design a fuzzy controller to eliminate the chattering phenomenon‎. ‎According to the communication graph topology and the Lyapunov stability condition‎, ‎the proposed FSMC satisfies the consensus condition‎. ‎One significant advantage of our approach is that the system states converge to the sliding surface quickly and remain on the surface‎, ‎thereby ensuring better tracking performance‎. ‎We validate the effectiveness of our proposed approach through simulation results‎.

Keywords

Main Subjects

[1] Antonelli, G. (2013). “Interconnected dynamic systems: An overview on distributed control”, IEEE, Control Systems Magazine, 33(1), 76-88.
[2] Boyd, S., Vandenberghe, L. (2004). “Convex optimization”, Cambridge University Press, USA.
[3] Cao, Y., Yu, W., Ren, W., Chen, G. (2013). “An overview of recent progress in the study of distributed multi-agent coordination”, IEEE, Transactions on Industrial Informatics, 9(1), 427-438.
[4] Carli, R., Bullo, F., Zampieri, S. (2010). “Quantized average consensus via dynamic coding/decoding schemes”, International Journal of Robust and Nonlinear Control, 20(2), 156-175.
[5] Grocholsky, B., Keller, J., Kumar, V., Pappas, G. (2006). “Cooperative air and ground surveillance”, IEEE, Robotics Automation Magazine, 13(3), 16-25.
[6] Jadbabaie, A., Lin J., Morse, A.S. (2003). “Coordination of groups of mobile autonomous agents using nearest neighbour rules”, IEEE, Transactions on Automatic Control , 48(6), 988-1001.
[7] Jeon, I., Lee, J., Tahk, M. (2010). “Homing guidance law for cooperative attack of multiple missiles”, Journal of Guidance Control and Dynamics, 33(1), 275-280.
[8] Jiang, F., Wang, L. (2010). “Consensus seeking of high-order dynamic multi-agent systems with fixed and switching topologies”, International Journal of Control, 83(2), 404-420.
[9] Kennedy, J., Eberhart, R. (1995). “Particle swarm optimization”, In Proceedings of ICNN’95 International Conference on Neural Networks, 4, 1942-1948.
[10] Larson, J., Kammer, C., Liang, K., Johansson, K.H. (2013). “Coordinated route optimization for heavy-duty vehicle platoons”, IEEE, In 16th International IEEE Conference on Intelligent Transportation Systems, 1196-1202.
[11] Li, Z., Duan, Z., Chen, G. (2011). “Dynamic consensus of linear multi-agent systems”, IET, Control Theory & Applications, 5, 19-28.
[12] Li, T., Fu, M., Xie, L., Zhang, J. (2011). “Distributed consensus with limited communication data rate”, IEEE, Transactions on Automatic Control, 56(2), 279-292.
[13] Li, K., Zheng, B., Park, J.H. (2018). “Event based robust consensus for multi-agent systems via sliding mode control”, 2018 Chinese Control And Decision Conference, 4483-4488.
[14] Li, Z., Duan, Z., Chen, G., Huang, L. (2011). “Consensus of multi-agent systems and synchronization of complex networks: A unified viewpoint”, IEEE, Transactions on Circuits and Systems I: Regular Papers, 57(1), 213-224.
[15] Lin, P., Jia, Y. (2009). “Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies”, Automatica, 45(9), 2154-2158.
[16] Liu, X., Du, C., Liu, H., Lu, P. (2018). “Distributed event-triggered consensus control with fully continuous communication free for general linear multi-agent systems under directed graph”, International Journal of Robust and Nonlinear Control, 28(1), 132-143.
[17] Ma, C., Zhang, J. (2010). “Necessary and sufficient conditions for consensusability of linear multi-agent systems”, IEEE, Transactions on Automatic Control, 55(5), 1263-1268.
[18] Michael, N., Fink, J., Kumar, V. (2011). “Cooperative manipulation and transportation with aerial robots”, Autonomous Robots, 30(1), 73-86.
[19] Murray, R.M., Sastry, S.S., Li, Z. (1994). “A mathematical introduction to robotic manipulation”, 1st edition, RC Press, Inc., USA.
[20] Oh, R., Shi, Y., Woong, J. (2021). “A hybrid Newton-Raphson and particle swarm optimization method for target motion analysis by batch processing”, Sensors, 21(6), 2033.
[21] OlfatiSaber, R., Fax, J.A., Murray, R.M. (2007). “Consensus and cooperation in networked multi-agent systems”, Proceedings of the IEEE, 95(1), 215-233.
[22] OlfatiSaber, R., Murray, R.M. (2004). “Consensus problems in networks of agents with switching topology and time-delays”, IEEE, Transactions on Automatic Control, 49(9), 1520-1533.
[23] Ren, W. (2008). “On consensus algorithms for double-integrator dynamics”, IEEE, Transactions on Automatic Control, 53(6), 1503-1509.
[24] Ren, W., Atkins, E.M. (2007). “Distributed multi-vehicle coordinated control via local information exchange”, Journal of Robust and Nonlinear Control, 17(10-11), 1002-1033.
[25] Ren, W., Beard, R.W. (2005). “Consensus seeking in multi-agent systems under dynamically changing interaction topologies”, IEEE, Transactions on Automatic Control, 50(5), 655-661.
[26] Ren, W., Beard, R.W. (2007). “Distributed Consensus in Multi-Vehicle Cooperative Control: Theory and Applications”, 1st edition, Springer.
[27] Ren, W., Beard, R.W., Atkins, E.M. (2007). “Information consensus in multi vehicle cooperative control”, IEEE, Control Systems Magazine, 27(2), 71-82.
[28] Ren W., Moore K., Chen Y. (2007). “High-order and model reference consensus algorithms in cooperative control of multi-vehicle systems”, Journal of Dynamic Systems Measurement and Control-transactions of The Asme, 129(09), 678-688.
[29] Seo J. H., Shim H., Back J. (2009). “Consensus of high-order linear systems using dynamic output feedback compensator: Low gain approach”, Elsevier, Automatica, 45(11), 2659-2664.
[30] Song Q., Cao J., Yu W. (2010). “Second-order leader-following consensus of nonlinear multi-agent systems via pinning control”, IEEE, Systems & Control Letters, 59(9), 553-562.
[31] Tuna S. E. (2009). “Conditions for synchronizability in arrays of coupled linear systems”, IEEE, Transactions on Automatic Control, 54(10), 2416-2420.
[32] Vicsek T. S., Czirók A., Eshel B. J., Inon C., Ofer S. (1995). “Novel type of phase transition in a system of self-driven particles”, Physical Review Letters, 75(6), 1226-1229.
[33] Wand D., Zhou Q., Zhu W. (2018). “Adaptive event-based consensus of multi-agent systems with general linear dynamics”, Springer, Journal of Systems Science and Complexity, 31(1), 120-129.
[34] Ye D., Chen M., Yang H. (2019). “Distributed adaptive event-triggered fault-tolerant consensus of multi agent systems with general linear dynamics”, IEEE, Transactions on Cybernetics, 49(3), 757-767.
[35] You K., Xie L. (2011). “Network topology and communication data rate for consensus ability of discrete-time multi-agent systems”, IEEE, Transactions on Automatic Control, 56(10), 2262-2275.
[36] Yu W., Chen G., Cao M., Kurths J. (2010). “Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics”, IEEE, Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 40(3), 881-891.
[37] Zhang H., Lewis F. L., Das A. (2011). “Optimal design for synchronization of cooperative systems: State feedback, observer and output feedback”, IEEE, Transactions on Automatic Control, 56(8), 1948-1952.
[38] Zhang Q., Wei X., Xu J. (2005). “Delay-dependent exponential stability of cellular neural networks with time-varying delays”, Chaos, Solitons & Fractals, 23(4), 1363-1369.
[39] Zhang Z., Zhang Z., Li L. (2017). “Dynamical sliding-mode control of leader-following multi-agent systems”, IEEE, 43rd Annual Conference of the IEEE Industrial Electronics Society, 6273-6278.
[40] Zhu W., Cheng D. (2010). “Leader-following consensus of second-order agents with multiple time varying delays”, Elsevier, Automatica, 1994-1999.