Sampled-Data Flocking of Multi-Agent Systems Under the Cyber-Attack Problem
Subject Areas : Multimedia Processing, Communications Systems, Intelligent Systems
1 - 1. Department of Electrical Engineering, Zanjan Branch, Islamic Azad University, Zanjan, Iran
Keywords: Flocking, sampled-data, cyber-attack problem, multi-agent systems,
Abstract :
Introduction: Flocking is a type of collective behavior which is observed in the nature. In the design of a flocking algorithm, it should be ensured connectivity of agents’ network and the collision avoidance, and velocities convergence of agents to that of virtual leader. In practice due to the limitations in the measurement and control units, it is often impossible to ensure the continuity of information. Thus, the study of the flocking problem under the sampled data frameworks is indispensable. However, to the best of the authors’ knowledge, there are very few works on the sampled-data flocking. On the other hand, in many practical applications, the multi-agent systems are controlled through some communication networks. The transmitted data among agents could be easily exploited by adversaries due to the open network links among sensors, controllers and actuators. Since in practice often the attacks are capable to destroy a number of edges within the network or cause to collide among agents, the study of networked system under the cyber-attacks is very important. In the cyber-attacks, successful but recoverable attacks have attracted more attention. Successful attacks refer to a class of attacks by which the network is broken dow n into a group of isolated clusters. Recoverable attacks refer to a class of attacks that the network can recover from after a period of time. In this paper, we study the sampled-data flocking of multi-agent systems under the successful but recoverable network attacks.
Method: Here, defining a new discrete-time energy function we prove the asymptotic velocity convergence of agents to the velocity of virtual leader. Then, through the upper bound of the energy function, we find an upper bound for the sampling period such that the connectivity of network is preserved and collision is avoided, and also, the velocity convergence is ensured. After that, we modify the algorithm for application in cyber-attacks.
Results: We show that under our proposed sampled-data algorithm, no link is lost from initial network, no collision is occurred among agents, and the velocity convergence of agents to that of virtual leader is ensured. Also, demonstrate the proposed algorithm is applicable for the flocking under the attack problem.
[1] C. Reynolds, “Flocks, birds, and schools: A distributed behavioral model,” Computer Graphics, vol. 21, pp. 25-34, 1987.
[2] H. Tanner, “Flocking with obstacle avoidance in switching networks of interconnected vehicles,” in Proc. IEEE Int. Conf. Robot. Automat., New Orleans, LA, Apr. 2004, vol. 3, pp. 3006-3011.
[3] A. Jadbabaie, J. Lin, S.A. Morse, “Coordination of groups of mobile agents using nearest neighbor rules,” IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 988-1001, June 2003.
[4] N. Leonard, E. Friorelli, “Virtual leaders, artificial potentials and coordinated control of groups,” in Proc. 40thIEEE Conf. Decision and Control, Orlando, FL, Dec. 2001, pp. 2968-2973.
[5] R. Olfati-Saber, “Flocking for multi-agent dynamic systems: Algorithms and theory,” IEEE Transactions on Automatic Control, vol. 51, no. 3, pp. 401-420, March 2006.
[6] H. Su, X. Wang, G. Chen, “Flocking of multi agents with a virtual leader,” IEEE Transactions on Automatic Control, vol. 82, no. 7, pp. 1334-1343, July 2009.
[7] H. Su, X. Wang, Z. Lin, “A connectivity-preserving flocking algorithm for multi-agent systems based only on position measurements,” International Journal of Control, vol. 54, no. 2, pp. 293-307, Feb. 2009.
[8] H. Su, “Flocking in multi-agent systems with multiple virtual leaders based only on position measurements,” Communications in Theoretical Physics, vol. 57, no. 5, May 15, 2012.
[9] H. Shi, L. Wang, T. Chu, “Flocking of multi-agent systems with a dynamic virtual leader,” International Journal of Control, vol. 82, no. 1, pp. 43-58, Jan. 2009.
[10] Z. Yang, Q. Zhang, Z. Jiang, Z. Chen, “Flocking of multi-agents with time delay,” International Journal of Systems Science, vol. 43, no. 11, pp. 2125-2134, Nov. 2012.
[11] S. Li, X. Liu, W. Tang, J. Zhang, “Flocking of multi-agents following a leader with adaptive protocol in a noisy environment,” Asian Journal of Control, vol. 16, no. 6, pp. 1771-1778, 2014.
[12] H. Wang, “Flocking of networked uncertain Euler–Lagrange systems on directed graphs,”Automatica, vol. 49, no. 9, pp. 2774-2779, 2013.
[13] Y. Dong, J. Huang, Flocking with connectivity preservation of multiple double integrator systems subject to external disturbances by a distributed control law, Automatica, Vol. 55, 197-203, 2015.
[14] Q. Zhang, P. Li,Z. Yang,Z. Chen, “Adaptive flocking of non-linear multi-agents systems with uncertain parameters,”IET Control Theory and Applications,vol. 9, no. 3,pp.351-357, Feb. 2015.
[15] P. Yu, D. Li, Z.W. Liu, Z.H. Guan, “Leader-follower flocking based on distributed event-triggered hybrid control,” International Journal of Robust and Nonlinear Control, Article first published online: 4 Feb. 2015.
[16] Y. Cao, W. Ren, “Multi-vehicle coordination for double-integrator dynamics under fixed undirected/directed interaction in a sampled data setting,” International Journal of Robust and Nonlinear Control, vol. 20, no. 9, pp. 987-1000, June 2010.
[17] J. Qin, H. Gao, “A sufficient condition for convergence of sampled-data consensus for double-integrator dynamics with non-uniform and time-varying communication delays,” IEEE Transactions on Automatic Control, vol. 57, no. 9, pp. 2417-2422, Sep. 2012.
[18] W. Yu, L. Zhou, X. Yu, J. Lu, R. Lu, “Consensus in multi-agent systems with second-order dynamics and sampled data,”IEEE Transactions on Industrial Informatics, vol. 9, no. 4, pp. 2137-2146, 2013.
[19] Q. Ma, S. Xu, F.L. Lewis, “Second-order consensus for directed multi-agent systems with sampled data,”International Journal of Robust and Nonlinear Control, vol. 24, no. 16, pp. 2560-2573, 2014.
[20] S. Yazdani, M. Haeri, H. Su, ‘Sampled-data leader–follower algorithm for flocking of multi-agent systems’, IET Control Theory and Applications, 2019, 13, (5), pp. 609 – 619.
[21] S. Yazdani, M. Haeri, H. Su, ‘A Multi-Rate Sampled-Data Algorithm for Leader-Follower Flocking’, IET Control Theory and Applications, 2021, 10, (1), pp. 119 – 125.
[22] [Y. Wang, H. O. Wang, J. Xiao, et al.: ‘Synchronization of complex dynamical networks under recoverable attacks, Automatica, Vol. 46, 197-203, 2010.
[23] W. Zhang, Z. Wang, Y. Liu, et al., Sampled-data consensus of nonlinear multi-agent systems subject to cyber attacks, Int J Robust Nonlinear Control, Vol. 28, 53-67, 2018.
[24] M.. Nazarpour1, N. .Nezafati, S. Shokouhyar, ‘Using the Modified Colonial Competition Algorithm to Increase the Speed and Accuracy of the Intelligent Intrusion Detection System, Intelligent Multimedia Processing and Communication Systems, Vol. 4, no.1, pp. 1-10, 2023 (Persian).
[25] S. H. Mousavi, M. Safaeian, A. H. A. Ghaleh, ‘A new method in the security of encryption systems by unbalanced gates, Intelligent Multimedia Processing and Communication Systems, Vol. 3, no.2, pp. 39-50, (Persian).
