Reach a nonlinear consensus for MAS via doubly stochastic quadratic operators

References

• Abdulghafor, R., Shahidi, F., Zeki, A., & Turaev, S. (2015). The convergence consensus of multi-agent systems controlled via doubly stochastic quadratic operators. In Agents, Multi-Agent Systems and Robotics (ISAMSR), International Symposium On IEEE (pp. 59–64), Putrajaya, Malaysia: IEEE.
   Google Scholar
• Abdulghafor, R., Shahidi, F., Zeki, A., & Turaev, S. (2016a). Dynamics classifications of extreme doubly stochastic quadratic operators on 2D simplex. In H. Sulaiman, M. Othman, M. Othman, Y. Rahim, N. Pee (Eds.) Advanced Computer and Communication Engineering Technology, (pp. 323–335), Springer International Publishing.
   Google Scholar
• Abdulghafor, R., Shahidi, F., Zeki, A., & Turaev, S. (2016b). Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex. Openmath, 14(1), 509–519.
   Google Scholar
• Abdulghafor, R., , Turaev, S., Abubakar, A., & Zeki, A. (2015). The extreme doubly stochastic quadratic operators on two dimensional simplex. In Proceedings of the 4th International Conference on Advanced Computer Science Applications and Technologies (pp. 192–197). Kuala Lumpur, Malaysia: IEEE. Retrieved fromhttp://doi.org/10.1109/ACSAT.2015.36
   Google Scholar
• Abdulghafor, R., Turaev, S., & Izzuddin, M. (2016). Nonlinear consensus for multi-agent systems using positive intractions of doubly stochastic quadratic operators. International Journal on Perceptive and Cognitive Computing, 2(1), 19–22.
   Google Scholar
• Ajorlou, A., Momeni, A., & Aghdam, A.G. (2011). Sufficient conditions for the convergence of a class of nonlinear distributed consensus algorithms. Automatica, 47(3), 625–629.
   Web of Science ®Google Scholar
• Ando, T. (1989). Majorization, doubly stochastic matrices, and comparison of eigenvalues. Linear Algebra and Its Applications, 118, 163–248.
   Web of Science ®Google Scholar
• Andreasson, M., Dimarogonas, D.V., & Johansson, K.H. (2012). Undamped nonlinear consensus using integral Lyapunov functions. In Proceedings of the American Control Conference (pp. 6644–6649). Montreal, QC: IEEE.
   Google Scholar
• Bauso, D., Giarre, L., & Pesenti, R. (2006). Non-linear protocols for optimal distributed consensus in networks of dynamic agents. Systems & Control Letters, 55(11), 918–928.
   Web of Science ®Google Scholar
• Berger, R.L. (1981). A necessary and sufficient condition for reaching a consensus using DeGroot's method. Journal of the American Statistical Association, 76(374), 415–418.
   Web of Science ®Google Scholar
• Bishop, A.N., & Doucet, A. (2014). Distributed nonlinear consensus in the space of probability measures, IFAC Proceedings Volumes, 47, 8662–8668, Elsevier. ( arXiv Preprint arXiv:1404.0145).
   Google Scholar
• Bolouki, S., (2014). Linear consensus algorithms : structural properties and Connections with Markov Chains, Doctoral dissertation, Ecole Polytechnique de Montreal.
   Google Scholar
• Borkar, V.B.V., & Varaiya, P.V.P. (1979). Adaptive control of Markov chains, I: Finite parameter set. 18th IEEE Conference on Decision and Control Including the Symposium on Adaptive Processes, 18(6), 2–6. Retrieved from http://doi.org/10.1109/CDC.1979.270287
   Google Scholar
• Buoniu, L., & Morrescu, I.C. (2014). Consensus for black-box nonlinear agents using optimistic optimization. Automatica, 50(4), 1201–1208. Retrieved fromhttp://doi.org/10.1016/j.automatica.2014.02.021
   Web of Science ®Google Scholar
• Cao, M., Morse, A.S., & Anderson, B.D.O. (2008). Reaching a consensus in a dynamically changing environment: A graphical approach. SIAM Journal on Control and Optimization, 47(2), 575–600.
   Web of Science ®Google Scholar
• Cao, Y., Li, Y., Ren, W., & Chen, Y. (2010). Distributed coordination of networked fractional-order systems. IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, 40(2), 362–370.
   PubMed Web of Science ®Google Scholar
• Cucker, F., Smale, S., & Zhou, D.-X. (2004). Modeling language evolution. Foundations of Computational Mathematics, 4(3), 315–343.
   Web of Science ®Google Scholar
• Cui, G., Xu, S., Lewis, F.L., Zhang, B., & Ma, Q. (2016). Distributed consensus tracking for non-linear multi-agent systems with input saturation: A command filtered backstepping approach. IET Control Theory & Applications, 10(5), 509–516.
   Web of Science ®Google Scholar
• DeGroot, M.H. (1974a). Reaching a consensus. Journal of the American Statistical Association, 69(345), 118–121.
   Web of Science ®Google Scholar
• DeGroot, M.H. (1974b). Reaching a consensus. Journal of the American Statistical Association, 69(345), 118–121. Retrieved fromhttp://doi.org/10.2307/2285509
   Web of Science ®Google Scholar
• Ding, D., Wang, Z., Shen, B., & Wei, G. (2015). Event-triggered consensus control for discrete-time stochastic multi-agent systems: The input-to-state stability in probability. Automatica, 62, 284–291.
   Web of Science ®Google Scholar
• Dong, J.-G., & Qiu, L. (2014). Complex Laplacians and applications in multi-agent systems. (arXiv Preprint arXiv:1406.1862 1–6). Retrieved fromhttp://arxiv.org/abs/ 1406.1862
   Google Scholar
• Fagnani, F. (2014). Consensus dynamics over networks, Technical Paper, 66.
   Google Scholar
• Fax, J.A., & Murray, R.M. (2004). Information flow and cooperative control of vehicle formations. IEEE Transactions on Automatic Control, 49(9), 1465–1476.
   Web of Science ®Google Scholar
• Feng, Y., Xu, S., Lewis, F.L., & Zhang, B. (2015). Consensus of heterogeneous first and second order multi agent systems with directed communication topologies. International Journal of Robust and Nonlinear Control, 25(3), 362–375.
   Web of Science ®Google Scholar
• Ganikhodzhaev, R. N. (1993a). On the definition of bistochastic quadratic operators. Russian Mathematical Surveys, 48(4), 244–246.
   Web of Science ®Google Scholar
• Ganikhodzhaev, R.N. (1993b). Quadratic stochastic operators, Lyapunov functions, and tournaments. Russian Academy of Sciences. Sbornik Mathematics, 76(2), 489.
   Google Scholar
• Ganikhodzhaev, R.N., & Rozikov, U.A. (2009). Quadratic stochastic operators: Results and open problems. ( arXiv Preprint arXiv:0902.4207).
   Google Scholar
• Ganikhodzhaev, R., & Shahidi, F. (2010a). Doubly stochastic quadratic operators and Birkhoff's problem. Linear Algebra and Its Applications, 432(1), 24–35.
   Web of Science ®Google Scholar
• Ganikhodzhaev, R., & Shahidi, F. (2010b). Doubly stochastic quadratic operators and Birkhoff's problem. Linear Algebra and Its Applications, 432(1), 24–35. Retrieved from http://doi.org/10.1016/j.laa.2009.07.002
   Web of Science ®Google Scholar
• Georgopoulos, L., & Hasler, M. (2009). Nonlinear average consensus. In Proceedings of the International Symposium on Nonlinear Theory and its Applications (pp. 10–13). IEICE.
   Google Scholar
• Goodwine, B. (2014). Fractional-order dynamics in a random, approximately scale-free network of agents. In Proceedings of the 13th International Conference on Control Automation Robotics & Vision (ICARCV) (pp. 1581–1586). Singapore: IEEE.
   Google Scholar
• Hardy, G.H., Littlewood, J.E., & Polya, G. (1929). Some simple inequalities satisfied by convex functions. Messenger Math, 58(145–152), 310.
   Google Scholar
• Helman, P., Moret, B.M.E., & Shapiro, H.D. (1993). An exact characterization of greedy structures. SIAM Journal on Discrete Mathematics, 6(2), 274–283.
   Web of Science ®Google Scholar
• Hui, Q., & Haddad, W.M. (2008). Distributed nonlinear control algorithms for network consensus. Automatica, 44(9), 2375–2381.
   Web of Science ®Google Scholar
• Jadbabaie, A., & Lin, J., Morse, A.S. (2003). Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions On Automatic Control, 48(6), 988–1001.
   Web of Science ®Google Scholar
• Kokotović, P., & Arcak, M. (2001). Constructive nonlinear control: A historical perspective. Automatica, 37(5), 637–662.
   Web of Science ®Google Scholar
• Lovasz, L. (1983). Submodular functions and convexity. In Bachem A., Korte B., & Grotschel M. (Eds.) Mathematical programming: The state of the art. (pp. 235–257). Berlin Heidelberg: Springer.
   Google Scholar
• Li, H., Chen, G., Dong, Z., & Xia, D. (2016). Consensus analysis of multiagent systems with second-order nonlinear dynamics and general directed topology: An event-triggered scheme. Information Sciences, 370, 598–622.
   Web of Science ®Google Scholar
• Li, H., Liao, X., Lei, X., Huang, T., & Zhu, W. (2013). Second-order consensus seeking in multi-agent systems with nonlinear dynamics over random switching directed networks.IEEE Transactions on Circuits and Systems I: Regular Papers, 60(6), 1595–1607.
   Web of Science ®Google Scholar
• Li, Y., Guan, X., & Hua, C. (2011). Nonlinear protocols for output performance value consensus of multi-agent systems. In Proceedings of the 30th Chinese Control Conference (pp. 4831–4834). Yantai, China: IEEE.
   Google Scholar
• Li, Y., Voos, H., Darouach, M., & Hua, C. (2015). Nonlinear protocols for distributed consensus in directed networks of dynamic agents. Journal of the Franklin Institute, 352(9), 3645–3669.
   Web of Science ®Google Scholar
• Li, Z., Ren, W., Liu, X., & Fu, M. (2013). Consensus of multi-agent systems with general linear and Lipschitz nonlinear dynamics using distributed adaptive protocols. IEEE Transactions on Automatic Control, 58(7), 1786–1791.
   Web of Science ®Google Scholar
• Li, Z., Wen, G., Duan, Z., & Ren, W. (2015). Designing fully distributed consensus protocols for linear multi-agent systems with directed graphs. Automatic Control, IEEE Transactions on, 60(4), 1152–1157.
   Web of Science ®Google Scholar
• Lin, Z., Francis, B., & Maggiore, M. (2007a). State agreement for continuous-time coupled nonlinear systems. SIAM Journal on Control and Optimization, 46(1), 288–307.
   Web of Science ®Google Scholar
• Lin, Z., Francis, B., & Maggiore, M. (2007b). State agreement for continuous-time coupled nonlinear systems. SIAM Journal on Control and Optimization, 46(1), 288–307.
   Web of Science ®Google Scholar
• Lin, Z., Francis, B., & Maggiore, M. (2007c). State agreement for continuous‐time coupled nonlinear systems. SIAM Journal on Control and Optimization, 46(1), 288–307. Retrieved fromhttp://doi.org/10.1137/050626405
   Web of Science ®Google Scholar
• Lovisari, E., & Zampieri, S. (2012). Performance metrics in the average consensus problem: A tutorial. Annual Reviews in Control, 36(1), 26–41. Retrieved fromhttp://doi.org/10.3182/20100915-3-IT-2017.00080
   Web of Science ®Google Scholar
• Lynch, N.A. (1996). Distributed algorithms, San Francisco, CA: Morgan Kaufmann.
   Google Scholar
• Meng, D., Jia, Y., Du, J., & Zhang, J. (2014). On iterative learning algorithms for the formation control of nonlinear multi-agent systems. Automatica, 50(1), 291–295.
   Web of Science ®Google Scholar
• Moreau, L. (2005). Stability of multiagent systems with time-dependent communication links. IEEE Transactions on Automatic Control, 50(2), 169–182. Retrieved fromhttp://doi.org/10.1109/TAC.2004.841888
   Web of Science ®Google Scholar
• Muirhead, R.F. (1902). Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters. Proceedings of the Edinburgh Mathematical Society, 21, 144–162.
   Google Scholar
• Murray, R.O.S.R.M. (2003). Consensus protocols for networks of dynamic agents. In Proceedings of the American Control Conference, Denver, CO: IEEE.
   Google Scholar
• Olfati-Saber, 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.
   Web of Science ®Google Scholar
• Olkin, I., & Marshall, A.W. (1979). Inequalities: Theory of majorization and its applications. New York, NY: Springer Series in Statistics.
   Google Scholar
• Pan, H., Nian, X., & Guo, L. (2014). Second-order consensus in multi-agent systems based on second-order neighbours' information. International Journal of Systems Science, 45(5), 902–914.
   Web of Science ®Google Scholar
• Parker, D.S., & Ram, P. (1994). Greed and majorization (ABSTRACT).
   Google Scholar
• Parker, D.S., & Ram, P. (1996). Greed and majorization. Los Angeles: Computer Science Department, University of California.
   Google Scholar
• Parker, D.S., & Ram, P. (1997). Greed and Majorization. Retrieved fromhttp://citeseerx.ist.psu.edu/viewdoc/ summary?doi=10.1.1.30.9727
   Google Scholar
• Proskurnikov, A. (2013). Consensus in switching networks with sectorial nonlinear couplings: Absolute stability approach. Automatica, 49(2), 488–495.
   Web of Science ®Google Scholar
• Qu, Z., Wang, J., & Chunyu, J. (2007). Lyapunov design of cooperative control and its application to the consensus problem. In Proceedings of the IEEE International Conference on Control Applications (pp. 100–107). Singapore: IEEE.
   Google Scholar
• Ren, W., Beard, R.W., & Atkins, E.M. (2005). A survey of consensus problems in multi-agent coordination. In Proceedings of the American Control Conference (pp. 1859–1864, Postland, OR: IEEE.
   Google Scholar
• Saber, R.O., & Murray, R.M. (2003). Agreement problems in networks with directed graphs and switching topology. In Proceedings of the 42nd IEEE Conference on Decision and Control (Vol. 4, pp. 4126–4132). Maui, Hl: IEEE.
   Google Scholar
• Schwarz, V., & Matz, G. (2012). Nonlinear average consensus based on weight morphing. In ICASSP (pp. 3129–3132). Kyoto, Japan: IEEE.
   Google Scholar
• Shahidi, F. (2008). On the extreme points of the set of bistochastic operators. Mathematical Notes, 84(3–4), 442–448. Retrieved from http://doi.org/10.1134/ S0001434608090150
   Web of Science ®Google Scholar
• Shahidi, F.A. (2009). Doubly stochastic operators on a finite-dimensional simplex. Siberian Mathematical Journal, 50(2), 368–372.
   Web of Science ®Google Scholar
• Shahidi, F., Ganikhodzhaev, R., & Abdulghafor, R. (2013). The dynamics of some extreme doubly stochastic quadratic operators. Middle-East Journal of Scientific Research (Mathematical Applications in Engineering), 13, 59–63. Retrieved fromhttp://doi.org/10.5829/idosi.mejsr.2013.13.mae.99921
   Google Scholar
• Su, H., Chen, G., Wang, X., & Lin, Z. (2011). Adaptive second-order consensus of networked mobile agents with nonlinear dynamics. Automatica, 47(2), 368–375.
   Web of Science ®Google Scholar
• Su, Y., & Huang, J. (2013). Cooperative global output regulation of heterogeneous second-order nonlinear uncertain multi-agent systems. Automatica, 49(11), 3345–3350.
   Web of Science ®Google Scholar
• Tang, Y., Gao, H., Zou, W., & Kurths, J. (2013). Distributed synchronization in networks of agent systems with nonlinearities and random switchings. IEEE Transactions on Cybernetics, 43(1), 358–370.
   PubMed Web of Science ®Google Scholar
• Tsitsiklis, J.N. (1984). Problems in decentralized decision making and computation (Technical Report). DTIC Document, ADA150025. US: Department of Defense.
   Google Scholar
• Tsitsiklis, J.N., Bertsekas, D.P., & Athans, M. (1986). Distributed asynchronous deterministic and stochastic gradient optimization algorithms, IEEE transactions on automatic control. 31(9), 803–812. IEEE. Retrieved from http://doi.org/10.1109/TAC.1986.1104412
   Google Scholar
• Vicsek, T. (1995). Novel type of phase transition in a system of self-driven particles. Physical Review Letters, 75(4), 729–732.
   PubMedGoogle Scholar
• Wang, L., Feng, W., Chen, M.Z.Q., & Wang, Q. (2014). Global bounded consensus in heterogeneous multi-agent systems with directed communication graph. IET Control Theory & Applications, 9(1), 147–153. Retrieved fromhttp://doi.org/10.1049/iet-cta.2014.0530
   Web of Science ®Google Scholar
• Wang, X., Zhao, K., You, Z., & Zheng, L. (2013). A nonlinear consensus protocol of multiagent systems considering measuring errors. Mathematical Problems in Engineering, 2013.
   Google Scholar
• Wen, G., Yu, Y., Peng, Z., & Rahmani, A. (2016). Distributed finite-time consensus tracking for nonlinear multi-agent systems with a time-varying reference state. International Journal of Systems Science, 47(8), 1856–1867.
   Web of Science ®Google Scholar
• Wooldridge, M. (2009). An introduction to multi agent systems [Paperback]. United Kingdom: Wiley. Retrieved fromhttp://www.amazon.com/Introduction-MultiAgent-Systems-Michael-Wooldridge/dp/0470519460/ref=sr_1_ 2?ie=UTF8&qid=1401393249&sr=8-2&keywords= wooldridge+agent
   Google Scholar
• Wu, Q., Zhou, J., & Xiang, L. (2012). Impulsive consensus seeking in directed networks of multi-agent systems with communication time delays. International Journal of Systems Science, 43(8), 1479–1491.
   Web of Science ®Google Scholar
• Yu-Mei, L., & Xin-Ping, G. (2009). Nonlinear consensus protocols for multi-agent systems based on centre manifold reduction. Chinese Physics B, 18(8), 3355.
   Web of Science ®Google Scholar
• Yu, S., & Long, X. (2015). Finite-time consensus for second-order multi-agent systems with disturbances by integral sliding mode. Automatica, 54, 158–165.
   Web of Science ®Google Scholar
• Yu, W., Chen, G., & Cao, M. (2011). Consensus in directed networks of agents with nonlinear dynamics. IEEE Transactions on Automatic Control, 56(6), 1436–1441.
   Web of Science ®Google Scholar
• 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 B: Cybernetics, 40(3), 881–891. Retrieved fromhttp://doi.org/10.1109/TSMCB.2009.2031624
   PubMed Web of Science ®Google Scholar
• Zhang, W., Tang, Y., Wu, X., & Fang, J.-A. (2014). Synchronization of nonlinear dynamical networks with heterogeneous impulses. IEEE Transactions on Circuits and Systems: Regular Papers, 61(4), 1220–1228.
   Web of Science ®Google Scholar
• Zhao, L., & Jia, Y. (2015). Finite-time consensus for second-order stochastic multi-agent systems with nonlinear dynamics. Applied Mathematics and Computation, 270, 278–290.
   Web of Science ®Google Scholar
• Zheng, L., Yao, Y., Deng, M., & Yau, S.S.T. (2012). Decentralized detection in ad hoc sensor networks with low data rate inter sensor communication. IEEE Transactions on Information Theory, 58(5), 3215–3224.
   Web of Science ®Google Scholar
• Zheng, Y., & Wang, L. (2012). Distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies. International Journal of Control, 85(12), 1967–1976.
   Web of Science ®Google Scholar
• Zhu, M., & Martínez, S. (2010). Discrete-time dynamic average consensus. Automatica, 46(2), 322–329.
   Web of Science ®Google Scholar
• Zhu, Y.-K., Guan, X.-P., & Luo, X.-Y. (2013). Finite-time consensus for multi-agent systems via nonlinear control protocols. International Journal of Automation and Computing, 10(5), 455–462.
   Google Scholar
• Zuo, Z., & Tie, L. (2014). A new class of finite-time nonlinear consensus protocols for multi-agent systems. International Journal of Control, 87(2), 363–370.
   Web of Science ®Google Scholar