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Original Articles

Consensus with a reference state for fractional-order multi-agent systems

, , , &
Pages 222-234 | Received 17 Nov 2014, Accepted 21 May 2015, Published online: 02 Jul 2015

References

  • Bhalekar, S., & Daftardar-gejji, V. (2011). A predictor-corrector scheme for solving nonlinear delay differential equations of fractional order. Journal of Fractional Calculus and Applications, 1(5), 1–9.
  • Cao, Y., Li, Y., Ren, W., & Chen, Y.Q. (2008). Distributed coordination algorithms for multiple fractional-order systems. Cancun: IEEE.
  • Cao, Y., Li, Y., Ren, W., & Chen, Y. (2010). Distributed coordination of networked fractional-order systems. Transactions on Systems, Man, and Cyber. Part B, 40(2), 362–370.
  • Cao, Y., & Ren, W. (2010). Distributed formation control for fractional-order systems: Dynamic interaction and absolute/relative damping. Systems & Control Letters, 59, 233–240.
  • Diao, M., Duan, Z., & Wen, G. (2014). Consensus tracking of linear multi-agent systems under networked observability conditions. International Journal of Control, 87(8), 1478–1486.
  • Diethelm, K. (1997). An algorithm for the numerical solution of differential equations of fractional order. Electronic Transactions on Numerical Analysis, 5, 1–6.
  • Diethelm, K., Ford, N., & Freed, A. (2002). A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynamics, 29(1–4), 3–22.
  • Dong, W. (2012). Adaptive consensus seeking of multiple nonlinear systems. International Journal of Adaptive Control and Signal Processing, 26(5), 419–434.
  • Gao, L., Zhu, X., Chen, W., & Zhang, H. (2013). Leader-following consensus of linear multiagent systems with state observer under switching topologies. Mathematical Problems in Engineering. Advance online publication. doi: 10.1155/2013/873140
  • Hong, Y., Hu, J., & Gao, L. (2006). Tracking control for multi-agent consensus with an active leader and variable topology. Automatica, 42(7), 1177–1182.
  • Hu, J., & Hong, Y. (2007). Leader-following coordination of multi-agent systems with coupling time delays. Physica A: Statistical Mechanics and its Applications, 374(2), 853–863.
  • Jadbabaie, A., Lin, J., & Morse, A. (2003). Coordination of groups of mobile autonomous agents using nearest neighbor rules. Automatic Control, IEEE Transactions on, 48(6), 988–1001.
  • Ji, M., Ferrari-Trecate, G., Egerstedt, M., & Buffa, A. (2008). Containment control in mobile networks. IEEE Transactions on Automatic Control, 53(8), 1972–1975.
  • Jing, G., Zheng, Y., & Wang, L. (2014). Flocking of multi-agent systems with multiple groups. International Journal of Control, 87(12), 2573–2582.
  • Li, H. (2012). Observer-type consensus protocol for a class of fractional-order uncertain multiagent systems. Abstract and Applied Analysis. Advance online publication. doi: 10.1155/2012/672346
  • Li, Y., Yu, W., Wen, G., & Yu, X. (2014). (pp. 1529–1533). Nanjing: IEEE.
  • Liao, Z., Peng, C., Li, W., & Wang, Y. (2011). Robust stability analysis for a class of fractional order systems with uncertain parameters. Journal of the Franklin Institute, 348(6), 1101–1113.
  • Lin, P., Jia, Y., & Li, L. (2008). Distributed robust consensus control in directed networks of agents with time-delay. Systems, Control Letters, 57(8), 643–653.
  • Liu, X., Xu, B., & Xie, L. (2012). Distributed containment control of networked fractional-order systems with delay-dependent communications. Journal of Applied Mathematics. Advance online publication doi: 10.1155/2012/840873
  • Matignon, D. (1996). Stability results for fractional differential equations with applications to control processing. In Computational engineering in systems applications (pp. 963–968). Retrieved from http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.40.4859
  • Moore, K., & Lucarelli, D. (2007). Decentralized adaptive scheduling using consensus variables. Robust Nonlinear Control, 17(10–11), 921–940.
  • Moreau, L. (2005). Stability of multiagent systems with time-dependent communication links. IEEE Transactions on Automatic Control, 50(2), 169–182.
  • Murray, R.M. (2007). Recent research in cooperative control of multi-vehicle systems. ASME Journal of Dynamic Systems & Measurement, and Control, 129(5), 571–583.
  • Ni, W., & Cheng, D. (2010). Leader-following consensus of multi-agent systems under fixed and switching topologies. Systems & Control Letters, 59(3–4), 209–217.
  • Oldham, K., & Spanier, J. (1974). The fractional calculus. New York, NY: Academic.
  • Olfati-Saber, R. (2007, Dec). Distributed Kalman filtering for sensor networks. In Proceedings of the 46th IEEE Conference on Decision and Control (pp. 5492–5498). New Orleans, LA: IEEE.
  • Peng, Z., Wen, G., Rahmani, A., & Yu, Y. (2015). Distributed consensus-based formation control for multiple nonholonomic mobile robots with a specified reference trajectory. International Journal of Systems Science, 46(8), 1447–1457.
  • Peng, Z., Wen, G., Rahmani, A., & Yu, Y. (2013). Leader-follower formation control of nonholonomic mobile robots based on a bioinspired neurodynamic-based approach. Robotics and Autonomous Systems, 61(9), 988–996.
  • Podlubny, I. (1999). Fractional differential equations. New York, NY: Acdamic Press.
  • Powell, M.J.D. (1970). A fortran subroutine for solving systems of nonlinear algebraic equations. In P. Rabinowitz (Ed.), Numerical methods for nonlinear algebraic equations. London: Gordon and Breach Science Publishers.
  • Ran, X., & Wu, Q. (2013). Leader-follower consensus for multi-agent systems based on error predictor. In 2013 Fifth International Conference on Measuring Technology and Mechatronics Automation (ICMTMA) (pp. 681–684). Hong Kong: IEEE.
  • Rao, S., & Ghose, D. (2011). Sliding mode control-based algorithms for consensus in connected swarms. International Journal of Control, 84(9), 1477–1490.
  • Ren, W. (2007). Multi-vehicle consensus with a time-varying reference state. Systems & Control Letters, 56(7–8), 474–483.
  • Ren, W., & Beard, R. (2005). Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Transactions on Automatic Control, 50(5), 655–661.
  • Ren, W., & Beard, R.W. (2008). Distributed consensus in multi-vehicle cooperative control. London: Springer.
  • Reynolds, C.W. (1987). Flocks, herds and schools: A distributed behavioral model. SIGGRAPH Computer Graphics, 21(4), 25–34.
  • Sabatier, J., Agrawal, O.P., & Tenreiro Machado, J.A. (2007). Advances in fractional calculus: Theoretical developments and applications in physics and engineering. Berlin: Springer.
  • Shao, J., Wang, L., & Yu, J. (2007). Development of multiple robotic fish cooperation platform. International Journal of Systems Science, 38(3), 257–268.
  • Shen, J., & Cao, J. (2011). Necessary and sufficient conditions for consensus of delayed fractional-order systems over directed graph. Asian Journal of Control, 14, 1690–1697.
  • Shen, J., Cao, J., & Lu, J. (2012). Consensus of fractional-order systems with non-uniform input and communication delays. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 226(2), 271–283.
  • Smith, S., Broucke, M., & Francis, B. (2007). Curve shortening and the rendezvous problem for mobile autonomous robots. IEEE Transactions on Automatic Control, 52(6), 1154–1159.
  • Štula, M., Stipaničev, D., & Maras, J. (2013). Distributed computation multi-agent system. New Generation Computing, 31(3), 187–209.
  • Tricaud, C., & Chen, Y. (2010). Time-optimal control of systems with fractional dynamics. International Journal of Differential Equations. Advance online publication doi: 10.1155/2010/461048.
  • Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., & Shochet, O. (1995). Novel type of phase transition in a system of self-driven particles. Physical Review Letters, 75(4), 1226–1229.
  • Wang, J., Yang, Z., Huang, T., & Xiao, M. (2012). Synchronization criteria in complex dynamical networks with nonsymmetric coupling and multiple time-varying delays. Applicable Analysis, 91(5), 923–935.
  • Wang, J.L., & Wu, H.N. (2012). Local and global exponential output synchronization of complex delayed dynamical networks. Nonlinear Dynamics, 67(1), 497–504.
  • Wen, G., Li, Z., Duan, Z., & Chen, G. (2013). Distributed consensus control for linear multi-agent systems with discontinuous observations. International Journal of Control, 86(1), 95–106.
  • Wen, G., Peng, Z., Rahmani, A., & Yu, Y. (2013). Distributed leader-following consensus for second-order multi-agent systems with nonlinear inherent dynamics. International Journal of Systems Science, 45(9), 1892–1901.
  • Wu, B., Wang, D., & Poh, E.K. (2010, June). Decentralized control for satellite formation using local relative measurements only. In 2010 8th IEEE International Conference on Control and Automation (ICCA) (pp. 661–666). Xiamen: IEEE.

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