Department of Electrical Engineering, Malek Ashtar University of Technology, Shahin Shar, Iran
This paper is concerned with the consensus tracking problem of high order MIMO nonlinear multi-agent systems. The agents must follow a leader node in presence of unknown dynamics and uncertain external disturbances. The communication network topology of agents is assumed to be a fixed undirected graph. A distributed adaptive control method is proposed to solve the consensus problem utilizing relative information of neighbors of each agent and characteristics of the communication topology. A radial basis function neural network is used to represent the controller’s structure. The proposed method includes a robust term with adaptive gain to counter the approximation error of the designed neural network as well as the effect of external disturbances. The stability of the overall system is guaranteed through Lyapunov stability analysis. Simulations are performed for two examples: a benchmark nonlinear systems and multiple of autonomous surface vehicles (ASVs). The simulation results verify the merits of the proposed method against uncertainty and disturbances.
 W. Ren, R. Beard and E. Atkins, “Information consensus in multivehicle cooperative control,” IEEE Control Systems Mag., vol. 27, pp. 71-82, March 2007.  R. Olfati-Saber, J. Fax, and R. Murray, “Consensus and cooperation in networked multi-agent systems,” Proc. IEEE 95, pp 215-233, 2007.  W. Ren and R. Beard, Distributed consensus in multi-vehicle cooperative control: Theory and applications, Springer-Verlag, London, 2008.  W. Ren, R. Beard and E. Atkins, “A survey of consensus problems in multi-agent coordination,” Proc. American Control Conf., pp. 1859-1864, 2005.  W. Ren, K. Moore and Y. Chen, “High-order and model reference consensus algorithms in cooperative control of multivehicle systems,” Proc. IEEE Int. Conf. Networking, Sensing and Control, Ft. Lauderdale, FL, pp 457-462. 2006.  Z. Li, Z. Duan, G. Chen and L. Huang, “Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint,” IEEE Trans. Circuits and Systems, vol. 57, pp. 213-224, April 2010.  Z. Li, Z. Duan and G. Chen, “Dynamic consensus of linear multi-agent systems,” IET Control Theory Appl., vol. 5, pp. 19-28, January 2011.  D. Meng, Y. Jia and J. Du, “Robust iterative learning protocols for finite time consensus of multi-agent systems with interval uncertain topologies,” Int. J. Syst. Sci., vol. 46, pp. 857-871, May.  W. Yu, G. Chen and M. Cao, “Consensus in directed networks of agents with nonlinear dynamics”, IEEE Trans. Automaic Control, vol. 56, pp. 1436-1441, June 2011.  G. Wen, A. Rahmani and Y. Yu, “Consensus tracking for multi-agent systems with nonlinear dynamics under fixed communication topologies,” Proc. World Congress on Engineering and Computer Science, San Francisco, USA, 2011.  Z. Li, X. Liu, M. Fu and L. Xi, “Global H∞ consensus of multi-agent systems with Lipschitz nonlinear dynamics”, IET Control Theory Appl., vol. 6, pp. 2041-2048, September 2012.  W. Yu, G. Chen, M. Cao and J. Kurths, “Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics,” IEEE Trans. Syst. Man Cybern. Part B, vol. 40, pp. 881-891, June 2010.  G. Wen, Z. Peng, A. Rahmani, and Y. Yu, “Distributed leader-following consensus for second-order multi-agent systems with nonlinear inherent dynamics,” Int. J. Syst. Sci., vol. 45, pp. 1892-1901, January 2014.  Z. G. Wu, P. Shi, H. Su and J. Chu, “Sampled-data synchronization of chaotic Lur’e systems with time delays,” IEEE Trans. Neural Netw., vol. 24, pp. 410-421, March 2013.  Z.G. Wu, P. Shi, H. Su and J. Chu, “Sampled-data exponential synchronization of complex dynamical networks with time-varying coupling delay,” IEEE Trans. Neural Netw., vol. 24, pp. 1177- 1187, August2013.  E. Nuño, R. Ortega, L. Basañez and D. Hill, “Synchronization of networks of nonidentical Euler-Lagrange systems with uncertain parameters and communication delays,” IEEE Trans. Autom. Control, vol. 56, pp. 935-941, April 2011.  W. Ren, “Distributed leaderless consensus algorithms for networked Euler–Lagrange systems,” Int. J. Control, vol. 82, pp. 2137-2149, November 2009.  B. Karimi and M.B. Menhaj, “Non-affine nonlinear adaptive control of decentralized large-scale systems using neural networks,” Inf. Sci., vol. 180, pp. 3335-3347, September 2010.  B. Karimi, M.B. Menhaj, M. Karimi-Ghartemani and I. Saboori, “Decentralized adaptive control of large-scale affine and nonaffine nonlinear systems” IEEE Trans. Instrum. Meas., vol. 58, pp. 2239-2247, August 2007.  G.P. Liu, V. Kadirkamanathan and S.A. Billings, “Variable neural networks for adaptive control of nonlinear systems,” IEEE Trans. Syst. Man Cybern. Part C, vol. 29, pp. 34-43, February 1999.  C.Y. Lee and J.J. Lee, “Adaptive control for uncertain nonlinear systems based on multiple neural networks,” IEEE Trans. Syst. Man Cybern. Part B, vol. 34, pp. 325-333, February 1999.  I. Kar, and L. Behera, “Direct adaptive neural control for affine nonlinear systems,” Appl. Soft Comput., vol. 9, pp. 756–764, March 2009.  L.X. Wang and J.M. Mendel, “Fuzzy basis function, universal approximation, and orthogonal least-squares learning,” IEEE Trans. Neural Netw., vol. 3, pp. 807-814, September 1992.  Z. Hou, L. Cheng and M. Tan, “Decentralized robust adaptive control for the multiagent system consensus problem using neural networks,” IEEE Trans. Syst. Man Cybern. Part B, vol. 39, pp. 636-647, June 2009.  L. Cheng, Z. Hou, M. Tan, Y. Lin and Zhang, W. “Neural-network-based adaptive leader-following control for multiagent systems with uncertainties,” IEEE Trans. Neural Netw., vol. 21, pp. 1351-1358, August 2010.  A. Das and F.L. Lewis, “Distributed adaptive control for synchronization of unknown nonlinear networked systems,” Automatica, vol. 46, pp. 2014-2021, August 2010.  H. Zhang and F.L. Lewis, “Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics,” Automatica, vol. 48, pp. 1432-1439, December 2012.  R. Cui, B., Ren and S.S. Ge, “Synchronized tracking control of multi-agent system with high-order dynamics,” IET Control Theory Appl., vol. 6, pp. 603-614, July 2012.  Y. Liu and Y. Jia, “Adaptive consensus protocol for networks of multiple agents with nonlinear dynamics using neural networks,” Asian J. Control, vol. 14, pp. 1328-1339, September 2012.
 A.M. Zou, K.D. Kumar and Z.G. Hou, “Distributed consensus control for multi-agent systems using terminal sliding mode and Chebyshev neural networks,” Int. J. Robust Nonlinear, vol. 23, pp. 334-357, February 2013.  A. Das and F.L. Lewis, “Cooperative adaptive control for synchronization of second-order systems with unknown nonlinearities,” Int. J. Robust Nonlinear Control, vol. 21, pp. 1509-1524, September 2011.  G.X. Wen, C.L.P. Chen, Y.J. Liu and Z. Liu, “Neural-network-based adaptive leader-following consensus control for second-order non-linear multi-agent systems,” IET Control Theory Appl., vol. 9, pp. 1927–1934, August.  H. Xu, and P.A. Ioannou, “Robust adaptive control for a class of MIMO nonlinear systems with guaranteed error bounds,” IEEE Trans. Automat. Control, vol. 48, pp. 728-742, May 2003.  W. Yu, G. Chen and J. Lu, “On pinning synchronization of complex dynamical networks,” Automatica, vol. 45, pp. 429-435, February 2009.  H. Khalil, Nonlinear Systems, 3rd ed., Prentice-Hall, Englewood Cliffs, NJ 2002.  M. Fu, J. Jiao and S. Yin, “Robust coordinated formation for multiple surface vessels based on backstepping sliding mode control,” J Abstr. App. Anal., vol. 2013,July 2013.  J. Almeida, C. Silvestre and A.M. Pascoal, “Cooperative control of multiple surface vessels with discrete-time periodic communications,” Int. J. Robust Nonlinear Control, vol. 22, pp. 398-419, March 2012.