Consensus problem of high‐order multi‐agent systems with external disturbances: An H∞ analysis approach

This paper is devoted to the output consensus problem of directed networks of multiple high-order agents with external disturbances, and proposes a distributed protocol using the neighbors' measured outputs. By defining an appropriate controlled output and conducting a model transformation in two steps, consensus performance analysis of the multi-agent system under the proposed protocol is transformed into a normal H∞ problem. Then using H∞ theory of linear systems, conditions are derived to ensure the consensus performance with a prescribed H∞ index for networks with fixed and switching topologies, respectively. A numerical example of the formation control application is included to validate the theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.

[1]  Li Tao,et al.  Mean square average consensus of multi-agent systems with time-varying topologies and stochastic communication noises , 2008, 2008 27th Chinese Control Conference.

[2]  Michel Verhaegen,et al.  Robust output-feedback controller design via local BMI optimization , 2004, Autom..

[3]  Guangming Xie,et al.  Output agreement in high-dimensional multi-agent systems , 2009, 2009 American Control Conference.

[4]  Petter Ögren,et al.  Cooperative control of mobile sensor networks:Adaptive gradient climbing in a distributed environment , 2004, IEEE Transactions on Automatic Control.

[5]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[6]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[7]  Yang Liu,et al.  Tracking control for first-order multi-agent systems , 2008 .

[8]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[9]  Yang Liu,et al.  Average-consensus problem in multiagent systems , 2007, 2007 European Control Conference (ECC).

[10]  Junping Du,et al.  Distributed leadless coordination for networks of second-order agents with time-delay on switching topology , 2008, 2008 American Control Conference.

[11]  Stephen P. Boyd,et al.  A scheme for robust distributed sensor fusion based on average consensus , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[12]  Tong Heng Lee,et al.  A heuristic approach to solving a class of bilinear matrix inequality problems , 2002, Syst. Control. Lett..

[13]  Yingmin Jia,et al.  Distributed robust Hinfinity consensus control in directed networks of agents with time-delay , 2008, Syst. Control. Lett..

[14]  J. Toner,et al.  Flocks, herds, and schools: A quantitative theory of flocking , 1998, cond-mat/9804180.

[15]  Pierre-Alexandre Bliman,et al.  Average consensus problems in networks of agents with delayed communications , 2005, CDC 2005.

[16]  Jiangping Hu,et al.  Tracking control for multi-agent consensus with an active leader and variable topology , 2006, Autom..

[17]  Andrea Bacciotti,et al.  An invariance principle for nonlinear switched systems , 2005, Syst. Control. Lett..

[18]  M. Tomizuka,et al.  Rank minimization approach for solving BMI problems with random search , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[19]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[20]  Stephen P. Boyd,et al.  Distributed average consensus with least-mean-square deviation , 2007, J. Parallel Distributed Comput..

[21]  Guangming Xie,et al.  Consensus control for a class of networks of dynamic agents , 2007 .

[22]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[23]  R. Olfati-Saber,et al.  Distributed Kalman Filter with Embedded Consensus Filters , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[24]  Liu Yang,et al.  Leader-following consensus protocol for second-order multi-agent systems using neural networks , 2008, 2008 27th Chinese Control Conference.

[25]  YangQuan Chen,et al.  High-Order Consensus Algorithms in Cooperative Vehicle Systems , 2006, 2006 IEEE International Conference on Networking, Sensing and Control.

[26]  Ella M. Atkins,et al.  Distributed multi‐vehicle coordinated control via local information exchange , 2007 .

[27]  G. Papavassilopoulos,et al.  Biaffine matrix inequality properties and computational methods , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[28]  Mireille E. Broucke,et al.  Local control strategies for groups of mobile autonomous agents , 2004, IEEE Transactions on Automatic Control.

[29]  Long Wang,et al.  Virtual leader approach to coordinated control of multiple mobile agents with asymmetric interactions , 2006 .