Distributed Robust H∞ Consensus for Multi‐Agent Systems with Nonlinear Dynamics and Parameter Uncertainties

In this study, the consensus problem is discussed for a class of multi‐agent systems with unknown Lipschitz nonlinear dynamics, external disturbances, and parameter uncertainties under a fixed directed graph. By some model transformations, the consensus problem becomes a reduced‐order H∞ control problem. Based on the reduced‐order control problem, sufficient conditions to achieve the consensus with the desired H∞ performance are presented. These conditions are to check the solvability of only one linear matrix inequality (LMI) and the dimension of the LMI independent of the number of agents in the network. Moreover, an algorithm is proposed to design the dynamic output feedback controller. Simulation on networked multi‐agents is provided to show the effectiveness of the theoretical results.

[1]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[2]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[3]  Stephen P. Boyd,et al.  Fast linear iterations for distributed averaging , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[4]  P. Marannino,et al.  Discussion on "Stability, l2-Gain and Asynchronous H¿ Control of Discrete-Time Switched Systems with Average Dwell Time" , 2004 .

[5]  M.W. Spong,et al.  Output Synchronization of Nonlinear Systems with Time Delay in Communication , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[6]  Murat Arcak,et al.  Passivity as a Design Tool for Group Coordination , 2007, IEEE Transactions on Automatic Control.

[7]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

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

[9]  Wei Ren,et al.  Information consensus in multivehicle cooperative control , 2007, IEEE Control Systems.

[10]  Peng Shi,et al.  H∞ model reduction for uncertain switched linear discrete-time systems , 2008, Autom..

[11]  J.M. Maciejowski,et al.  Collective behavior coordination with predictive mechanisms , 2008, IEEE Circuits and Systems Magazine.

[12]  Peng Shi,et al.  $l_{2}-l_{\infty}$ Model Reduction for Switched LPV Systems With Average Dwell Time , 2008, IEEE Transactions on Automatic Control.

[13]  Randal W. Beard,et al.  Distributed Consensus in Multi-vehicle Cooperative Control - Theory and Applications , 2007, Communications and Control Engineering.

[14]  Long Wang,et al.  Asynchronous Consensus in Continuous-Time Multi-Agent Systems With Switching Topology and Time-Varying Delays , 2006, IEEE Transactions on Automatic Control.

[15]  Yang Liu,et al.  H ∞ consensus control of multi-agent systems with switching topology: a dynamic output feedback protocol , 2010, Int. J. Control.

[16]  Yingmin Jia,et al.  Robust h ∞ consensus analysis of a class of second-order multi-agent systems with uncertainty , 2010 .

[17]  Tao Li,et al.  Consensus Conditions of Multi-Agent Systems With Time-Varying Topologies and Stochastic Communication Noises , 2010, IEEE Transactions on Automatic Control.

[18]  Yang Liu,et al.  Consensus problem of high‐order multi‐agent systems with external disturbances: An H∞ analysis approach , 2010 .

[19]  Frank L. Lewis,et al.  Cooperative adaptive control for synchronization of second‐order systems with unknown nonlinearities , 2011 .

[20]  Guy-Bart Stan,et al.  Fast Consensus Via Predictive Pinning Control , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[21]  Lihua Xie,et al.  Global H∞ Consensus of Multi-Agent Systems with Lipschitz Nonlinear Dynamics , 2012, ArXiv.

[22]  Lihua Xie,et al.  Global $H_\infty$ Consensus of Multi-Agent Systems with Lipschitz Nonlinear Dynamics , 2012 .

[23]  Lihua Xie,et al.  Distributed robust control of linear multi-agent systems with parameter uncertainties , 2011, Int. J. Control.

[24]  Frank L. Lewis,et al.  Distributed Tracking Control for Networked Mechanical Systems , 2012 .

[25]  Zhong-Ping Jiang,et al.  Asynchronous Distributed Algorithms for Heading Consensus of Multi‐Agent Systems with Communication Delay , 2013 .