Group consensus for multiple networked Euler-Lagrange systems with parametric uncertainties

In this paper, a group consensus problem is investigated for multiple networked agents with parametric uncertainties where all the agents are governed by the Euler-Lagrange system with uncertain parameters. In the group consensus problem, the agents asymptotically reach several different states rather than one consistent state. A novel group consensus protocol and a time-varying estimator of the uncertain parameters are proposed for each agent in order to solve the couple-group consensus problem. It is shown that the group consensus is reachable even when the system contains the uncertain parameters. Furthermore, the multi-group consensus is discussed as an extension of the couple-group consensus, and then the group consensus with switching topology is considered. Simulation results are finally provided to validate the effectiveness of the theoretical analysis.

[1]  Jinde Cao,et al.  Global Synchronization of Linearly Hybrid Coupled Networks with Time-Varying Delay , 2008, SIAM J. Appl. Dyn. Syst..

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

[3]  Romeo Ortega,et al.  Synchronization of Networks of Nonidentical Euler-Lagrange Systems With Uncertain Parameters and Communication Delays , 2011, IEEE Transactions on Automatic Control.

[4]  Yingmin Jia,et al.  Multi-agent consensus with diverse time-delays and jointly-connected topologies , 2011, Autom..

[5]  Long Wang,et al.  Consensus seeking of high-order dynamic multi-agent systems with fixed and switching topologies , 2010, Int. J. Control.

[6]  Riccardo Scattolini,et al.  Model Predictive Control Schemes for Consensus in Multi-Agent Systems with Single- and Double-Integrator Dynamics , 2009, IEEE Transactions on Automatic Control.

[7]  Guangming Xie,et al.  Containment of linear multi-agent systems under general interaction topologies , 2012, Syst. Control. Lett..

[8]  Albert-László Barabási,et al.  Controllability of complex networks , 2011, Nature.

[9]  Xiaoli Wang,et al.  Distributed finite-time χ-consensus algorithms for multi-agent systems with variable coupling topology , 2010, J. Syst. Sci. Complex..

[10]  Wenwu Yu,et al.  Applications of Collective Circular Motion Control to Multirobot Systems , 2013, IEEE Transactions on Control Systems Technology.

[11]  Long Wang,et al.  Group consensus in multi-agent systems with switching topologies and communication delays , 2010, Syst. Control. Lett..

[12]  Long Wang,et al.  Finite-time formation control for multi-agent systems , 2009, Autom..

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

[14]  Jinde Cao,et al.  Second-order consensus in multi-agent dynamical systems with sampled position data , 2011, Autom..

[15]  Long Wang,et al.  Finite-time weighted average consensus with respect to a monotonic function and its application , 2011, Syst. Control. Lett..

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

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

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

[19]  Wenwu Yu,et al.  Distributed Higher Order Consensus Protocols in Multiagent Dynamical Systems , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[20]  Wenwu Yu,et al.  Synchronization via Pinning Control on General Complex Networks , 2013, SIAM J. Control. Optim..

[21]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[22]  Guangfu Ma,et al.  Distributed containment control for Lagrangian networks with parametric uncertainties under a directed graph , 2012, Autom..

[23]  Zhiyong Chen,et al.  No-beacon collective circular motion of jointly connected multi-agents , 2011, Autom..

[24]  Frank Allgöwer,et al.  Robust Consensus Controller Design for Nonlinear Relative Degree Two Multi-Agent Systems With Communication Constraints , 2011, IEEE Transactions on Automatic Control.

[25]  R. Ortega.  Passivity-based control of Euler-Lagrange systems : mechanical, electrical and electromechanical applications , 1998 .

[26]  C. Desoer,et al.  Feedback Systems: Input-Output Properties , 1975 .

[27]  Guanghui Wen,et al.  Consensus in multi‐agent systems with communication constraints , 2012 .

[28]  David Angeli,et al.  Nonlinear norm-observability notions and stability of switched systems , 2005, IEEE Transactions on Automatic Control.

[29]  Jinde Cao,et al.  Local Synchronization of a Complex Network Model , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[30]  Wei Ren.  On Consensus Algorithms for Double-Integrator Dynamics , 2008, IEEE Trans. Autom. Control..

[31]  Wei Ren,et al.  Distributed leaderless consensus algorithms for networked Euler–Lagrange systems , 2009, Int. J. Control.

[32]  Wenwu Yu,et al.  Distributed Adaptive Control of Synchronization in Complex Networks , 2012, IEEE Transactions on Automatic Control.

[33]  Bo Liu,et al.  Consensus in Networks of Multiagents With Cooperation and Competition Via Stochastically Switching Topologies , 2008, IEEE Transactions on Neural Networks.