Consensus for multiple heterogeneous Euler-Lagrange systems with time-delay and jointly connected topologies

Abstract In this paper, we consider the consensus problem of multiple agents modeled by Euler–Lagrange (EL) equation, among which two classes of agents are addressed, i.e., some agents with exactly known parameters and the others with parametric uncertainties. We propose a distributed consensus protocol for the heterogeneous EL systems in which both time-delay and jointly connected topologies are taken into consideration. Based on graph theory, Lyapunov theory and Barbalat׳s lemma, the stability of the controller is proved. A distinctive feature of this work is to investigate the consensus problem of EL systems with heterogeneous dynamics, time-delay and jointly connected topologies in a unified theoretical framework. Simulation results are also provided to illustrate the effectiveness of the obtained results.

[1]  Wenwu Yu,et al.  An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination , 2012, IEEE Transactions on Industrial Informatics.

[2]  Yingmin Jia,et al.  Consensus of a Class of Second-Order Multi-Agent Systems With Time-Delay and Jointly-Connected Topologies , 2010, IEEE Transactions on Automatic Control.

[3]  Jie Huang,et al.  Stability of a Class of Linear Switching Systems with Applications to Two Consensus Problems , 2011, IEEE Transactions on Automatic Control.

[4]  Zhihong Man,et al.  Robust Finite-Time Consensus Tracking Algorithm for Multirobot Systems , 2009, IEEE/ASME Transactions on Mechatronics.

[5]  Ilia G. Polushin,et al.  Synchronization of multiple Euler-Lagrange systems with communication delays , 2012, 2012 American Control Conference (ACC).

[6]  Wenjie Dong,et al.  On consensus algorithms of multiple uncertain mechanical systems with a reference trajectory , 2011, Autom..

[7]  A. Jadbabaie,et al.  Effects of Delay in Multi-Agent Consensus and Oscillator Synchronization , 2010, IEEE Transactions on Automatic Control.

[8]  Peng Lin,et al.  A new approach to average consensus problems with multiple time-delays and jointly-connected topologies , 2012, J. Frankl. Inst..

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

[10]  Mohammad Bagher Menhaj,et al.  Synthesis and analysis of robust dynamic linear protocols for dynamic average consensus estimators , 2009 .

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

[12]  Guangfu Ma,et al.  Distributed adaptive coordination for multiple Lagrangian systems under a directed graph without using neighbors' velocity information , 2013, Autom..

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

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

[15]  Masoud Shafiee,et al.  Time-Delay Dependent Stability Robustness of Small-World Protocols for Fast Distributed Consensus Seeking , 2007, 2007 5th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks and Workshops.

[16]  Fei Liu,et al.  Consensus problem of second-order multi-agent systems with time-varying communication delay and switching topology , 2011 .

[17]  George J. Pappas,et al.  Flocking in Fixed and Switching Networks , 2007, IEEE Transactions on Automatic Control.

[18]  Huai-Ning Wu,et al.  Leader-following formation control of multi-agent systems under fixed and switching topologies , 2012, Int. J. Control.

[19]  Ziyang Meng,et al.  Leaderless and Leader-Following Consensus With Communication and Input Delays Under a Directed Network Topology , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[21]  Guangfu Ma,et al.  Distributed Coordinated Tracking With a Dynamic Leader for Multiple Euler-Lagrange Systems , 2011, IEEE Transactions on Automatic Control.

[22]  F. Sun,et al.  Distributed adaptive consensus algorithm for networked Euler-Lagrange systems , 2011 .

[23]  Soon-Jo Chung,et al.  Cooperative Robot Control and Concurrent Synchronization of Lagrangian Systems , 2007, IEEE Transactions on Robotics.

[24]  Cheng-Lin Liu,et al.  Robust consensus of multi-agent systems with diverse input delays and asymmetric interconnection perturbations , 2009, Autom..

[25]  Ziyang Meng,et al.  Distributed finite-time attitude containment control for multiple rigid bodies , 2010, Autom..

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

[27]  Daizhan Cheng,et al.  Leader-following consensus of multi-agent systems under fixed and switching topologies , 2010, Syst. Control. Lett..

[28]  M. Spong,et al.  Output synchronization of networked passive systems , 2006 .

[29]  Haibo Min,et al.  Distributed six degree-of-freedom spacecraft formation control with possible switching topology , 2011 .

[30]  Guangming Xie,et al.  Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays , 2008, Syst. Control. Lett..

[31]  Fuchun Sun,et al.  Decentralized adaptive attitude synchronization of spacecraft formation , 2012, Syst. Control. Lett..

[32]  Khashayar Khorasani,et al.  State Synchronization of Networked Euler-Lagrange Systems with Switching Communication Topologies Subject to Actuator Faults , 2011 .

[33]  Frank Allgöwer,et al.  Delay robustness in consensus problems , 2010, Autom..

[34]  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.

[35]  Frank Allgöwer,et al.  Consensus in Multi-Agent Systems With Coupling Delays and Switching Topology , 2011, IEEE Transactions on Automatic Control.