Leader–Following Consensus of Multiple Uncertain Euler–Lagrange Systems With Unknown Dynamic Leader

In this paper, we consider the leader–following consensus problem of uncertain Euler–Lagrange multi-agent systems. In comparison with existing results, the leader system is used to formulate both the reference trajectory and external disturbances, and the dynamics of the leader system contains unknown parameters. The current setting makes our problem formulation more realistic while at the same time, it poses significant technical challenges to the solvability of the problem. Inspired by the robust control approach and the adaptive control approach, we propose a novel adaptive distributed control law. It is shown that by the proposed control law, consensus of multiple uncertain Euler–Lagrange systems can be achieved in spite of unknown dynamic leader systems. Our main result is demonstrated by its exemplary application to cooperative control of a group of two-link robot arms.

[1]  Frank L. Lewis,et al.  Control of Robot Manipulators , 1993 .

[2]  Jie Huang,et al.  Cooperative Output Regulation With Application to Multi-Agent Consensus Under Switching Network , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[3]  Lu Liu,et al.  Leader-Following Consensus of Multiple Uncertain Euler–Lagrange Systems Subject to Communication Delays and Switching Networks , 2018, IEEE Transactions on Automatic Control.

[4]  B. Francis.  The linear multivariable regulator problem , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

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

[6]  Dong Sun,et al.  A MODEL-FREE CROSS-COUPLED CONTROL FOR POSITION SYNCHRONIZATION OF MULTI-AXIS MOTIONS: THEORY AND EXPERIMENTS , 2005 .

[7]  Zhong-Ping Jiang,et al.  Distributed Global Output-Feedback Control for a Class of Euler–Lagrange Systems , 2017, IEEE Transactions on Automatic Control.

[8]  Jie Huang,et al.  Cooperative Output Regulation of Linear Multi-Agent Systems , 2012, IEEE Transactions on Automatic Control.

[9]  E. Davison.  The robust control of a servomechanism problem for linear time-invariant multivariable systems , 1976 .

[10]  V. O. Nikiforov,et al.  Adaptive Non-linear Tracking with Complete Compensation of Unknown Disturbances , 1998, Eur. J. Control.

[11]  Jie Huang,et al.  Nonlinear Output Regulation: Theory and Applications , 2004 .

[12]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[13]  Jie Huang,et al.  Leader-following consensus of multiple uncertain Euler–Lagrange systems under switching network topology , 2014, Int. J. Gen. Syst..

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

[15]  Shengyuan Xu,et al.  Coordinated control with multiple dynamic leaders for uncertain Lagrangian systems via self‐tuning adaptive distributed observer , 2017 .

[16]  Jie Huang,et al.  Adaptive Leader-Following Consensus for Uncertain Euler-Lagrange Systems under Directed Switching Networks , 2016, CCC 2016.

[17]  S. Tafazoli,et al.  Cooperative tracking control of Euler-Lagrange systems with switching communication network topologies , 2010, 2010 IEEE/ASME International Conference on Advanced Intelligent Mechatronics.

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

[19]  Bruce A. Francis,et al.  The internal model principle of control theory , 1976, Autom..

[20]  Ziyang Meng,et al.  Leader–Follower Coordinated Tracking of Multiple Heterogeneous Lagrange Systems Using Continuous Control , 2014, IEEE Transactions on Robotics.