Cooperative controller design for synchronization of networked uncertain Euler–Lagrange systems

Summary This paper addresses the synchronization problems with/without a dynamic leader for a team of distributed Lagrange systems on digraph. A systematic way to design and analyze the distributed control algorithms is presented. The contributions of the paper are twofold. First, the adaptive coordination control protocols are proposed for synchronization of networked uncertain Lagrange systems with/without tracking. This protocol can guarantee synchronization in finite time. Second, the design of the distributed tracking controller for the networked dynamic systems is proposed by using Lyapunov methods. The development is suitable for the general digraph communication topologies. Simulation examples are included to demonstrate the effectiveness of the proposed algorithms. Copyright © 2014 John Wiley & Sons, Ltd.

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

[2]  Mark W. Spong,et al.  Semiautonomous control of multiple networked Lagrangian systems , 2009 .

[3]  Naomi Ehrich Leonard,et al.  Stable Synchronization of Mechanical System Networks , 2008, SIAM J. Control. Optim..

[4]  Frank L. Lewis,et al.  Robust consensus of multiple inertial agents with coupling delays and variable topologies , 2011 .

[5]  F. Bullo,et al.  Motion Coordination with Distributed Information , 2007 .

[6]  Zhihong Man,et al.  Continuous finite-time control for robotic manipulators with terminal sliding mode , 2003, Autom..

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

[8]  Gang Feng,et al.  A Model-Free Cross-Coupled Control for Position Synchronization of Multi-Axis Motions: Theory and Experiments , 2007, IEEE Transactions on Control Systems Technology.

[9]  Zhihong Man,et al.  Non-singular terminal sliding mode control of rigid manipulators , 2002, Autom..

[10]  B. Paden,et al.  Lyapunov stability theory of nonsmooth systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[11]  Romeo Ortega,et al.  Globally stable adaptive formation control of Euler-Lagrange agents via potential functions , 2009, 2009 American Control Conference.

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

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

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

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

[16]  Jaime A. Moreno,et al.  Strict Lyapunov Functions for the Super-Twisting Algorithm , 2012, IEEE Transactions on Automatic Control.

[17]  Perry Y. Li,et al.  Passive Decomposition Approach to Formation and Maneuver Control of Multiple Rigid Bodies , 2007 .

[18]  Leonid M. Fridman,et al.  Second-order sliding-mode observer for mechanical systems , 2005, IEEE Transactions on Automatic Control.

[19]  A. Bacciotti,et al.  Stability and Stabilization of Discontinuous Systems and Nonsmooth Lyapunov Functions , 1999 .

[20]  Yen-Chen Liu,et al.  Synchronization of networked robotic systems on strongly connected graphs , 2010, 49th IEEE Conference on Decision and Control (CDC).

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

[22]  Henk Nijmeijer,et al.  Mutual synchronization of robots via estimated state feedback: a cooperative approach , 2004, IEEE Transactions on Control Systems Technology.

[23]  Ziyang Meng,et al.  Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking , 2010, Syst. Control. Lett..

[24]  Frank L. Lewis,et al.  Distributed adaptive controller design for the unknown networked Lagrangian systems , 2010, 49th IEEE Conference on Decision and Control (CDC).

[25]  Mark W. Spong,et al.  Passivity-Based Control of Multi-Agent Systems , 2006 .

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

[27]  A. Levant Sliding order and sliding accuracy in sliding mode control , 1993 .

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