Fully distributed adaptive sliding-mode controller design for containment control of multiple Lagrangian systems

Abstract In this paper, we study the containment control problem for multiple Lagrangian systems with multiple dynamic leaders in the presence of parametric uncertainties and external disturbances with fully distributed controllers under an undirected graph. We first propose a fully distributed adaptive sliding-mode control algorithm combined with distributed sliding-mode estimators, without requiring the upper bounds of the derivatives of the leaders’ states and any other global information to be known by each follower. To reduce the effect on the varying gain during the adaption mainly caused by the initial error, fully distributed adaptive time-varying sliding-mode control is presented for controller design. To tackle the chattering effect caused by the discontinuous controller, we further propose a fully distributed continuous adaptive controller, under which both the containment errors and the adaptive gains are ultimately bounded. Simulation results are given to illustrate the theoretical results.

[1]  Dimos V. Dimarogonas,et al.  Leader-follower cooperative attitude control of multiple rigid bodies , 2008, 2008 American Control Conference.

[2]  Chien Chern Cheah,et al.  Region-based shape control for a swarm of robots , 2009, Autom..

[3]  M. Spong,et al.  Robot Modeling and Control , 2005 .

[4]  Rafael Kelly,et al.  Control of Robot Manipulators in Joint Space , 2005 .

[5]  John T. Wen,et al.  Rigid body attitude coordination without inertial frame information , 2008, Autom..

[6]  Long Cheng,et al.  Distributed Adaptive Coordinated Control of Multi-Manipulator Systems Using Neural Networks , 2010 .

[7]  Mengyin Fu,et al.  Distributed containment control of multi‐agent systems with general linear dynamics in the presence of multiple leaders , 2013 .

[8]  Jonathan P. How,et al.  Spacecraft Formation Flying: Dynamics, Control and Navigation , 2009 .

[9]  Seung-Bok Choi,et al.  A time-varying sliding surface for fast and robust tracking control of second-order uncertain systems , 1994, Autom..

[10]  Giancarlo Ferrari-Trecate,et al.  Containment Control in Mobile Networks , 2008, IEEE Transactions on Automatic Control.

[11]  Hanlei Wang,et al.  Flocking of networked uncertain Euler-Lagrange systems on directed graphs , 2013, Autom..

[12]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[13]  Youcheng Lou,et al.  Multi-leader set coordination of multi-agent systems with random switching topologies , 2010, 49th IEEE Conference on Decision and Control (CDC).

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

[15]  Chen Zhen,et al.  Exponential Time-varying Sliding Mode Control for Large Angle Attitude Eigenaxis Maneuver of Rigid Spacecraft , 2010 .

[16]  Mengyin Fu,et al.  Consensus of Multi-Agent Systems With General Linear and Lipschitz Nonlinear Dynamics Using Distributed Adaptive Protocols , 2011, IEEE Transactions on Automatic Control.

[17]  Yury Stepanenko,et al.  A Sliding Mode Controller with Improved Adaptation Laws for the Upper Bounds on the Norm of Uncertainties , 1998, Autom..

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

[19]  Guangming Xie,et al.  Necessary and sufficient conditions for containment control of networked multi-agent systems , 2012, Autom..

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

[21]  Ziyang Meng,et al.  Distributed Containment Control for Multiple Autonomous Vehicles With Double-Integrator Dynamics: Algorithms and Experiments , 2011, IEEE Transactions on Control Systems Technology.

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

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

[24]  Andrzej Bartoszewicz,et al.  Time-varying sliding modes for second-order systems , 1996 .

[25]  Dapeng Yang,et al.  Distributed adaptive attitude tracking of multiple spacecraft with a leader of nonzero input , 2013 .

[26]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[27]  Petar V. Kokotovic,et al.  Instability analysis and improvement of robustness of adaptive control , 1984, Autom..

[28]  Yongcan Cao,et al.  Distributed Coordinated Tracking With Reduced Interaction via a Variable Structure Approach , 2012, IEEE Transactions on Automatic Control.

[29]  Gang Feng,et al.  Coordinated tracking of multi-agent systems with a leader of bounded unknown input using distributed continuous controllers , 2012, 2012 12th International Conference on Control Automation Robotics & Vision (ICARCV).

[30]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .