Robust finite-time containment control for high-order multi-agent systems with matched uncertainties under directed communication graphs

ABSTRACT In this paper, we study the robust finite-time containment control problem for a class of high-order uncertain nonlinear multi-agent systems modelled as high-order integrator systems with bounded matched uncertainties. When relative state information between neighbouring agents is available, an observer-based distributed controller is proposed for each follower using the sliding mode control technique which solves the finite-time containment control problem under general directed communication graphs. When only relative output information is available, robust exact differentiators and high-order sliding-mode controllers are employed together with the distributed finite-time observers. It is shown that robust finite-time containment control can still be achieved in this situation. An application in the coordination of multiple non-holonomic mobile robots is used as an example to illustrate the effectiveness of the proposed control strategies.

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

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

[3]  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.

[4]  P. Olver.  Nonlinear Systems , 2013 .

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

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

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

[8]  Dennis S. Bernstein,et al.  Geometric homogeneity with applications to finite-time stability , 2005, Math. Control. Signals Syst..

[9]  Magnus Egerstedt,et al.  Containment in leader-follower networks with switching communication topologies , 2011, Autom..

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

[11]  Jinde Cao,et al.  Robust containment tracking of uncertain linear multi-agent systems: a non-smooth control approach , 2014, Int. J. Control.

[12]  Frank L. Lewis,et al.  Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics , 2012, Autom..

[13]  Long Wang,et al.  Containment control of heterogeneous multi-agent systems , 2014, Int. J. Control.

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

[15]  Wenwu Yu,et al.  Distributed finite-time containment control for second-order nonlinear multi-agent systems , 2015, Appl. Math. Comput..

[16]  Arie Levant,et al.  Quasi-continuous high-order sliding-mode controllers , 2005, IEEE Transactions on Automatic Control.

[17]  Yunpeng Wang,et al.  Distributed exponential finite-time coordination of multi-agent systems: containment control and consensus , 2015, Int. J. Control.

[18]  Zhihong Man,et al.  Multi‐surface sliding control for fast finite‐time leader–follower consensus with high order SISO uncertain nonlinear agents , 2014 .

[19]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

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

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

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

[23]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[24]  Shengyuan Xu,et al.  Distributed Containment Control with Multiple Dynamic Leaders for Double-Integrator Dynamics Using Only Position Measurements , 2012, IEEE Transactions on Automatic Control.

[25]  A. Levant.  Robust exact differentiation via sliding mode technique , 1998 .

[26]  Arie Levant,et al.  Higher-order sliding modes, differentiation and output-feedback control , 2003 .

[27]  Peng Shi,et al.  Distributed Finite-Time Containment Control for Double-Integrator Multiagent Systems , 2014, IEEE Transactions on Cybernetics.

[28]  Hua O. Wang,et al.  Containment control for coupled harmonic oscillators with multiple leaders under directed topology , 2015, Int. J. Control.

[29]  Yu Zhao,et al.  Finite-time containment control without velocity and acceleration measurements , 2015 .

[30]  Karl Henrik Johansson,et al.  Connectivity and Set Tracking of Multi-Agent Systems Guided by Multiple Moving Leaders , 2011, IEEE Transactions on Automatic Control.

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

[32]  Guanghui Wen,et al.  Distributed finite-time tracking control for multi-agent systems: An observer-based approach , 2013, Syst. Control. Lett..

[33]  Richard M. Murray,et al.  Information flow and cooperative control of vehicle formations , 2004, IEEE Transactions on Automatic Control.

[34]  Bing Li,et al.  Distributed Containment Control for Multiple Unknown Second-Order Nonlinear Systems With Application to Networked Lagrangian Systems , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[35]  Avrie Levent,et al.  Robust exact differentiation via sliding mode technique , 1998, Autom..

[36]  Magnus Egerstedt,et al.  Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks , 2012, Autom..

[37]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.