Distributed finite-time tracking of multiple non-identical second-order nonlinear systems with settling time estimation

This paper investigates the distributed finite-time consensus tracking problem for a group of autonomous agents modeled by multiple non-identical second-order nonlinear systems. First, a class of distributed finite-time protocols are proposed based on the relative position and relative velocity measurements. By providing a topology-dependent Lyapunov function, it is shown that distributed consensus tracking can be achieved in finite time under the condition that the nonlinear errors between the leader and the followers are bounded. Then, a new class of observer-based algorithms are designed to solve the finite-time consensus tracking problem without using relative velocity measurements. The main contribution of this paper is that, by computing the value of the Lyapunov function at the initial point, the finite settling time can be theoretically estimated for second-order multi-agent systems with the proposed control protocols. Finally, the effectiveness of the analytical results is illustrated by an application in low-Earth-orbit spacecraft formation flying.

[1]  Guoqiang Hu,et al.  Robust consensus tracking of a class of second-order multi-agent dynamic systems , 2010, 49th IEEE Conference on Decision and Control (CDC).

[2]  Leonid M. Fridman,et al.  Optimal Lyapunov function selection for reaching time estimation of Super Twisting algorithm , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[3]  Guanrong Chen,et al.  Adaptive second-order consensus of networked mobile agents with nonlinear dynamics , 2011, Autom..

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

[5]  Tianping Chen,et al.  Pinning Complex Networks by a Single Controller , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[6]  Shihua Li,et al.  Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics , 2011, Autom..

[7]  Wenwu Yu,et al.  Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems , 2010, Autom..

[8]  Pramod P. Khargonekar,et al.  Lyapunov-based adaptive state estimation for a class of nonlinear stochastic systems , 2012, Autom..

[9]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[10]  Yiguang Hong,et al.  Finite-Time Consensus for Multi-Agent Networks with Second-Order Agent Dynamics , 2008 .

[11]  Yiguang Hong,et al.  Distributed Observers Design for Leader-Following Control of Multi-Agent Networks (Extended Version) , 2017, 1801.00258.

[12]  Guoqiang Hu,et al.  Robust consensus tracking for an integrator-type multi-agent system with disturbances and unmodelled dynamics , 2011, Int. J. Control.

[13]  Guanghui Wen,et al.  Distributed finite‐time tracking of multiple Euler–Lagrange systems without velocity measurements , 2015 .

[14]  Guanghui Wen,et al.  Distributed finite-time tracking for a multi-agent system under a leader with bounded unknown acceleration , 2015, Syst. Control. Lett..

[15]  Jean-Jacques E. Slotine,et al.  Sliding controller design for non-linear systems , 1984 .

[16]  Brian D. O. Anderson,et al.  Agreeing Asynchronously , 2008, IEEE Transactions on Automatic Control.

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

[18]  F.Y. Hadaegh,et al.  A survey of spacecraft formation flying guidance and control. Part II: control , 2004, Proceedings of the 2004 American Control Conference.

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

[20]  Long Wang,et al.  Finite-time formation control for multi-agent systems , 2009, Autom..

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

[22]  Ziyang Meng,et al.  Robust cooperative tracking for multiple non-identical second-order nonlinear systems , 2013, Autom..

[23]  Wenwu Yu,et al.  Second-Order Consensus for Multiagent Systems With Directed Topologies and Nonlinear Dynamics , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[25]  Jorge Cortés,et al.  Finite-time convergent gradient flows with applications to network consensus , 2006, Autom..

[26]  Zhisheng Duan,et al.  On H∞ and H2 performance regions of multi-agent systems , 2011, Autom..

[27]  Jinde Cao,et al.  Second-order leader-following consensus of nonlinear multi-agent systems via pinning control , 2010, Syst. Control. Lett..

[28]  Lin Huang,et al.  Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[29]  Lihua Xie,et al.  Distributed Tracking Control for Linear Multiagent Systems With a Leader of Bounded Unknown Input , 2013, IEEE Transactions on Automatic Control.