Distributed consensus protocol for leader-following multi-agent systems with functional observers

Abstract This paper considers the consensus problem of the leader-following multi-agent systems under directed interaction topology. The dynamics of each agent is modeled by a general form of linear system. It is assumed that the state information of all following agents cannot be obtained directly, but only its output information can be obtained. Two types of linear functional observers are proposed for the following agents to estimate its state feedback inputs, by which two kinds of distributed consensus protocols are constructed to solve the leader-following consensus problem. Based on the graph theory, matrix theory and Lyapunov theory, some consensus conditions are established. The related consensus stability problem is investigated by use of the piecewise Lyapunov functions incorporated with the average dwell time approach. It is shown that if the average dwell time is chosen sufficiently large and all directed switching topologies have a directed spanning tree, then the multi-agent system can achieve consensus via the proposed protocols. Finally, a simulation example is provided to illustrate the effectiveness of our proposed approach.

[1]  Xiaobo Li,et al.  Observer‐based consensus of second‐order multi‐agent system with fixed and stochastically switching topology via sampled data , 2014 .

[2]  Lixin Gao,et al.  On Distributed Reduced-Order Observer-Based Protocol for Linear Multiagent Consensus under Switching Topology , 2013 .

[3]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

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

[5]  Yongduan Song,et al.  Consensus stability of a class of second-order multi-agent systems with nonuniform time-delays , 2014, J. Frankl. Inst..

[6]  A. Michel,et al.  PIECEWISE LYAPUNOV FUNCTIONS FOR SWITCHED SYSTEMS WITH AVERAGE DWELL TIME , 2000 .

[7]  W. M. Wonham,et al.  Linear Multivariable Control , 1979 .

[8]  Lixin Gao,et al.  Leader-following consensus problem with an accelerated motion leader , 2012 .

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

[10]  Xiangdong Liu,et al.  Consensus of linear multi-agent systems with reduced-order observer-based protocols , 2011, Syst. Control. Lett..

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

[12]  Xiaoli Wang,et al.  Multi-agent tracking of a high-dimensional active leader with switching topology , 2009, J. Syst. Sci. Complex..

[13]  Zhiyong Chen,et al.  Semi-Global Consensus of Nonlinear Second-Order Multi-Agent Systems With Measurement Output Feedback , 2014, IEEE Transactions on Automatic Control.

[14]  Yongcan Cao,et al.  Sampled-data discrete-time coordination algorithms for double-integrator dynamics under dynamic directed interaction , 2010, Int. J. Control.

[15]  Jiangping Hu,et al.  Tracking control for multi-agent consensus with an active leader and variable topology , 2006, Autom..

[16]  Z. Duan,et al.  Dynamic consensus of linear multi-agent systems , 2011 .

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

[18]  Gang Feng,et al.  Observer-Based Output Feedback Event-Triggered Control for Consensus of Multi-Agent Systems , 2014, IEEE Transactions on Industrial Electronics.

[19]  Xianping Liu,et al.  Consensus of second-order multi-agent systems with disturbances generated by nonlinear exosystems under switching topologies , 2014, J. Frankl. Inst..

[20]  Lixin Gao,et al.  Distributed reduced-order observer-based approach to consensus problems for linear multi-agent systems , 2015 .

[21]  Kai Liu,et al.  Leader-following consensus of multi-agent systems with jointly connected topology using distributed adaptive protocols , 2014, J. Frankl. Inst..

[22]  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.

[23]  Jiangping Hu,et al.  Leader-following coordination of multi-agent systems with coupling time delays , 2007, 0705.0401.

[24]  Hiroshi Ishiguro,et al.  Consensus of linear multi-agent systems based on full-order observer , 2014, J. Frankl. Inst..

[25]  ChenGuanrong,et al.  Consensus of multiagent systems and synchronization of complex networks , 2010 .

[26]  Bo Hu,et al.  Disturbance attenuation properties of time-controlled switched systems , 2001, J. Frankl. Inst..

[27]  Yongcan Cao,et al.  Distributed Coordination of Multi-agent Networks , 2011 .

[28]  Daizhan Cheng,et al.  Leader-following consensus of multi-agent systems under fixed and switching topologies , 2010, Syst. Control. Lett..

[29]  Xiaole Xu,et al.  Observer-based consensus tracking for second-order leader-following nonlinear multi-agent systems with adaptive coupling parameter design , 2015, Neurocomputing.

[30]  Jun Zhao,et al.  Observer-based reliable exponential stabilization and H∞ control for switched systems with faulty actuators: An average dwell time approach☆ , 2011 .

[31]  Frank L. Lewis,et al.  Optimal Design for Synchronization of Cooperative Systems: State Feedback, Observer and Output Feedback , 2011, IEEE Transactions on Automatic Control.

[32]  Yutao Tang,et al.  Consensus seeking in multi-agent systems with an active leader and communication delays , 2011, Kybernetika.

[33]  Xiaole Xu,et al.  Leader-following consensus of discrete-time multi-agent systems with observer-based protocols , 2013, Neurocomputing.

[34]  James Lam,et al.  Consensus of multi-agent systems with Luenberger observers , 2013, J. Frankl. Inst..

[35]  Abdelkader Abdessameud,et al.  On consensus algorithms for double-integrator dynamics without velocity measurements and with input constraints , 2010, Syst. Control. Lett..