Dynamic leader-following consensus for asynchronous sampled-data multi-agent systems under switching topology

Abstract This paper investigates the leader-following consensus problem for asynchronous sampled-data multi-agent systems with an active leader and under switching topology, in which the asynchrony means that each agent’s update actions are independent of the others’. First, the dynamic leader-following consensus problem for asynchronous sampled-data systems is transformed into the convergence problem of products of infinite general sub-stochastic matrices (PIGSSM), where the general sub-stochastic matrices are matrices with row sum no more than 1 but their elements are not necessarily nonnegative. We develop a method to cope with the corresponding convergence problem by matrix decomposition. In particular, we split the general sub-stochastic matrix into a sub-stochastic matrix which is a nonnegative matrix with row sum no more than 1, and a matrix with negative elements and row sum 0. Then based on a graphical approach and matrix analysis technique, we present a sufficient condition for the achievement of dynamic leader-following consensus in the asynchronous setting. Finally, simulation examples are demonstrated to verify the theoretical results.

[1]  Sandra Hirche,et al.  Stationary Consensus of Asynchronous Discrete-Time Second-Order Multi-Agent Systems Under Switching Topology , 2012, IEEE Transactions on Industrial Informatics.

[2]  Wei Xing Zheng,et al.  Adaptive Sliding Mode Consensus Tracking for Second-Order Nonlinear Multiagent Systems With Actuator Faults , 2019, IEEE Transactions on Cybernetics.

[3]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[4]  Tongwen Chen,et al.  Sampled-data consensus in multi-agent systems with asynchronous hybrid event-time driven interactions , 2016, Syst. Control. Lett..

[5]  Long Wang,et al.  Asynchronous Consensus in Continuous-Time Multi-Agent Systems With Switching Topology and Time-Varying Delays , 2006, IEEE Transactions on Automatic Control.

[6]  John N. Tsitsiklis,et al.  On the Nonexistence of Quadratic Lyapunov Functions for Consensus Algorithms , 2007, IEEE Transactions on Automatic Control.

[7]  Wei Xing Zheng,et al.  Containment control for heterogeneous multi-agent systems with asynchronous updates , 2017, Inf. Sci..

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

[9]  Brian D. O. Anderson,et al.  Reaching a Consensus in a Dynamically Changing Environment: Convergence Rates, Measurement Delays, and Asynchronous Events , 2008, SIAM J. Control. Optim..

[10]  Jingyuan Zhan,et al.  Asynchronous Consensus of Multiple Double-Integrator Agents With Arbitrary Sampling Intervals and Communication Delays , 2015, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  Lei Shi,et al.  Asynchronous group consensus for discrete-time heterogeneous multi-agent systems under dynamically changing interaction topologies , 2018, Inf. Sci..

[12]  Wei Xing Zheng,et al.  Consensus tracking in heterogeneous nonlinear multi-agent networks with asynchronous sampled-data communication , 2016, Syst. Control. Lett..

[13]  Jinhu Lu,et al.  Consensus of Discrete-Time Second-Order Multiagent Systems Based on Infinite Products of General Stochastic Matrices , 2013, SIAM J. Control. Optim..

[14]  Long Wang,et al.  Asynchronous consensus of continuous-time multi-agent systems with intermittent measurements , 2010, Int. J. Control.

[15]  Huijun Gao,et al.  A Sufficient Condition for Convergence of Sampled-Data Consensus for Double-Integrator Dynamics With Nonuniform and Time-Varying Communication Delays , 2012, IEEE Transactions on Automatic Control.

[16]  Wei Xing Zheng,et al.  A novel analysis on the efficiency of hierarchy among leader-following systems , 2016, Autom..

[17]  Shiji Song,et al.  Second-order consensus of multi-agent systems under limited interaction ranges , 2016, Autom..

[18]  Wei Xing Zheng,et al.  On Leader–Follower Consensus With Switching Topologies: An Analysis Inspired by Pigeon Hierarchies , 2018, IEEE Transactions on Automatic Control.

[19]  Yingmin Jia,et al.  Consensus of a Class of Second-Order Multi-Agent Systems With Time-Delay and Jointly-Connected Topologies , 2010, IEEE Transactions on Automatic Control.

[20]  N. Pullman,et al.  Infinite products of substochastic matrices. , 1966 .

[21]  Tongwen Chen,et al.  Sampled-Data Consensus for Multiple Double Integrators With Arbitrary Sampling , 2012, IEEE Transactions on Automatic Control.

[22]  Yurong Liu,et al.  Sampled‐data consensus of nonlinear multiagent systems subject to cyber attacks , 2018 .

[23]  Long Wang,et al.  Recent Advances in Consensus of Multi-Agent Systems: A Brief Survey , 2017, IEEE Transactions on Industrial Electronics.

[24]  Tao Dong,et al.  Algebraic criteria for second-order global consensus in multi-agent networks with intrinsic nonlinear dynamics and directed topologies , 2014, Inf. Sci..

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

[26]  Long Wang,et al.  Asynchronous Rendezvous Analysis via Set-valued Consensus Theory , 2012, SIAM J. Control. Optim..

[27]  Long Wang,et al.  Partial state consensus for networks of second-order dynamic agents , 2010, Syst. Control. Lett..

[28]  Qing-Long Han,et al.  A survey on recent advances in distributed sampled-data cooperative control of multi-agent systems , 2018, Neurocomputing.

[29]  Wei Ren,et al.  Robustness Analysis of Asynchronous Sampled-Data Multiagent Networks With Time-Varying Delays , 2017, IEEE Transactions on Automatic Control.

[30]  Brian D. O. Anderson,et al.  Reaching a Consensus in a Dynamically Changing Environment: Convergence Rates, Measurement Delays, and Asynchronous Events , 2008, SIAM J. Control. Optim..