A new framework for consensus for discrete-time directed networks of multi-agents with distributed delays

In this article, the distributed consensus problem is considered for discrete-time delayed networks of dynamic agents with fixed topologies, where the networks under investigation are directed and the time delays involved are distributed time delays including a single or multiple time delay(s) as special cases. By using the invariance principle of delay difference systems, a new unified framework is established to deal with the consensus for the discrete-time delayed multi-agent system. It is shown that the addressed discrete-time network with arbitrary distributed time delays reaches consensus provided that it is strongly connected. A numerical example is presented to illustrate the proposed methods.

[1]  A. Jadbabaie,et al.  Effects of Delay in Multi-Agent Consensus and Oscillator Synchronization , 2010, IEEE Transactions on Automatic Control.

[2]  Zidong Wang,et al.  Synchronization and State Estimation for Discrete-Time Complex Networks With Distributed Delays , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[3]  P.J. Antsaklis,et al.  Information consensus of asynchronous discrete-time multi-agent systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[4]  Reza Olfati-Saber,et al.  Flocking for multi-agent dynamic systems: algorithms and theory , 2006, IEEE Transactions on Automatic Control.

[5]  Mehran Mesbahi,et al.  Agreement over random networks , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[6]  H. Su,et al.  Reliable $H_\infty$ Control for Discrete-Time Fuzzy Systems With Infinite-Distributed Delay , 2009 .

[7]  E.M. Atkins,et al.  A survey of consensus problems in multi-agent coordination , 2005, Proceedings of the 2005, American Control Conference, 2005..

[8]  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..

[9]  A. Jadbabaie,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[10]  Zidong Wang,et al.  Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays , 2009, IEEE Transactions on Neural Networks.

[11]  Frank Allgöwer,et al.  Delay robustness in consensus problems , 2010, Autom..

[12]  A. Zuger.  A New Approach to , 2013 .

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

[14]  L. Moreau,et al.  Stability of continuous-time distributed consensus algorithms , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

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

[16]  Luc Moreau,et al.  Stability of multiagent systems with time-dependent communication links , 2005, IEEE Transactions on Automatic Control.

[17]  Long Wang,et al.  A new approach to consensus problems in discrete-time multiagent systems with time-delays , 2006, 2006 American Control Conference.

[18]  Craig W. Reynolds.  Flocks, herds, and schools: a distributed behavioral model , 1987, SIGGRAPH.

[19]  H.G. Tanner,et al.  State synchronization in local-interaction networks is robust with respect to time delays , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[20]  Elena Braverman,et al.  Oscillation of equations with an infinite distributed delay , 2010, Comput. Math. Appl..

[21]  Jonathan H. Manton,et al.  Stochastic Consensus Seeking With Noisy and Directed Inter-Agent Communication: Fixed and Randomly Varying Topologies , 2010, IEEE Transactions on Automatic Control.

[22]  Yang Liu,et al.  Stability analysis of M-dimensional asynchronous swarms with a fixed communication topology , 2003, IEEE Trans. Autom. Control..

[23]  Lihua Xie,et al.  Distributed Consensus With Limited Communication Data Rate , 2011, IEEE Transactions on Automatic Control.

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

[25]  Randal W. Beard,et al.  Distributed Consensus in Multi-vehicle Cooperative Control - Theory and Applications , 2007, Communications and Control Engineering.

[26]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[27]  Xiao Fan Wang,et al.  Synchronization in Small-World Dynamical Networks , 2002, Int. J. Bifurc. Chaos.

[28]  Y. Kuang.  Delay Differential Equations: With Applications in Population Dynamics , 2012 .

[29]  Jürgen Kurths,et al.  Consensus over directed static networks with arbitrary finite communication delays. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Shunian Zhang,et al.  Invariance principle for autonomous delay difference systems , 1995 .

[31]  R. Olfati-Saber,et al.  Distributed Kalman Filter with Embedded Consensus Filters , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[32]  Guangming Xie,et al.  Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays , 2008, Syst. Control. Lett..

[33]  Zheng-Guang Wu,et al.  Reliable $H_\infty$ Control for Discrete-Time Fuzzy Systems With Infinite-Distributed Delay , 2009, IEEE Transactions on Fuzzy Systems.

[34]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[35]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[36]  A. Ōkubo.  Dynamical aspects of animal grouping: swarms, schools, flocks, and herds. , 1986, Advances in biophysics.

[37]  Zhi Liu,et al.  A Probabilistic Wavelet System for Stochastic and Incomplete Data-Based Modeling , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[38]  Francesco Bullo,et al.  Coordination and Geometric Optimization via Distributed Dynamical Systems , 2003, SIAM J. Control. Optim..

[39]  M. Fiedler.  Algebraic connectivity of graphs , 1973 .

[40]  Huajing Fang,et al.  Observer-based fault detection for networked discrete-time infinite-distributed delay systems with packet dropouts , 2012 .

[41]  Gang Feng,et al.  Reliable H∞ control for discrete-time piecewise linear systems with infinite distributed delays , 2009, at - Automatisierungstechnik.

[42]  Amir F. Atiya,et al.  How delays affect neural dynamics and learning , 1994, IEEE Trans. Neural Networks.