Scale-free Design for Delayed Regulated Synchronization of Discrete-time Heterogeneous Multi-agent Systems subject to Unknown Non-uniform and Arbitrarily Large Communication Delays

In this paper, we study delayed regulated state/output synchronization for discrete-time homogeneous and heterogeneous networks of multi-agent systems (MAS) subject to unknown, non-uniform and arbitrarily large communication delays. A delay transformation is utilized to transform the original MAS to a new system without delayed states. The proposed scale-free dynamic protocols are developed solely based on agent models and localized information exchange with neighbors such that we do not need any information about the communication networks and the number of agents.

[1]  H. Nijmeijer,et al.  Partial synchronization: from symmetry towards stability , 2002 .

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

[3]  Pierre-Alexandre Bliman,et al.  Average consensus problems in networks of agents with delayed communications , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[4]  Yu-Ping Tian,et al.  Consensus of Multi-Agent Systems With Diverse Input and Communication Delays , 2008, IEEE Transactions on Automatic Control.

[5]  Sezai Emre Tuna,et al.  Synchronizing linear systems via partial-state coupling , 2008, Autom..

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

[7]  Ali Saberi,et al.  Output synchronization for heterogeneous networks of introspective right‐invertible agents , 2014 .

[8]  Nikhil Chopra,et al.  Output Synchronization on Strongly Connected Graphs , 2012, IEEE Transactions on Automatic Control.

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

[10]  S. E. Tuna.  LQR-based coupling gain for synchronization of linear systems , 2008, 0801.3390.

[11]  Leonardo L. Gollo,et al.  Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays , 2008, Proceedings of the National Academy of Sciences.

[12]  Zhiyong Chen,et al.  Feedforward design for output synchronization of nonlinear heterogeneous systems with output communication , 2019, Automatica.

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

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

[15]  Frank L. Lewis,et al.  Cooperative Output Regulation of Heterogeneous Linear Multi-Agent Networks via ${H_{\infty }}$ Performance Allocation , 2019, IEEE Transactions on Automatic Control.

[16]  Ali Saberi,et al.  Output synchronization for heterogeneous networks of non-introspective agents , 2012, Autom..

[17]  Meirong Zhang,et al.  Synchronization in a network of identical continuous‐ or discrete‐time agents with unknown nonuniform constant input delay , 2018 .

[18]  Jean-Jacques E. Slotine,et al.  Contraction analysis of time-delayed communications and group cooperation , 2006, IEEE Transactions on Automatic Control.

[19]  Rong Li,et al.  Delayed state synchronization of homogeneous discrete-time multi-agent systems in the presence of unknown communication delays , 2019, 2019 Chinese Control And Decision Conference (CCDC).

[20]  Zhi-Hong Guan,et al.  Passive stability and synchronization of complex spatio-temporal switching networks with time delays , 2009, Autom..

[21]  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.

[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]  Peng Lin,et al.  Average consensus in networks of multi-agents with both switching topology and coupling time-delay , 2008 .

[24]  Ljupco Kocarev,et al.  Consensus and Synchronization in Complex Networks , 2013 .

[25]  Frank L. Lewis,et al.  Optimal Synchronization of Heterogeneous Nonlinear Systems With Unknown Dynamics , 2018, IEEE Transactions on Automatic Control.

[26]  Carlos Silvestre,et al.  Synchronization in multi-agent systems with switching topologies and non-homogeneous communication delays , 2007, 2007 46th IEEE Conference on Decision and Control.

[27]  R. Murray,et al.  Agreement problems in networks with directed graphs and switching topology , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[28]  M.W. Spong,et al.  Output Synchronization of Nonlinear Systems with Time Delay in Communication , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[29]  Gang Feng,et al.  Output Consensus of Heterogeneous Linear Multi-Agent Systems with Adaptive Event-Triggered Control , 2019, IEEE Transactions on Automatic Control.

[30]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[31]  Frank Allgöwer,et al.  An internal model principle is necessary and sufficient for linear output synchronization , 2011, Autom..

[32]  Ali Saberi,et al.  Synchronization in networks of minimum-phase, non-introspective agents without exchange of controller states: Homogeneous, heterogeneous, and nonlinear , 2015, Autom..

[33]  Kestutis Pyragas.  Continuous control of chaos by self-controlling feedback , 1992 .

[34]  Sezai Emre Tuna,et al.  Conditions for Synchronizability in Arrays of Coupled Linear Systems , 2008, IEEE Transactions on Automatic Control.

[35]  Ali Saberi,et al.  On the existence of virtual exosystems for synchronized linear networks , 2013, Autom..

[36]  Zidong Wang,et al.  Global Synchronization Control of General Delayed Discrete-Time Networks With Stochastic Coupling and Disturbances , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[37]  Rong Li,et al.  Delayed state synchronization of continuous-time multi-agent systems in the presence of unknown communication delays , 2019, 2019 Chinese Control And Decision Conference (CCDC).

[38]  Long Wang,et al.  Consensus protocols for discrete-time multi-agent systems with time-varying delays , 2008, Autom..

[39]  Frank Allgöwer,et al.  Delay Robustness in Non-Identical Multi-Agent Systems , 2012, IEEE Transactions on Automatic Control.

[40]  Chai Wah Wu,et al.  Synchronization in Complex Networks of Nonlinear Dynamical Systems , 2008 .

[41]  Wenwu Yu,et al.  An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination , 2012, IEEE Transactions on Industrial Informatics.

[42]  Warren E. Dixon,et al.  Synchronization of uncertain Euler-Lagrange systems with unknown time-varying communication delays , 2015, 2015 American Control Conference (ACC).

[43]  Mark W. Spong,et al.  Passivity-Based Control of Multi-Agent Systems , 2006 .

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

[45]  Hyungbo Shim,et al.  Output Consensus of Heterogeneous Uncertain Linear Multi-Agent Systems , 2011, IEEE Transactions on Automatic Control.

[46]  Meirong Zhang,et al.  Synchronization in the presence of unknown, nonuniform and arbitrarily large communication delay , 2017, Eur. J. Control.