A Unified Approach to Practical Consensus with Quantized Data and Time Delay

In this paper, we study the consensus problem of multi-agent networks subject to communication constrains. Undirected and weighted network is considered here. Two types of communication constrains are discussed in this paper: i) each agent can only exchange quantized data with its neighbors and ii) each agent can only obtain the delayed information from its neighbors. The main contribution of this paper is to provide a precise mathematical treatment for the continuous multi-agent network with quantization and time delay. The existence of a global solution to the resulting system is firstly proved in the Filippov sense and then we prove that the solution converges to a practical consensus set asymptotically. Here, practical consensus means that the final consensus values are bounded within an interval, but not a value. Further, an explicit relationship among time delay, quantization parameter and the practical consensus set are theoretically presented. Numerical examples are finally given to demonstrate the effectiveness of the obtained theoretical results.

[1]  Shankar Sastry,et al.  A calculus for computing Filippov's differential inclusion with application to the variable structure control of robot manipulators , 1986, 1986 25th IEEE Conference on Decision and Control.

[2]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[3]  Seif Haridi,et al.  Distributed Algorithms , 1992, Lecture Notes in Computer Science.

[4]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[5]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[6]  Guanrong Chen,et al.  Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint , 2003 .

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

[8]  M. Forti,et al.  Global convergence of neural networks with discontinuous neuron activations , 2003 .

[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]  Duccio Papini,et al.  Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain , 2005, IEEE Transactions on Neural Networks.

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

[12]  Wen Yang,et al.  Consensus in a heterogeneous influence network. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[14]  R. Srikant,et al.  Quantized Consensus , 2006, 2006 IEEE International Symposium on Information Theory.

[15]  Huijun Gao,et al.  ${\cal H}_{\infty}$ Estimation for Uncertain Systems With Limited Communication Capacity , 2007, IEEE Transactions on Automatic Control.

[16]  T. C. Aysal,et al.  Distributed Average Consensus With Dithered Quantization , 2008, IEEE Transactions on Signal Processing.

[17]  Huijun Gao,et al.  A new approach to quantized feedback control systems , 2008, Autom..

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

[19]  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..

[20]  Ruggero Carli,et al.  Average consensus on networks with quantized communication , 2009 .

[21]  Wei Wu,et al.  Cluster Synchronization of Linearly Coupled Complex Networks Under Pinning Control , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[22]  Wenwu Yu,et al.  Distributed Consensus Filtering in Sensor Networks , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[23]  Jinde Cao,et al.  Cluster synchronization in an array of hybrid coupled neural networks with delay , 2009, Neural Networks.

[24]  Tianping Chen,et al.  Consensus problem in directed networks of multi-agents via nonlinear protocols☆ , 2009 .

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

[26]  John N. Tsitsiklis,et al.  On distributed averaging algorithms and quantization effects , 2007, 2008 47th IEEE Conference on Decision and Control.

[27]  Soummya Kar,et al.  Distributed Consensus Algorithms in Sensor Networks: Quantized Data and Random Link Failures , 2007, IEEE Transactions on Signal Processing.

[28]  Zidong Wang,et al.  Robust Hinfinity finite-horizon filtering with randomly occurred nonlinearities and quantization effects , 2010, Autom..

[29]  Qing Hui,et al.  Quantized near-consensus via quantized communication links , 2010, Proceedings of the 2010 American Control Conference.

[30]  Zidong Wang,et al.  RobustH∞ Finite-HorizonFilteringwithRandomly OccurredNonlinearitiesandQuantizationEffects ⋆ , 2010 .

[31]  Wenwu Yu,et al.  Distributed leader-follower flocking control for multi-agent dynamical systems with time-varying velocities , 2010, Syst. Control. Lett..

[32]  Yeung Sam Hung,et al.  Distributed H∞-consensus filtering in sensor networks with multiple missing measurements: The finite-horizon case , 2010, Autom..

[33]  Jinde Cao,et al.  Exponential Synchronization of Linearly Coupled Neural Networks With Impulsive Disturbances , 2011, IEEE Transactions on Neural Networks.

[34]  Wei Xing Zheng,et al.  Second-order consensus for multi-agent systems with switching topology and communication delay , 2011, Syst. Control. Lett..

[35]  Qing Hui,et al.  Quantised near-consensus via quantised communication links , 2011, Int. J. Control.

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

[37]  Wenwu Yu,et al.  Distributed Higher Order Consensus Protocols in Multiagent Dynamical Systems , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[38]  Shengyuan Xu,et al.  Distributed Primal–Dual Subgradient Method for Multiagent Optimization via Consensus Algorithms , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[39]  Yang Tang,et al.  Multiobjective synchronization of coupled systems. , 2011, Chaos.

[40]  Deming Yuan,et al.  Distributed Primal-Dual Subgradient Method for Multiagent Optimization via Consensus Algorithms. , 2011, IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society.

[41]  Claudio De Persis,et al.  Discontinuities and hysteresis in quantized average consensus , 2010, Autom..

[42]  Huijun Gao,et al.  Evolutionary Pinning Control and Its Application in UAV Coordination , 2012, IEEE Transactions on Industrial Informatics.

[43]  Jinde Cao,et al.  Synchronization Control for Nonlinear Stochastic Dynamical Networks: Pinning Impulsive Strategy , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[44]  Daniel W. C. Ho,et al.  Partial-Information-Based Distributed Filtering in Two-Targets Tracking Sensor Networks , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[45]  Guo-Ping Liu,et al.  Global bounded consensus of multi-agent systems with non-identical nodes and communication time-delay topology , 2013, Int. J. Syst. Sci..