Mean square consensus of multi-agent systems over fading networks with directed graphs

Abstract This paper studies the mean square consensus problem of discrete-time linear multi-agent systems (MASs) over analog fading networks with directed graphs. Compressed in-incidence matrix (CIIM), compressed incidence matrix (CIM) and compressed edge Laplacian (CEL) are firstly proposed to facilitate the modeling and consensus analysis. It is then shown that the mean square consensusability is solely determined by the edge state dynamics on a directed spanning tree. As a result, sufficient conditions are provided for mean square consensus over fading networks with directed graphs in terms of fading parameters, the network topology and the agent dynamics. Moreover, the role of network topology on the mean square consensusability is discussed. In the end, simulations are conducted to verify the derived results.

[1]  Jamie S. Evans,et al.  Kalman filtering with faded measurements , 2009, Autom..

[2]  Bruno Sinopoli,et al.  Foundations of Control and Estimation Over Lossy Networks , 2007, Proceedings of the IEEE.

[3]  Zhiwen Zeng,et al.  Edge Agreement of Multi-agent System with Quantized Measurements via Directed Edge Laplacian , 2015, ArXiv.

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

[5]  Lihua Xie,et al.  A survey on recent progress in control of swarm systems , 2016, Science China Information Sciences.

[6]  Ji-Feng Zhang,et al.  Necessary and Sufficient Conditions for Consensusability of Linear Multi-Agent Systems , 2010, IEEE Transactions on Automatic Control.

[7]  Nan Xiao,et al.  Consensusability of discrete-time linear multi-agent systems over analog fading networks , 2016, Autom..

[8]  Wei Ren,et al.  Distributed consensus of linear multi-agent systems with adaptive dynamic protocols , 2011, Autom..

[9]  Nicola Elia,et al.  Remote stabilization over fading channels , 2005, Syst. Control. Lett..

[10]  Nan Xiao,et al.  Feedback Stabilization of Discrete-Time Networked Systems Over Fading Channels , 2012, IEEE Transactions on Automatic Control.

[11]  Lihua Xie,et al.  Network Topology and Communication Data Rate for Consensusability of Discrete-Time Multi-Agent Systems , 2011, IEEE Transactions on Automatic Control.

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

[13]  Lihua Xie,et al.  Distributed Tracking Control for Linear Multiagent Systems With a Leader of Bounded Unknown Input , 2013, IEEE Transactions on Automatic Control.

[14]  D. Bernstein Matrix Mathematics: Theory, Facts, and Formulas , 2009 .

[15]  Zhiwen Zeng,et al.  Convergence analysis using the edge Laplacian: Robust consensus of nonlinear multi‐agent systems via ISS method , 2015, ArXiv.

[16]  Abbas Jamalipour,et al.  Wireless communications , 2005, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005..

[17]  Mehran Mesbahi,et al.  Edge Agreement: Graph-Theoretic Performance Bounds and Passivity Analysis , 2011, IEEE Transactions on Automatic Control.

[18]  Giuseppe Caire,et al.  Optimum power control over fading channels , 1999, IEEE Trans. Inf. Theory.

[19]  Ziyang Meng,et al.  Distributed Containment Control for Multiple Autonomous Vehicles With Double-Integrator Dynamics: Algorithms and Experiments , 2011, IEEE Transactions on Control Systems Technology.

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

[21]  Darrell Schmidt,et al.  EIGENVALUES OF TRIDIAGONAL PSEUDO-TOEPLITZ MATRICES , 1999 .

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

[23]  Jie Chen,et al.  Robust Consensus of Linear Feedback Protocols Over Uncertain Network Graphs , 2017, IEEE Transactions on Automatic Control.

[24]  Dimos V. Dimarogonas,et al.  Consensus with quantized relative state measurements , 2013, Autom..

[25]  Mengyin Fu,et al.  Consensus of Multi-Agent Systems With General Linear and Lipschitz Nonlinear Dynamics Using Distributed Adaptive Protocols , 2011, IEEE Transactions on Automatic Control.

[26]  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.