Discrete-time consensus strategy for a class of high-order linear multiagent systems under stochastic communication topologies

Abstract Achieving consensus in a class of high-order discrete-time multiagent systems is studied. It is supposed that the network topology is dynamic and the existence of a communication link between each two agents is stochastic. Based on the concept of discrete-time super-martingales, we propose a Lyapunov-based high-order protocol which guarantees achieving almost sure consensus in the network in the presence of some conditions. The main contribution of the paper compared with existing results for consensus control of high-order multiagent systems under stochastic networks is that the proposed consensus protocol in this paper requires no knowledge on the set of feasible topologies (topologies with nonzero probabilities), and can be designed without computing the eigenvalues of the coupling matrices associated with the feasible topologies. In this condition, the computational costs of the consensus protocol design will be decreased significantly. The results are validated via a numerical example.

[1]  Yongcan Cao,et al.  Reaching consensus in the sense of probability , 2013, 2013 American Control Conference.

[2]  Babak Hassibi,et al.  Communication over a wireless network with random connections , 2006, IEEE Transactions on Information Theory.

[3]  Tao Li,et al.  Consensus Conditions of Multi-Agent Systems With Time-Varying Topologies and Stochastic Communication Noises , 2010, IEEE Transactions on Automatic Control.

[4]  Maurizio Porfiri,et al.  Synchronization in Random Weighted Directed Networks , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[5]  José M. Claver.  Parallel Wavefront Algorithms Solving Lyapunov Equations for the Cholesky Factor on Message Passing Multiprocessors , 2004, The Journal of Supercomputing.

[6]  Wei Xing Zheng,et al.  Coordination of Multiple Agents With Double-Integrator Dynamics Under Generalized Interaction Topologies , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[7]  Hanlei Wang,et al.  Consensus of Networked Mechanical Systems With Communication Delays: A Unified Framework , 2014, IEEE Transactions on Automatic Control.

[8]  Huanyu Zhao,et al.  Distributed output feedback consensus of discrete-time multi-agent systems , 2014, Neurocomputing.

[9]  B. Levinger.  Minimal Gerschgorin sets, III , 1969 .

[10]  Yu-Ping Tian,et al.  Consentability and protocol design of multi-agent systems with stochastic switching topology , 2009, Autom..

[11]  Huanyu Zhao.  Leader-following consensus of data-sampled multi-agent systems with stochastic switching topologies , 2015, Neurocomputing.

[12]  Jie Ding,et al.  Consensus in second-order multiple flying vehicles with random delays governed by a Markov chain , 2015, J. Frankl. Inst..

[13]  Farzaneh Abdollahi,et al.  Decentralized H∞ consensus protocol for a class of high-order multiagent systems , 2016 .

[14]  Shaheen Ahmad,et al.  Dynamical sliding mode control approach for vertical flight regulation in helicopters , 1994 .

[15]  Sandro Zampieri,et al.  Randomized consensus algorithms over large scale networks , 2007, 2007 Information Theory and Applications Workshop.

[16]  David Williams,et al.  Probability with Martingales , 1991, Cambridge mathematical textbooks.

[17]  C. Pozrikidis,et al.  An Introduction to Grids, Graphs, and Networks , 2014 .

[18]  Farzaneh Abdollahi,et al.  Pursuit Formation of Double-Integrator Dynamics Using Consensus Control Approach , 2015, IEEE Transactions on Industrial Electronics.

[19]  Chai Wah Wu,et al.  Synchronization and convergence of linear dynamics in random directed networks , 2006, IEEE Transactions on Automatic Control.

[20]  Z. Guan,et al.  Consensus of second-order and high-order discrete-time multi-agent systems with random networks☆ , 2012 .

[21]  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.

[22]  Qingjie Zhang,et al.  Average consensus seeking of high-order continuous-time multi-agent systems with multiple time-varying communication delays , 2011 .

[23]  Zhi-Hong Guan,et al.  Distributed tracking control of second-order multi-agent systems with sampled data , 2014, J. Frankl. Inst..

[24]  Farzaneh Abdollahi,et al.  Average Consensus Over High-Order Multiagent Systems , 2015, IEEE Transactions on Automatic Control.

[25]  M. Mesbahi,et al.  Agreement over random networks , 2004, CDC.

[26]  Jie Huang,et al.  Two consensus problems for discrete-time multi-agent systems with switching network topology , 2012, Autom..

[27]  Zunshui Cheng,et al.  Brief paper - r-consensus control for discrete-time high-order multi-agent systems , 2013 .

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

[29]  W. He,et al.  Consensus control for high-order multi-agent systems [Brief Paper] , 2011 .

[30]  Jun Liu,et al.  Group Consensus in Networked Mechanical Systems with Communication Delays , 2017 .

[31]  Changbin Yu,et al.  Reach almost sure consensus with only group information , 2015, Autom..

[32]  Jiang-Wen Xiao,et al.  Dynamic Average Consensus and Consensusability of General Linear Multiagent Systems with Random Packet Dropout , 2013 .

[33]  Gang Wang,et al.  Consensus stabilization of stochastic multi-agent system with Markovian switching topologies and stochastic communication noise , 2015, J. Frankl. Inst..

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

[35]  Hanlei Wang,et al.  Reaching a consensus in networks of high-order integral agents under switching directed topologies , 2013, Int. J. Syst. Sci..

[36]  Alireza Tahbaz-Salehi,et al.  Consensus Over Ergodic Stationary Graph Processes , 2010, IEEE Transactions on Automatic Control.

[37]  Maurizio Porfiri,et al.  Consensus Seeking Over Random Weighted Directed Graphs , 2007, IEEE Transactions on Automatic Control.

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

[39]  Alireza Tahbaz-Salehi,et al.  A Necessary and Sufficient Condition for Consensus Over Random Networks , 2008, IEEE Transactions on Automatic Control.

[40]  Behrouz Touri,et al.  On Ergodicity, Infinite Flow, and Consensus in Random Models , 2010, IEEE Transactions on Automatic Control.

[41]  Xiaoyu Liu,et al.  Consensus for networked multi-agent systems with unknown communication delays , 2016, J. Frankl. Inst..

[42]  R. Tempo,et al.  Randomized Algorithms for Analysis and Control of Uncertain Systems , 2004 .

[43]  Hyungbo Shim,et al.  Consensus of output-coupled high-order linear multi-agent systems under deterministic and Markovian switching networks , 2015, Int. J. Syst. Sci..

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

[45]  Dongya Zhao,et al.  Stochastic averaging approach to leader-following consensus of linear multi-agent systems , 2016, J. Frankl. Inst..

[46]  Wei Ren,et al.  Consensus strategies for cooperative control of vehicle formations , 2007 .

[47]  Xiaobo Li,et al.  Observer‐based consensus of second‐order multi‐agent system with fixed and stochastically switching topology via sampled data , 2014 .

[48]  A. J. Healey,et al.  Multivariable sliding mode control for autonomous diving and steering of unmanned underwater vehicles , 1993 .

[49]  Dongmei Xie,et al.  Consensus problem of networked multi-agent systems with constant communication delay: stochastic switching topology case , 2012, Int. J. Control.

[50]  Ella M. Atkins,et al.  Distributed multi‐vehicle coordinated control via local information exchange , 2007 .

[51]  Jie Huang,et al.  Stability of a Class of Linear Switching Systems with Applications to Two Consensus Problems , 2011, IEEE Transactions on Automatic Control.

[52]  Xiuxian Li,et al.  Finite-time consensus of second-order multi-agent systems via a structural approach , 2016, J. Frankl. Inst..

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

[54]  Wenlian Lu,et al.  Mathematik in den Naturwissenschaften Leipzig Consensus and synchronization in discrete-time networks of multi-agents with stochastically switching topologies and time delays by , 2011 .

[55]  Tingwen Huang,et al.  Second-Order Global Consensus in Multiagent Networks With Random Directional Link Failure , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[56]  Reza Olfati-Saber,et al.  Distributed Kalman filtering for sensor networks , 2007, 2007 46th IEEE Conference on Decision and Control.

[57]  Ming Wang,et al.  Consensus seeking in a network of discrete-time linear agents with communication noises , 2015, Int. J. Syst. Sci..

[58]  Jing-Wen Yi,et al.  Consensus in Markovian jump second-order multi-agent systems with random communication delay , 2014 .