Consensus stabilization of stochastic multi-agent system with Markovian switching topologies and stochastic communication noise

In this paper, we study stochastic consensus stabilization problems for a stochastic high-order multi-agent system with Markovian switching topologies and stochastic communication noise. By using the generalized Ito^ formula for the Markovian switching multi-agent system with stochastic communication noise, a state-feedback controller is constructed to ensure that the stochastic high-order multi-agent system reaches consensus in mean square sense when each agent's dynamics has unstable open-loop poles. A necessary and sufficient condition for the stochastic mean square consensus stabilization of the stochastic multi-agent system subject to Markovian switching topologies and additive disturbance is established under a distributed control protocol, i.e., the digraph is balanced and the union of the communication topology set contains a spanning tree. Numerical simulation is presented to demonstrate the theoretical analysis.

[1]  Francisco Herrera,et al.  A Consensus Model to Detect and Manage Noncooperative Behaviors in Large-Scale Group Decision Making , 2014, IEEE Transactions on Fuzzy Systems.

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

[3]  Chi-Tsong Chen,et al.  Linear System Theory and Design , 1995 .

[4]  V. Utkin,et al.  Sliding mode control design based on Ackermann's formula , 1998, IEEE Trans. Autom. Control..

[5]  S. Karlin,et al.  A second course in stochastic processes , 1981 .

[6]  Long Cheng,et al.  A Mean Square Consensus Protocol for Linear Multi-Agent Systems With Communication Noises and Fixed Topologies , 2014, IEEE Transactions on Automatic Control.

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

[8]  M. Vidyasagar,et al.  Qualitative Analysis of Large Scale Dynamical Systems , 2012, IEEE Transactions on Systems, Man, and Cybernetics.

[9]  Carlos Sagüés,et al.  Distributed Consensus on Robot Networks for Dynamically Merging Feature-Based Maps , 2012, IEEE Transactions on Robotics.

[10]  Lihua Xie,et al.  Consensus condition for linear multi-agent systems over randomly switching topologies , 2013, Autom..

[11]  Qiang Zhang,et al.  Distributed Parameter Estimation Over Unreliable Networks With Markovian Switching Topologies , 2012, IEEE Transactions on Automatic Control.

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

[13]  KarSoummya,et al.  Distributed consensus algorithms in sensor networks with imperfect communication , 2009 .

[14]  Shengyuan Xu,et al.  Consentability for high-order multi-agent systems under noise environment and time delays , 2013, J. Frankl. Inst..

[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]  John S. Baras,et al.  Convergence Results for the Linear Consensus Problem under Markovian Random Graphs , 2013, SIAM J. Control. Optim..

[17]  Xinzhi Liu,et al.  Distributed stochastic consensus of multi-agent systems with noisy and delayed measurements , 2013 .

[18]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

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

[20]  Joe Brewer,et al.  Kronecker products and matrix calculus in system theory , 1978 .

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

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

[23]  Lihua Xie,et al.  Network Topology and Communication Data Rate for Consensusability of Discrete-Time Multi-Agent Systems , 2011, IEEE Trans. Autom. Control..

[24]  Jorge Cortés,et al.  Distributed algorithms for reaching consensus on general functions , 2008, Autom..

[25]  Hyo-Sung Ahn,et al.  Distributed Coordination and Control for a Freeway Traffic Network Using Consensus Algorithms , 2016, IEEE Systems Journal.

[26]  Soummya Kar,et al.  Distributed Consensus Algorithms in Sensor Networks With Imperfect Communication: Link Failures and Channel Noise , 2007, IEEE Transactions on Signal Processing.

[27]  A. Friedman.  Stochastic Differential Equations and Applications , 1975 .

[28]  Daizhan Cheng,et al.  Leader-following consensus of second-order agents with multiple time-varying delays , 2010, Autom..

[29]  Marcelo D. Fragoso,et al.  A Unified Approach for Stochastic and Mean Square Stability of Continuous-Time Linear Systems with Markovian Jumping Parameters and Additive Disturbances , 2005, SIAM J. Control. Optim..

[30]  John N. Tsitsiklis,et al.  On the Nonexistence of Quadratic Lyapunov Functions for Consensus Algorithms , 2007, IEEE Transactions on Automatic Control.

[31]  Tingwen Huang,et al.  Second-Order Consensus Seeking in Multi-Agent Systems With Nonlinear Dynamics Over Random Switching Directed Networks , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[32]  A. Hamdan,et al.  Measures of Modal Controllability and Observability for First- and Second-Order Linear Systems , 1989 .

[33]  Ioannis Karatzas,et al.  Brownian Motion and Stochastic Calculus , 1987 .

[34]  J. Lam,et al.  Brief paper - Consensus of multi-agent systems: a simultaneous stabilisation approach , 2012 .

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

[36]  Yisheng Zhong,et al.  Consensus for high-order time-delayed swarm systems with uncertainties and external disturbances , 2011, Proceedings of the 30th Chinese Control Conference.