Stochastic finite-time consensualisation for Markov jump networks with disturbance

This study is devoted to the finite-time consensus control for directed networks with stochastic Markov jump topologies and external disturbances. The purpose of the study is to design a control protocol to ensure that the disagreement dynamics of interconnected networks stay in a given bound over a finite-time interval rather than asymptotically converge to zero in infinite settling time. Through utilisation of certain features of Laplacian matrix in real Jordan form, sufficient conditions for the existence of finite-time consensus protocol is derived by allowing Lyapunov function to increase in a fixed-time interval. Finite-time convergence result for stochastic consensus problem is validated via a simulation study.

[1]  Sanjay P. Bhat,et al.  Finite-Time Semistability and Consensus for Nonlinear Dynamical Networks , 2008, IEEE Transactions on Automatic Control.

[2]  Francesco Amato,et al.  Finite-time control of discrete-time linear systems , 2005, IEEE Transactions on Automatic Control.

[3]  Yanjun Shen.  Finite-time control of linear parameter-varying systems with norm-bounded exogenous disturbance , 2008 .

[4]  Steve Goddard,et al.  Localization and follow-the-leader control of a heterogeneous group of mobile robots , 2006 .

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

[6]  Valery A. Ugrinovskii,et al.  Distributed robust filtering with Hinfinity consensus of estimates , 2011, Autom..

[7]  Richard M. Murray,et al.  Information flow and cooperative control of vehicle formations , 2004, IEEE Transactions on Automatic Control.

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

[9]  V A Ugrinovskii,et al.  Distributed robust filtering with H∞ consensus of estimates , 2010, Proceedings of the 2010 American Control Conference.

[10]  Yigang He,et al.  Finite-Time Synchronization of a Class of Second-Order Nonlinear Multi-Agent Systems Using Output Feedback Control , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  Francesco Amato,et al.  Finite-time control of linear systems subject to parametric uncertainties and disturbances , 2001, Autom..

[12]  P. Dorato.  SHORT-TIME STABILITY IN LINEAR TIME-VARYING SYSTEMS , 1961 .

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

[14]  Francesco Amato,et al.  Necessary and sufficient conditions for finite-time stability of impulsive dynamical linear systems , 2013, Autom..

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

[16]  Shihua Li,et al.  Attitude synchronization control for a group of flexible spacecraft , 2014, Autom..

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

[18]  Zhiqiang Zuo,et al.  Finite-time stability for continuous-time switched systems in the presence of impulse effects , 2012 .

[19]  Fei Liu,et al.  Finite-time stabilisation for Markov jump systems with Gaussian transition probabilities , 2013 .

[20]  A. S. Morse,et al.  Coordination of Groups of Mobile Autonomous Agents , 2004 .

[21]  Richard M. Murray,et al.  INFORMATION FLOW AND COOPERATIVE CONTROL OF VEHICLE FORMATIONS , 2002 .

[22]  Shihua Li,et al.  Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics , 2011, Autom..

[23]  Rodolphe Sepulchre,et al.  Synchronization in networks of identical linear systems , 2009, Autom..

[24]  Zhisheng Duan,et al.  On H∞ and H2 performance regions of multi-agent systems , 2011, Autom..

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

[26]  Zhengtao Ding,et al.  Consensus Control of a Class of Lipschitz Nonlinear Systems With Input Delay , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[27]  Ying-Xu Yang,et al.  Finite‐time stability of switched positive linear systems , 2014 .

[28]  Zhengtao Ding,et al.  Consensus Output Regulation of a Class of Heterogeneous Nonlinear Systems , 2013, IEEE Transactions on Automatic Control.

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

[30]  Jorge Cortés,et al.  Finite-time convergent gradient flows with applications to network consensus , 2006, Autom..

[31]  Yingmin Jia,et al.  Distributed robust Hinfinity consensus control in directed networks of agents with time-delay , 2008, Syst. Control. Lett..

[32]  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.

[33]  Wenwu Yu,et al.  Consensus in Directed Networks of Agents With Nonlinear Dynamics , 2011, IEEE Transactions on Automatic Control.