Robust consensus of fractional multi-agent systems with external disturbances

In this paper, the problem of robust consensus for fractional multi-agent systems with external disturbances is investigated over a directed fixed interaction graph. Based on Mittag-Leffler stability theory and the inequality techniques, both linear and nonlinear systems are considered. Firstly, for fractional linear multi-agent systems, it is shown that consensus can be achieved asymptotically in the absence of disturbances. In the presence of disturbances, the steady-state errors of any two agents can reach a small region determined by the bound of disturbances. Secondly, for fractional nonlinear multi-agent systems, a pinning control input is proposed such that robust consensus can be realized. Finally, the numerical simulations are given to verify the correctness of the presented theories.

[1]  Peng Shi,et al.  Robust consensus algorithm for second-order multi-agent systems with external disturbances , 2012, Int. J. Control.

[2]  Hongye Su,et al.  Distributed consensus of multi-agent systems with nonlinear dynamics via adaptive intermittent control , 2015, J. Frankl. Inst..

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

[4]  Guanrong Chen,et al.  Formation control of networked multi-agent systems , 2010 .

[5]  Jinde Cao,et al.  Robust consensus of fractional-order multi-agent systems with positive real uncertainty via second-order neighbors information , 2015, Neurocomputing.

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

[7]  Yongcan Cao,et al.  Distributed Coordination of Networked Fractional-Order Systems , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[8]  Tiedong Ma,et al.  Impulsive consensus of multi-agent nonlinear systems with control gain error , 2016, Neurocomputing.

[9]  Hairong Dong,et al.  Robust Consensus of Nonlinear Multiagent Systems With Switching Topology and Bounded Noises , 2016, IEEE Transactions on Cybernetics.

[10]  Eshel Ben-Jacob,et al.  Biofluiddynamics of lubricating bacteria , 2001 .

[11]  Zhiyong Yu,et al.  Leader-following consensus of fractional-order multi-agent systems via adaptive pinning control , 2015, Int. J. Control.

[12]  Manuel A. Duarte-Mermoud,et al.  Lyapunov functions for fractional order systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

[13]  Guanghui Wen,et al.  Flocking of multi‐agent dynamical systems with intermittent nonlinear velocity measurements , 2012 .

[14]  I. Podlubny.  Fractional differential equations , 1998 .

[15]  Jinde Cao,et al.  $M$-Matrix Strategies for Pinning-Controlled Leader-Following Consensus in Multiagent Systems With Nonlinear Dynamics , 2013, IEEE Transactions on Cybernetics.

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

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

[18]  Yiguang Hong,et al.  Distributed Observers Design for Leader-Following Control of Multi-Agent Networks (Extended Version) , 2017, 1801.00258.

[19]  Hongjie Li,et al.  Second-order consensus in multi-agent systems with directed topologies and communication constraints , 2016, Neurocomputing.

[20]  Guanghui Wen,et al.  Consensus Tracking of Multi-Agent Systems With Lipschitz-Type Node Dynamics and Switching Topologies , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[21]  Xiaoming Hu,et al.  Sufficient conditions for connectivity maintenance and rendezvous in leader-follower networks , 2010, Autom..

[22]  Hong-yong Yang,et al.  Distributed coordination of fractional order multi-agent systems with communication delays , 2014 .

[23]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2004, IEEE Trans. Autom. Control..

[24]  Yongcan Cao,et al.  Distributed Coordination of Multi-agent Networks , 2011 .

[25]  E Ben-Jacob,et al.  Lubricating bacteria model for branching growth of bacterial colonies. , 1998, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[27]  Jinde Cao,et al.  Second-order leader-following consensus of nonlinear multi-agent systems via pinning control , 2010, Syst. Control. Lett..

[28]  Yu-Ping Tian,et al.  Consensus of Multi-Agent Systems With Diverse Input and Communication Delays , 2008, IEEE Transactions on Automatic Control.

[29]  W. K. Wong,et al.  Robust synchronization of fractional-order complex dynamical networks with parametric uncertainties , 2012 .

[30]  Yangquan Chen,et al.  Computers and Mathematics with Applications Stability of Fractional-order Nonlinear Dynamic Systems: Lyapunov Direct Method and Generalized Mittag–leffler Stability , 2022 .

[31]  Tao Li,et al.  Multiconsensus of fractional-order uncertain multi-agent systems , 2015, Neurocomputing.

[32]  Yongcan Cao,et al.  Distributed Coordination of Multi-agent Networks: Emergent Problems, Models, and Issues , 2010 .

[33]  Li Xiao,et al.  Distributed consensus of multi-agent systems over general directed networks with limited bandwidth communication , 2016, Neurocomputing.

[34]  Zhiyong Yu,et al.  Leader-following consensus of fractional-order multi-agent systems under fixed topology , 2015, Neurocomputing.

[35]  Jing Bai,et al.  Consensus with a reference state for fractional-order multi-agent systems , 2016, Int. J. Syst. Sci..

[36]  Yongguang Yu,et al.  Leader-Following Consensus of Fractional Nonlinear Multiagent Systems , 2015 .

[37]  Liu Fei,et al.  Distributed Coordination of Fractional Dynamical Systems with Exogenous Disturbances , 2014 .