Sampled-Data Control Based Consensus of Fractional-Order Multi-Agent Systems

In this letter, we investigate consensus control of fractional-order multi-agent systems with the order within (0, 1) via sampled-data control. A new scheme to design distributed controllers with rigorous analysis is presented by utilizing the unique properties of fractional-order calculus, namely hereditary and infinite memory. It is established that global boundedness of all closed-loop signals is ensured and asymptotic consensus is realized. Simulation studies are conducted to illustrate the effectiveness of the proposed control method and verify the obtained results.

[1]  Cheng-Lin Liu,et al.  Average-Consensus Tracking of Sensor Network via Distributed Coordination Control of Heterogeneous Multi-Agent Systems , 2019, IEEE Control Systems Letters.

[2]  Wei Wang,et al.  Distributed adaptive asymptotically consensus tracking control of nonlinear multi-agent systems with unknown parameters and uncertain disturbances , 2017, Autom..

[3]  Yongduan Song,et al.  Smooth control design for adaptive leader-following consensus control of a class of high-order nonlinear systems with time-varying reference , 2017, Autom..

[4]  Guangming Xie,et al.  Consensus of fractional-order double-integrator multi-agent systems , 2019, Neurocomputing.

[5]  I. Podlubny.  Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .

[6]  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 .

[7]  V. Lakshmikantham,et al.  Theory of Fractional Dynamic Systems , 2009 .

[8]  Qing-Long Han,et al.  A survey on recent advances in distributed sampled-data cooperative control of multi-agent systems , 2018, Neurocomputing.

[9]  Wei Wang,et al.  Distributed adaptive control for consensus tracking with application to formation control of nonholonomic mobile robots , 2014, Autom..

[10]  Xu Wang,et al.  Necessary and Sufficient Conditions for Consensus of Double-Integrator Multi-Agent Systems With Measurement Noises , 2011, IEEE Transactions on Automatic Control.

[11]  Jinde Cao,et al.  Necessary and Sufficient Conditions for Consensus of Delayed Fractional‐order Systems , 2012 .

[12]  Zhigang Zeng,et al.  Synchronization and Consensus in Networks of Linear Fractional-Order Multi-Agent Systems via Sampled-Data Control , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[13]  Peng Shi,et al.  Sampled-data control of networked linear control systems , 2007, Autom..

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

[15]  Fei Wang,et al.  Leader-following consensus of nonlinear fractional-order multi-agent systems via event-triggered control , 2017, Int. J. Syst. Sci..

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

[17]  Housheng Su,et al.  Consensus of Delayed Fractional-Order Multiagent Systems With Intermittent Sampled Data , 2020, IEEE Transactions on Industrial Informatics.

[18]  Hamidreza Modares,et al.  Distributed Consensus Control for a Network of Incommensurate Fractional-Order Systems , 2019, IEEE Control Systems Letters.

[19]  Zhiyong Yu,et al.  Necessary and Sufficient Conditions for Consensus of Fractional-Order Multiagent Systems via Sampled-Data Control , 2017, IEEE Transactions on Cybernetics.

[20]  Francesco Bullo,et al.  Coordination and Geometric Optimization via Distributed Dynamical Systems , 2003, SIAM J. Control. Optim..

[21]  Wenwu Yu,et al.  Distributed Consensus Filtering in Sensor Networks , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

[23]  Haibo He,et al.  Necessary and Sufficient Conditions for Consensus in Fractional-Order Multiagent Systems via Sampled Data Over Directed Graph , 2021, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[24]  Yaxin Peng,et al.  Consensus in Fractional-Order Multi-Agent Systems With Intermittence Sampled Data Over Directed Networks , 2020, IEEE Transactions on Circuits and Systems II: Express Briefs.

[25]  Dingyu Xue,et al.  Fractional-Order Control Systems: Fundamentals and Numerical Implementations , 2017 .

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

[27]  Wei Sun,et al.  Convergence speed of a fractional order consensus algorithm over undirected scale‐free networks , 2011 .

[28]  Yongduan Song,et al.  Adaptive finite-time consensus control of a group of uncertain nonlinear mechanical systems , 2015, Autom..

[29]  Changpin Li,et al.  Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative , 2011 .

[30]  Yunpeng Wang,et al.  On Convergence Rate of Leader-Following Consensus of Linear Multi-Agent Systems With Communication Noises , 2015, IEEE Transactions on Automatic Control.

[31]  Igor Podlubny,et al.  Mittag-Leffler stability of fractional order nonlinear dynamic systems , 2009, Autom..

[32]  Tingwen Huang,et al.  Stabilization for sampled-data systems under noisy sampling interval , 2016, Autom..

[33]  Zengqiang Chen,et al.  Reaching a consensus via pinning control , 2009, Autom..

[34]  Jinde Cao,et al.  Observer Design for Tracking Consensus in Second-Order Multi-Agent Systems: Fractional Order Less Than Two , 2017, IEEE Transactions on Automatic Control.

[35]  Ahmed Rahmani,et al.  Consensus of fractional-order multiagent system via sampled-data event-triggered control , 2019, J. Frankl. Inst..

[36]  Ling Zhao,et al.  Smooth control design for adaptive leader-following consensus control of a class of high-order nonlinear systems with time-varying reference and unknown control directions , 2017, Autom..

[37]  Weihua Deng,et al.  Remarks on fractional derivatives , 2007, Appl. Math. Comput..

[38]  Bijnan Bandyopadhyay,et al.  Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach , 2014 .