Distributed formation control of fractional-order multi-agent systems with relative damping and nonuniform time-delays.

A novel formation control law in the case of relative damping and nonuniform time-delays is proposed for fractional-order multi-agent systems(FOMASs) in this paper. The nonuniform time-delays can be generally divided into symmetric and asymmetric time-delays. Hence, the formation control algorithm for FOMASs in the case of symmetric time-delays and relative damping is first studied under an undirected network topology. Then, the formation control algorithm for FOMASs in the case of asymmetric time-delays and relative damping is studied under a directed network topology. By the means of frequency-domain theory, algebra graph theory and matrix theory, sufficient conditions are derived to ensure the formation control of FOMASs in the case of nonuniform time-delays and relative damping. Finally, several numerical examples are given and the corresponding simulations are provided to demonstrate the correctness of obtained results.

[1]  Y. Chen,et al.  Time-Optimal Control of Systems with Fractional Dynamics , 2010 .

[2]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[3]  Zhang Ren,et al.  Time-varying group formation analysis and design for second-order multi-agent systems with directed topologies , 2016, Neurocomputing.

[4]  Zhang Ren,et al.  Distributed fault-tolerant time-varying formation control for high-order linear multi-agent systems with actuator failures. , 2017, ISA transactions.

[5]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[6]  Lili Wang,et al.  Distributed Formation Control of Multi-Agent Systems Using Complex Laplacian , 2014, IEEE Transactions on Automatic Control.

[7]  Qing-Long Han,et al.  Achieving Cluster Formation of Multi-Agent Systems Under Aperiodic Sampling and Communication Delays , 2018, IEEE Transactions on Industrial Electronics.

[8]  Dong Shen,et al.  Learning formation control for fractional‐order multiagent systems , 2018 .

[9]  Jing Bai,et al.  Formation tracking of fractional-order multi-agent systems based on error predictor , 2015, The 27th Chinese Control and Decision Conference (2015 CCDC).

[10]  Jing Bai,et al.  Distributed consensus tracking for the fractional-order multi-agent systems based on the sliding mode control method , 2017, Neurocomputing.

[11]  José António Tenreiro Machado,et al.  Fractional-order hybrid control of robot manipulators , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

[12]  Yongcan Cao,et al.  Distributed formation control for fractional-order systems: Dynamic interaction and absolute/relative damping , 2010, Syst. Control. Lett..

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

[14]  Jie Yang,et al.  Consensus of fractional-order multi-agent systems with input time delay , 2017 .

[15]  Wei Chen,et al.  Distributed consensus control for double-integrator fractional-order multi-agent systems with nonuniform time-delays , 2018, Neurocomputing.

[16]  Wenjing Li,et al.  Consensus Analysis of Fractional-Order Multiagent Systems with Double-Integrator , 2017 .

[17]  Ping Gong,et al.  Distributed tracking of heterogeneous nonlinear fractional-order multi-agent systems with an unknown leader , 2017, J. Frankl. Inst..

[18]  Wei Chen,et al.  Consensus of Fractional-Order Multiagent Systems with Nonuniform Time Delays , 2018 .

[19]  Weiyao Lan,et al.  Adaptive robust tracking control for uncertain nonlinear fractional-order multi-agent systems with directed topologies , 2018, Autom..

[20]  Jing Bai,et al.  Distributed formation control of fractional-order multi-agent systems with absolute damping and communication delay , 2015, Int. J. Syst. Sci..

[21]  Yu Song,et al.  Distributed formation control of fractional-order multi-agent systems with relative damping and communication delay , 2017 .

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

[23]  Yingmin Jia,et al.  Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies , 2009, Autom..

[24]  Jiangping Hu,et al.  Tracking control for multi-agent consensus with an active leader and variable topology , 2006, Autom..

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

[26]  Wei Zhu,et al.  Consensus of Fractional-Order Multiagent Systems with Double Integrator under Switching Topologies , 2017 .