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Distributed Containment Control of Fractional-order Multi-agent Systems with Double-integrator and Nonconvex Control Input Constraints

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  • Control Theory and Applications
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Abstract

This paper mainly considers the distributed containment control problem for continuous-time fractional-order multi-agent systems (FOMASs) with double-integrator, where the control input of each agent is constrained to lie in a nonconvex set. A distributed projection containment control algorithm is designed for each follower. To finish the convergence analysis, the original closed-loop system is first changed into an equivalent one by a proper model transformation and the method of the L1 interpolation approximation is introduced to deal with the projection operator. Then, by using the properties of the convex hull and the Mittag-Leffler function, it is shown that the largest distance between the followers and the convex hull spanned by leaders tends to zero asymptotically, while all agents’ control inputs are constrained to stay in their corresponding nonconvex constraint sets. Finally, numerical simulations are provided to verify the effectiveness of the theoretical results.

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Technology and Business University, 11 FuCheng Road, Haidian District, Beijing, 100048, P. R. China

    Xiao-Lin Yuan & Li-Po Mo

  2. Department of Mathematics, Beijing Jiaotong University, 3 ShangYuanCun, Haidian District, Beijing, 100044, P. R. China

    Yong-Guang Yu & Guo-Jian Ren

Authors
  1. Xiao-Lin Yuan
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  2. Li-Po Mo
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Correspondence to Li-Po Mo.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Mathiyala-gan Kalidass under the direction of Jessie (Ju H.) Park. This work is supported by the National Natural Science Foundation of China (61973329 and 61772063), the Beijing Educational Committee Foundation (KM201910011007 and PXM2019_014213_000007), the Beijing Natural Science Foundation (Z180005 and 9192008) and the 2019 Graduate Research Capacity Improvement Program.

Xiao-Lin Yuan received her B.S. degree in school of Science, Beijing Technology and Business University, China, in 2017. Currently, she is pursuing a Master’s degree in control theory in School of Mathematics and Statistics, Beijing Technology and Business University. Her research interests include coordination control of fractional order multi-agent systems.

Li-Po Mo received his B.S. degree in Department of Mathematics, Shihezi University, China, in 2003, and a Ph.D. degree in School of Mathematics and Systems Science from the Beihang University, Beijing, in 2010. Currently, he is a professor at Beijing Technology and Business University. His research interests include stochastic systems, coordination control of multi-agent systems, and distributed optimization.

Yong-Guang Yu received his M.S. degree in Department of Mathematical Science, Inner Mongolia University, China, in 2001, and a Ph.D. degree in Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, China, in 2004. From 2007 to 2009, he was a research fellow in City University of Hong Kong, China. Since 2010, he has been a professor with the Department of Mathematics, School of Science, Beijing Jiaotong University, China. His research interests include chaotic dynamics, chaos control and synchronization, complex networks, nonlinear control, and multi-agent systems.

Guo-Jian Ren received his B.S. degree in 2014, and a Ph.D. degree in 2019, both in Department of Mathematics, School of Science, Beijing Jiaotong University, China. Currently he is a Lecturer in Beijing Jiaotong University. His current research interests include multi-agent systems, distributed coordination, complex networks, nonlinear dynamics and control and fractional order calculus.

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Yuan, XL., Mo, LP., Yu, YG. et al. Distributed Containment Control of Fractional-order Multi-agent Systems with Double-integrator and Nonconvex Control Input Constraints. Int. J. Control Autom. Syst. 18, 1728–1742 (2020). https://doi.org/10.1007/s12555-019-0431-8

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