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Strong Structural Controllability Based on Leader-Follower Framework

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Abstract

In this paper, the strong structural controllability of the leader-follower framework is discussed. Firstly, the authors analyze different edge augmentation methods to preserve the strong structural controllability of the path-bud topology. The following four cases are considered: Adding edges from the path to the bud; adding edges from the bud to the path; adding the reverse or forward edges to the path or bud; and adding both the reverse and forward edges to the path or bud. Then sufficient conditions are derived for the strong structural controllability of the new topologies which are generated by adding different edges. In addition, it is proved that rank[A B] = n is a necessary condition for the strong structural controllability. Finally, three examples are given to verify the effectiveness of the main results.

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References

  1. Ji Z J, Lin H, and Lee T H, A graph theory based characterization of controllability for multi-agent systems with fixed topology, Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico, 2008, 5262–5267.

  2. Godsil C and Severini S, Control by quantum dynamics on graphs, Physical Review A, 2010, 81(5): 052316.

    Article  MathSciNet  Google Scholar 

  3. Egerstedt M, Martini S, and Cao M, Interacting with networks: How does structure relate to controllability in single-leader, consensus networks, IEEE Control Systems Magazine, 2012, 32(4): 66–73.

    Article  MathSciNet  MATH  Google Scholar 

  4. Abbas W, Shabbir M, and Yazicioglu Y, Edge augmentation with controllability constraints in directed laplacian networks, IEEE Control Systems Letters, 2021, 99, DOI: https://doi.org/10.1109/LC-SYS.2021.3089372.

  5. Gambuzza L V and Frasca M, Distributed control of multi-consensus, IEEE Transactions on Automatic Control, 2020, 99, DOI: https://doi.org/10.1109/tac.2020.3006820.

  6. Chen X, Pequito S, and Pappas G J, Minimal edge addition for network controllability, IEEE Transactions on Control of Network Systems, 2018, 99, DOI: https://doi.org/10.1109/TCNS.2018.2814841.

  7. Kalman R, Controllability of linear dynamical systems, Contributions to Differential Equations, 1963, 1(3): 189–213.

    MathSciNet  Google Scholar 

  8. Herbert G and Tanner, On the controllability of nearest neighbor interconnections, Proceedings of the 43rd IEEE Conference on Decision and Control, Atlantis, Paradise Island, Bahamas, 2004, 2464–2472.

  9. Rahmani A and Mesbahi M, On the controlled agreement problem, Proceedings of the 2006 American Control Conference, Minneapolis, Minnesota, USA, 2006, 1376–1381.

  10. Rahmani A and Mesbahi M, Pulling the strings on agreement: Anchoring, controllability, and graph automorphisms, Proceedings of the 2007 American Control Conference, New York City, USA, 2007, 2738–2743.

  11. Rahmani A, Ji M, and Mesbahi M, Controllability of multi-agent systems from a graph-theoretic perspective, SIAM Journal on Control and Optimization, 2009, 48(1): 162–186.

    Article  MathSciNet  MATH  Google Scholar 

  12. Ji Z J, Lin H, and Yu H, Protocols design and uncontrollable topologies construction for multiagent networks, IEEE Transactions on Automatic Control, 2015, 3(60): 781–786.

    Article  MATH  Google Scholar 

  13. Ji Z J, Lin H, Cao S B, et al., The complexity in complete graphic characterizations of multi-agent controllability, IEEE Transactions on Cybernectics, 2021, 1(51): 64–76.

    Article  Google Scholar 

  14. Qu J J, Ji Z J, and Shi Y, The graphical conditions for controllability of multiagent systems under equitable partition, IEEE Transcations on Cybernetics, 2021, 9(51): 4661–4672.

    Article  Google Scholar 

  15. Huang Y X and Liu Y G, Practical tracking via adaptive event-triggered feedback for uncertain nonlinear systems, IEEE Transactions on Automatic Control, 2019, 64(9): 3920–3927.

    Article  MathSciNet  MATH  Google Scholar 

  16. Sun Y S, Ji Z J, and Liu K, Event-based consensus for general linear multiagent systems under switching topologies, Complexity, 2020, DOI: https://doi.org/10.1155/2020/5972749.

  17. Sun H, Liu Y G, and Li F Z, Distributed optimal consensus of second-order multi-agent system, SCIENCE CHINA Information Sciences, 2021, 64(10): 209201.

    Article  MathSciNet  Google Scholar 

  18. Tian L, Ji Z J, Liu Y G, et al., A unified approach for the influences of negative weights on system consensus, Systems and Control Letters, 2022, 160, DOI: https://doi.org/10.1016/j.sysconle.2021.105109.

  19. Lin C T, Structural controllability, IEEE Transactions on Automatic Control, 1974, 19(3): 201–208.

    Article  MathSciNet  MATH  Google Scholar 

  20. Shields R and Pearson J, Structural controllability of multi-input linear systems, IEEE Transactions on Automatic Control, 1976, 21(2): 203–212.

    Article  MathSciNet  MATH  Google Scholar 

  21. Hosoe S, Determination of generic dimensions of controllable subspaces and its application, IEEE Transactions on Automatic Control, 1980, 25(6): 1192–1196.

    Article  MathSciNet  MATH  Google Scholar 

  22. Mayeda H, On structural controllability theorem, IEEE Transactions on Automatic Control, 1981, 26(3): 795–798.

    Article  MathSciNet  MATH  Google Scholar 

  23. Mayeda H and Yamada T, Strong structural controllability, SIAM Journal on Control and Optimization, 1979, 17(1): 123–138.

    Article  MathSciNet  MATH  Google Scholar 

  24. Monshizadeh N, Zhang S, and Camlibel M K, Zero forcing sets and controllability of dynamical systems defined on graph, IEEE Transactions on Automatic Control, 2014, 59(9): 2562–2567.

    Article  MathSciNet  MATH  Google Scholar 

  25. Mousavi S S, Haeri M, and Mesbahi M, On the structural and strong structural controllability of undirected networks, IEEE Transactions on Automatic Control, 2017, 66(7): 2234–2241.

    Article  MATH  Google Scholar 

  26. Jia J, Trentelman H L, and Baar W, Strong structural controllability of systems on colored graphs, IEEE Transactions on Automatic Control, 2020, 65(10): 3977–3990.

    Article  MathSciNet  MATH  Google Scholar 

  27. Liu P, Tian Y P, and Zhang Y, Leader selection for strong structural controllability of singleintegrator multi-agent systems, Journal of Systems Science and Complexity, 2017, 30(6): 1227–1241.

    Article  MathSciNet  MATH  Google Scholar 

  28. Hartung C, Reissig G, and Svaricek F, Characterization of strong structural controllability of uncertain linear time-varying discrete-time systems, Proceedings of the 51st IEEE Conference on Decision and Control, Maui, Hawaii, USA, 2012, 2189–2194.

  29. Hartung C, Reissig G, and Svaricek F, Sufficient conditions for strong structural controllability of uncertain linear time-varying systems, Proceedings of 2013 American Control Conference, Washington, DC, USA, 2013, 5875–5880.

  30. Reissig G, Hartung C, and Svaricek F, Strong structural controllability and observability of linear time-varying systems, IEEE Transactions on Automatic Control, 2014, 59(11): 3087–3092.

    Article  MathSciNet  MATH  Google Scholar 

  31. Hou B, Xiang L, and Chen G, Structural controllability of temporally switching networks, IEEE Transactions on Circuits and Systems-I: Regular Papers, 2016, 63(10): 1771–1781.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Insitute of Complexity Science, College of Automation, Qingdao University, Qingdao, 266071, China

    Wei Qi, Zhijian Ji & Chong Lin

  2. Shandong Key Laboratory of Industrial Control Technology, Qingdao University, Qingdao, 266071, China

    Wei Qi, Zhijian Ji & Chong Lin

  3. School of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Yungang Liu

Authors
  1. Wei Qi
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  2. Zhijian Ji
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  3. Yungang Liu
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  4. Chong Lin
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Correspondence to Zhijian Ji.

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The authors declare no conflict of interest.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant Nos. 61873136 and 62033007, Taishan Scholars Climbing Program of Shandong Province of China and Taishan Scholars Project of Shandong Province of China under Grant No. ts20190930.

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Qi, W., Ji, Z., Liu, Y. et al. Strong Structural Controllability Based on Leader-Follower Framework. J Syst Sci Complex 36, 1498–1518 (2023). https://doi.org/10.1007/s11424-023-1516-2

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  • DOI: https://doi.org/10.1007/s11424-023-1516-2

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