On the structural controllability of distributed systems with local structure changes


This paper analyzes the structural controllability of distributed systems, which are composed of many subsystems and have complicated interconnections. Different from traditional methods in centralized systems where global information is required, the method proposed in this paper is based on local structural properties and simplified interconnections, by which the computational burden is highly decreased and the implementation is tractable. Moreover, a necessary condition for global structural controllability is obtained by combining local information. When the structure in any subsystems is changed, only corresponding local information needs to be re-evaluated instead of whole distributed systems, which makes the analysis easier. Finally, examples are given to illustrate the effectiveness of our proposed method.

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  1. 1

    Lin C T. Structural controllability. IEEE Trans Automat Contr, 1974, 19: 201–208

    Article  MATH  MathSciNet  Google Scholar 

  2. 2

    Shields R W, Pearson J B. Structural controllability of multi-input linear systems. IEEE Trans Automat Contr, 1976 21: 203–212

    Article  MATH  Google Scholar 

  3. 3

    Glover K, Silverman L M. Characterization of structural controllability. IEEE Trans Automat Contr, 1976, 21: 534–537

    Article  MATH  MathSciNet  Google Scholar 

  4. 4

    Mayeda H. On structural controllability theorem. IEEE Trans Automat Contr, 1981, 26: 795–798

    Article  MATH  MathSciNet  Google Scholar 

  5. 5

    Blackhall L, Hill D J. On the structural controllability of networks of linear systems. In: Proceedings of the 2nd IFAC Workshop on Distributed Estimation and Control in Networked Systems, Annecy, 2010. 245–250

    Google Scholar 

  6. 6

    Liu X M, Lin H, Chen B M. Structural controllability of switched linear systems. Automatica, 2013, 49: 3531–3537

    Article  MATH  MathSciNet  Google Scholar 

  7. 7

    Liu Y Y, Slotine J J, Barabási A L. Controllability of complex networks. Nature, 2011, 473: 167–173

    Article  Google Scholar 

  8. 8

    Maza S, Simon C, Boukhobza T. Impact of the actuator failures on the structural controllability of linear systems: a graph theoretical approach. IET Control Theory A, 2012, 6: 412–419

    Article  MathSciNet  Google Scholar 

  9. 9

    Ghosh S, Ruths J. Structural control of single-input rank one bilinear systems. Automatica, 2016, 64: 8–17

    Article  MATH  MathSciNet  Google Scholar 

  10. 10

    Christofides P D, Scattolini R, de la Pena D M, et al. Distributed model predictive control: a tutorial review and future research directions. Comput Chem Eng, 2013, 51: 21–41

    Article  Google Scholar 

  11. 11

    Negenborn R R, Maestre J M. Distributed model predictive control: an overview and roadmap of future research opportunities. IEEE Contr Syst Mag, 2014, 34: 87–97

    Article  MathSciNet  Google Scholar 

  12. 12

    Egerstedt M, Martini S, Cao M, et al. Interacting with networks: how does structure relate to controllability in single-leader, consensus networks? IEEE Contr Syst Mag, 2012, 32: 66–73

    Article  MathSciNet  Google Scholar 

  13. 13

    Chen G R. Problems and challenges in control theory under complex dynamical network environments. Acta Automat Sin, 2013, 39: 312–321

    Article  Google Scholar 

  14. 14

    Yuan Z Z, Zhao C, Di Z R, et al. Exact controllability of complex networks. Nat Commun, 2013, 4: 2447

    Google Scholar 

  15. 15

    Wang L, Jiang F C, Xie G M, et al. Controllability of multi-agent systems based on agreement protocols. Sci China Ser F-Inf Sci, 2009, 52: 2074–2088

    Article  MATH  MathSciNet  Google Scholar 

  16. 16

    Chen H W, Liang J L, Wang Z D. Pinning controllability of autonomous Boolean control networks. Sci China Inf Sci, 2016, 59: 070107

    Article  Google Scholar 

  17. 17

    Blanchini F, Franco E, Giordano G, et al. Compartmental flow control: decentralization, robustness and optimality. Automatica, 2016, 64: 18–28

    Article  MATH  MathSciNet  Google Scholar 

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This work was supported by National Nature Science Foundation of China (Grant Nos. 61233004, 61590924, 61473184).

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Correspondence to Shaoyuan Li.

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Mu, J., Li, S. & Wu, J. On the structural controllability of distributed systems with local structure changes. Sci. China Inf. Sci. 61, 052201 (2018). https://doi.org/10.1007/s11432-017-9166-0

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  • structural controllability
  • distributed systems
  • subsystems
  • structure changes
  • graph theory