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Decentralized control for linear systems with multiple input channels


In this paper, we consider the decentralized optimal control problem for linear discrete-time systems with multiple input channels. First, under centralized control, the optimal feedback gains are given in terms of two algebraic Riccati equations. A reduced order observer is then designed using only the local input and output information. By selecting an appropriate initial value for the observer, we derive an observer-based decentralized optimal controller where the feedback gain is the same as that obtained in the centralized optimal control problem. Last but not least, we study the optimal control problem of non-homogeneous multi-agent systems as an application. A suboptimal decentralized controller is obtained and the difference between the suboptimal cost and the optimal one is given.

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  1. 1

    Bellman R. Large systems. IEEE Trans Autom Control, 1974, 19: 464–465

  2. 2

    Lavaei J, Aghdam A G. Overlapping control design for multi-channel systems. Automatica, 2009, 45: 1326–1331

  3. 3

    Lamperski A, Lessard L. Optimal decentralized state-feedback control with sparsity and delays. Automatica, 2015, 58: 143–151

  4. 4

    Lessard L. A separation principle for decentralized state-feedback optimal control. In: Proceedings of the 51st Annual Allerton Conference, Illinois, 2013. 528–534

  5. 5

    Nishio Y, Murata Y, Yamaya Y, et al. Optimal calibration scheme for map-based control of diesel engines. Sci China Inf Sci, 2018, 61: 070205

  6. 6

    Mukaidani H, Xu H, Dragan V. Decentralized H2 control for multi-channel stochastic systems. IEEE Trans Autom Control, 2015, 60: 1080–1086

  7. 7

    Li T, Zhang J F. Asymptotically optimal decentralized control for large population stochastic multiagent systems. IEEE Trans Autom Control, 2008, 53: 1643–1660

  8. 8

    Pindyck R. Optimal economic stabilization policies under decentralized control and conflicting objectives. IEEE Trans Autom Control, 1977, 22: 517–530

  9. 9

    Bakule L. Decentralized control: an overview. Annu Rev Control, 2008, 32: 87–98

  10. 10

    Sandell N, Varaiya P, Athans M, et al. Survey of decentralized control methods for large scale systems. IEEE Trans Autom Control, 1978, 23: 108–128

  11. 11

    Wang S H, Davison E. On the stabilization of decentralized control systems. IEEE Trans Autom Control, 1973, 18: 473–478

  12. 12

    Wang Z J, Li H J, Xu Z. Real-world traffic analysis and joint caching and scheduling for in-RAN caching networks. Sci China Inf Sci, 2017, 60: 062302

  13. 13

    Xu D B, Ugrinovskii V. Decentralized measurement feedback stabilization of large-scale systems via control vector Lyapunov functions. Syst Control Lett, 2013, 62: 1187–1195

  14. 14

    You K Y, Xie L H. Coordination of discrete-time multi-agent systems via relative output feedback. Int J Robust Nonlinear Control, 2011, 21: 1587–1605

  15. 15

    Zhai G, Ikeda M, Fujisaki Y. Decentralized H8 controller design: a matrix inequality approach using a homotopy method. Automatica, 2001, 37: 565–572

  16. 16

    Ha Q P, Trinh H. Observer-based control of multi-agent systems under decentralized information structure. Int J Syst Sci, 2004, 35: 719–728

  17. 17

    Elmahdi A, Taha A F, Sun D. Observer-based decentralized control scheme for stability analysis of networked systems. In: Proceedings of the 11th IEEE International Conference on Control and Automation, Taiwan, 2014. 857–862

  18. 18

    Shu S L, Lin F. Decentralized control of networked discrete event systems with communication delays. Automatica, 2015, 50: 2108–2112

  19. 19

    Zhang F F, Wang W, Zhang H S. The design of distributed suboptimal controller for multi-agent systems. Int J Robust Nonlinear Control, 2015, 25: 2829–2842

  20. 20

    Cao Y C, Ren W. Optimal linear-consensus algorithms: an LQR perspective. IEEE Trans Syst Man Cybern B, 2010, 40: 819–830

  21. 21

    Rotkowitz M, Lall S. A characterization of convex problems in decentralized control. IEEE Trans Autom Control, 2006, 51: 274–286

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This work was supported by National Natural Science Foundation of China (Grant Nos. 61403235, 61573221, 61633014, 61873332) and Qilu Youth Scholar Discipline Construction Funding from Shandong University.

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Correspondence to Juanjuan Xu.

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Xu, J., Xu, L., Xie, L. et al. Decentralized control for linear systems with multiple input channels. Sci. China Inf. Sci. 62, 52202 (2019).

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  • decentralized control
  • reduced order observer
  • multiple channels
  • algebraic Riccati equation