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Distributed LQR control for discrete-time homogeneous systems

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  • Wei Wang
  • Fangfang Zhang
  • Chunyan Han

Abstract

This paper investigates the distributed linear quadratic regulation (LQR) controller design method for discrete-time homogeneous scalar systems. Based on the optimal centralised control theory, the existence condition for distributed optimal controller is firstly proposed. It shows that the globally optimal distributed controller is dependent on the structure of the penalty matrix. Such results can be used in consensus problems and used to find under which communication topology (may not be an all-to-all form) the optimal distributed controller exists. When the proposed condition cannot hold, a suboptimal design method with the aid of the decomposition of discrete algebraic Riccati equations and robustness of local controllers is proposed. The computation complexity and communication load for each subsystem are only dependent on the number of its neighbours.

Suggested Citation

  • Wei Wang & Fangfang Zhang & Chunyan Han, 2016. "Distributed LQR control for discrete-time homogeneous systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(15), pages 3678-3687, November.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:15:p:3678-3687
    DOI: 10.1080/00207721.2015.1112931
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