An Algebraic Approach to Hierarchical Optimal Control of Large-scale Dynamical Systems

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  • TSUBAKINO Daisuke
    Graduate School of Information Science and Technology, Hokkaido University
  • YOSHIOKA Taiki
    Graduate School of Information Science and Technology, The University of Tokyo
  • HARA Shinji
    Graduate School of Information Science and Technology, The University of Tokyo

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  • 代数的特徴付けに基づく大規模動的システムの階層化最適制御
  • ダイスウテキ トクチョウズケ ニ モトズク ダイキボ ドウテキ システム ノ カイソウカ サイテキ セイギョ

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Abstract

Large-scale dynamical systems often consist of a number of subsystems that are interconnected according to a hierarchical multi-scale network. This paper introduces a hierarchical control scheme as an efficient strategy to handle such systems and proposes a method for designing a hierarchical linear quadratic optimal regulator. The proposed framework employs an algebraic approach. We first characterize a hierarchy of systems as an algebra based on semigroups, the Kronecker product, and the linear combination. This allows us to prove that the stabilizing solution of the Riccati equation inherits a hierarchy if system matrices and weights in the cost function belong to the corresponding common algebra that characterizes the hierarchy. A couple of classes of systems that can be treated by our algebraic framework are also provided in the paper. We will see that the derived result gives a unified insight into several related previous works.

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