Boundary Control of Boundary Coupled Parabolic Distributed Parameter Systems based on Partial State Transformation

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  • Tsubakino Daisuke
    Graduate School of Information Science and Technology, Hokkaido University
  • Nomura Kazuya
    Graduate School of Information Science and Technology, Hokkaido University
  • Yamashita Yuh
    Graduate School of Information Science and Technology, Hokkaido University

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  • 部分変換を用いた境界結合放物型分布定数系の境界制御
  • ブブン ヘンカン オ モチイタ キョウカイ ケツゴウ ホウブツガタ ブンプ テイスウケイ ノ キョウカイ セイギョ

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Abstract

This paper considers a boundary stabilization problem of systems described by boundary coupled two one-dimensional parabolic partial differential equations based on the backstepping method. Unlike the conventional backstepping framework, we propose a state transformation that contains the state of the unforced subsystem partially. It is proved that this transformation is well-defined and converts the original system into an exponentially stable system together with an associated state feedback control law under a condition that ensures the stability of the unforced subsystem. The original system with this control law inherits the stability of the transfomed one. The effectiveness of the obtained control law is demonstrated numerically.<br>

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