# 梁振動の方程式のGevrey classによるべき級数を用いた解による制御方法ハリシンドウ ノ ホウテイシキ ノ Gevrey class ニヨル ベキキュウスウ オ モチイタ カイ ニヨル セイギョ ホウホウハリシンドウ ノ ホウテイシキ ノ ジェブレイ クラス ニヨル ベキキュウスウ オ モチイタ カイ ニヨル セイギョ ホウホウA control method of the plate equation by power series of Gevrey class

58 ( 4 )  , pp.216 - 223 , 2018-01-31 , 同志社大学ハリス理化学研究所 , Transcription:ドウシシャ ダイガク ハリス リカガク ケンキュウジョ , Alternative:Harris Science Research Institute of Doshisha University
ISSN:21895937
NII書誌ID(NCID):AA12716107

Motion planning which is construction of an input implementing a desired output on a system is a fundamental problem on both of the theory of control and its practical applications. In many cases, a system are represented as an ordinary differential equation or a partial differential equation. Here let us deal final states of a system with outputs. Then we can consider some control problems. A typical example is the control by boundary values. Laroche-Martin-Rouchon considered an approximate motion planning as a boundary control problem on the heat equation using Gevrey class functions. In this paper, we study an approximate motion planning on the one dimensional plate equation by boundary control using Gevrey class functions. More precisely, we consider the initial-boundary problem. The output is a given final state of the plate at time T>0, and the input is the Dirichlet boundary value and the Neumann boundary value at an endpoint of the plate. We construct this input using finitely truncated Gevrey functions so that the associated solution of the plate equation approximates the desired final state. Our main result is Theorem 6.

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