Predictors for linear parabolic systems with input delay
Predictors for linear parabolic systems with input delay
复制标题
具有输入延迟的线性抛物线系统的预测器
DOI：
10.1007/s13160-017-0286-4
复制
发表时间：
2018
影响因子：
0.9
通讯作者：
H. Sano and S. Morimoto
中科院分区：
文献类型：
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作者：
L. Loveridge;P. Busch;T. Miyadera;H. Sano and S. Morimoto
本文研究具有输入时滞的一维抛物型系统的镇定问题。特别是，我们考虑了“分布式控制”的情况。目的是利用反推方法和半群理论相结合的方法，在抽象空间中导出预估型镇定控制器。半群理论的应用使得逆变换连续性的证明变得容易。并证明了抽象控制器可以用有限个系统算子的特征值和特征函数来实现。最后，给出了一个数值模拟结果来验证我们的设计方法。
In this paper, we study the problem of stabilizing one-dimensional parabolic systems with input delay. Especially, we consider the case of “distributed control”. The purpose is to derive the stabilizing controller of predictor type in an abstract space, by using a backstepping method combined with the semigroup theory. The use of the semigroup theory makes the proof of continuity of the inverse transformation easy. Also, it is shown that the abstract controller can be actually implemented by using a finite number of eigenvalues and eigenfunctions of the system operator. Finally, a numerical simulation result is presented to demonstrate our design method.