A Theory of the Infinite Horizon LQ-Problem for Composite Systems of PDEs with Boundary Control
A Theory of the Infinite Horizon LQ-Problem for Composite Systems of PDEs with Boundary Control
复制标题
具有边界控制的偏微分复合系统无限视界LQ问题理论
DOI：
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发表时间：
2012
影响因子：
2
通讯作者：
I. Lasiecka
中科院分区：
文献类型：
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作者：
P. Acquistapace;F. Bucci;I. Lasiecka
我们研究无限水平线性二次 (LQ) 问题以及具有无界控制作用的系统的相关代数 Riccati 方程。算子理论背景是由具有边界或点控制的偏微分方程 (PDE) 复合系统驱动的。特别关注的是具有整体“主要”双曲特征的耦合双曲/抛物线偏微分方程系统，例如一些热弹性或流体-结构相互作用模型。虽然无界控制行为导致 Riccati 方程具有无界（算子）系数，但与抛物线情况不同，由于复合动力学的解缺乏足够的规律性，这些方程的可解性成为一个主要问题。在目前的情况下，即使是更一般的理论，呼吁对核显示的奇异性进行估计，这种奇异性出现在控制系统解的积分表示中，也失败了。一种新颖的框架，体现了可能的双曲复合...
We study the infinite horizon linear-quadratic (LQ) problem and the associated algebraic Riccati equations for systems with unbounded control actions. The operator-theoretic context is motivated by composite systems of partial differential equations (PDEs) with boundary or point control. Specific focus is placed on systems of coupled hyperbolic/parabolic PDE with an overall “predominant” hyperbolic character, such as, e.g., some models for thermoelastic or fluid-structure interactions. While unbounded control actions lead to Riccati equations with unbounded (operator) coefficients, unlike in the parabolic case solvability of these equations becomes a major issue, owing to the lack of sufficient regularity of the solutions to the composite dynamics. In the present case, even the more general theory appealing to estimates of the singularity displayed by the kernel which occurs in the integral representation of the solution to the control system fails. A novel framework which embodies possible hyperbolic com...