论文标题
代数riccati方程的近似，具有非脉动半群的发生器
Approximation of Algebraic Riccati Equations with Generators of Noncompact Semigroups
论文作者
论文摘要
在这项工作中，我们证明了代数riccati方程（AS）的BOCHNER积分表示，并且对系数和半群操作员没有任何紧凑的假设。从此结果，我们可以确定，在某些假设下，盖金素近似值的解决方案是收敛到无限尺寸溶液的。再进一步，我们应用了这一总体结果，以证明对$ h^1（ω）\ times l^2（ω）$ norm的有限元近似值是最佳的。在数值示例中证明了功能增益的最佳功能增益，在$ H^1（ω）\ times l^2（ω）$和$ l^2（ω）\ times l^2（ω）$规范中的功能增益的最佳收敛速率均在数值示例中证明。
In this work, we demonstrate that the Bochner integral representation of the Algebraic Riccati Equations (ARE) are well-posed without any compactness assumptions on the coefficient and semigroup operators. From this result, we then are able to determine that, under some assumptions, the solution to the Galerkin approximations to these equations are convergent to the infinite dimensional solution. Going further, we apply this general result to demonstrate that the finite element approximation to the ARE are optimal for weakly damped wave semigroup processes in the $H^1(Ω) \times L^2(Ω)$ norm. Optimal convergence rates of the functional gain for a weakly damped wave optimal control system in both the $H^1(Ω) \times L^2(Ω)$ and $L^2(Ω)\times L^2(Ω)$ norms are demonstrated in the numerical examples.
