Reduced basis approximation of large scale parametric algebraic Riccati equations
Reduced basis approximation of large scale parametric algebraic Riccati equations
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大规模参数代数 Riccati 方程的简化基近似
DOI：
10.1051/cocv/2017011
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
B. Haasdonk
中科院分区：
文献类型：
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作者：
A. Schmidt;B. Haasdonk
代数 Riccati 方程 (ARE) 是一个矩阵值二次方程，在控制理论领域具有许多重要应用，例如反馈控制、状态估计或 ℋ ∞ 鲁棒控制。然而，在半离散偏微分方程的应用中，求解 ARE 的成本可能会非常高。参数相关系统和快速获得变化参数的解决方案的愿望引入了更高水平的计算复杂性。因此，我们建议通过利用解矩阵的众所周知的低秩结构，将缩减基（RB）方法应用于参数化 ARE。我们讨论了基础生成过程，并通过推导严格的后验误差界限来分析引起的误差。我们研究了整个过程的计算复杂性，并给出了数值示例，证明了该方法在线性二次（LQ）控制背景下的效率。
The algebraic Riccati equation (ARE) is a matrix valued quadratic equation with many important applications in the field of control theory, such as feedback control, state estimation or ℋ ∞ -robust control. However, solving the ARE can get very expensive in applications that arise from semi-discretized partial differential equations. A further level of computational complexity is introduced by parameter dependent systems and the wish to obtain solutions rapidly for varying parameters. We thus propose the application of the reduced basis (RB) methodology to the parametric ARE by exploiting the well known low-rank structure of the solution matrices. We discuss a basis generation procedure and analyze the induced error by deriving a rigorous a posteriori error bound. We study the computational complexity of the whole procedure and give numerical examples that prove the efficiency of the approach in the context of linear quadratic (LQ) control.
使用降阶基法求解参数相关的 Lyapunov 方程并应用于参数模型降阶
DOI：
10.1137/15m1027097
发表时间：
2017
期刊：
SIAM J. Matrix Anal. Appl.
影响因子：
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作者：
N.T. Son;T. Stykel
通讯作者：
T. Stykel