An algorithm using the HR process for solving the closed-loopeigenvalues of a discrete-time algebraic Riccati equation

Lin-Zhang Lu; Xingzhi Ji; Hong Jiang

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An algorithm using the HR process for solving the closed-loopeigenvalues of a discrete-time algebraic Riccati equation

机译：使用HR过程求解离散时间代数Riccati方程的闭环特征值的算法

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摘要

Presents a numerical approach to the closed-loop spectrum of a discrete-time algebraic Riccati equation. The concerned symplectic pencil N-λL is proven to be equivalent to the pencil P-λQ, where P is skew-symmetric and Q is symmetric. Then the HR process, which can be viewed as a generalization of the QR method, is applied to compute the eigenvalue of P-λQ. Some numerical examples are included

机译：为离散时间代数Riccati方程的闭环谱提供了一种数值方法。证明所涉及的辛铅笔N-λL与铅笔P-λQ等效，其中P是斜对称的，而Q是对称的。然后，可以将HR过程（可以看作是QR方法的概括）应用于计算P-λQ的特征值。包括一些数值示例

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来源
《IEEE Transactions on Automatic Control》 |1994年第8期|p.1682-1685|共4页
作者
Lin-Zhang Lu; Xingzhi Ji; Hong Jiang;
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正文语种 eng
中图分类自动化系统;
关键词
difference equations; eigenvalues and eigenfunctions; matrix algebra; nonlinear differential equations; optimal control; HR process; QR method; closed-loop eigenvalues; closed-loop spectrum; discrete-time algebraic Riccati equation; numerical approach; symplectic p;

机译：差分方程;特征值和特征函数;矩阵代数;非线性微分方程;最优控制;HR过程;QR方法;闭环特征值;闭环谱;离散代数Riccati方程;数值逼近;渐近p;

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专利

1. An algorithm using the HR process for solving the closed-loop eigenvalues of a discrete-time algebraic Riccati equation [J] . Lin-Zhang Lu, Xingzhi Ji IEEE Transactions on Automatic Control . 1994,第8期

机译：使用HR过程求解离散时间代数Riccati方程的闭环特征值的算法
2. Structure-preserving algorithms for periodic discrete-time algebraic Riccati equations [J] . Chu EKW, Fan HY, Lin WW, International Journal of Control . 2004,第8期

机译：周期离散时间代数Riccati方程的保结构算法
3. An accelerated technique for solving one type of discrete-time algebraic Riccati equations [J] . Lin Matthew M., Chiang Chun-Yueh Journal of Computational and Applied Mathematics . 2018,第期

机译：一种求解一种离散时间代数Riccati方程的加速技术
4. Solving Large-scale Discrete-time Algebraic Riccati Equations by Doubling [C] . Xing-Long Lyu, Tiexiang Li, Eric King-wah Chu Chinese Control and Decision Conference . 2020

机译：通过加倍求解大规模离散时间代数Riccati方程
5. ALGORITHMS AND SOFTWARE FOR SOLVING COUPLED DISCRETE-TIME RICCATI EQUATIONS VIA THE L-A-S LANGUAGE (COMPUTER-AIDED DESIGN, CONTROL, GAME THEORY). [D] . WEST, PHILLIP JAMES. 1986

机译：通过L-A-S语言（计算机辅助设计，控制，游戏理论）解决离散离散RICCATI方程的算法和软件。
6. RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations [O] . Peter Benner, Zvonimir Bujanović, Patrick Kürschner, -1

机译：RADI：低阶ADI型算法用于大规模代数Riccati方程
7. An accelerated technique for solving one type of discrete-time algebraic Riccati equations [O] . Lin, Matthew M., Chiang, Chun-Yueh 2017

机译：一种求解一类离散时间代数的加速技术 Riccati方程
8. Algorithms and Software for Solving Coupled Discrete-Time Riccati Equations Via the L-A-S Language [R] . West, P. J. 1986

机译：用L-a-s语言求解耦合离散Riccati方程的算法和软件

An algorithm using the HR process for solving the closed-loopeigenvalues of a discrete-time algebraic Riccati equation

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