Solving Parametrized Non-symmetric Algebraic Riccati Equations: A Matrix Sign Function Approach

Marc Jungers; Cristian Oara

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Solving Parametrized Non-symmetric Algebraic Riccati Equations: A Matrix Sign Function Approach

机译：求解参数化的非对称代数Riccati方程：矩阵符号函数法

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We study numerical solutions of parameterized non--symmetric continuous--time algebraic Riccati equations (PNAREs) related to issues in control system theory and differential games. Thanks to good regularity properties of the solutions of PNAREs with respect to the parameter, our main tool involving an analytically determined matrix sign function is applied to the computation of various solutions, including the strongly stabilizing, the reverse dichotomic and the dichotomic ones.?? The efficiency of the proposed method is illustrated by several numerical experiments.

机译：我们研究了参数化非对称连续时间代数Riccati方程（PNARE）的数值解，该方程与控制系统理论和微分对策有关。由于PNARE的解相对于参数具有良好的规律性，我们将包含解析确定的矩阵符号函数的主要工具应用于各种解的计算，包括强稳定，逆二分和二分的解决方案。几种数值实验说明了该方法的有效性。

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《Journal of Control Engineering and Applied Informatics》 |2019年第2期|共8页
作者
Marc Jungers; Cristian Oara;
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正文语种
中图分类农业科学;
关键词
Non-symmetric Algebraic Riccati EquationsMatrix Sign FunctionParametrized Solutions;

机译：非对称代数Riccati方程矩阵符号函数参数化解;

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专利

1. SOLVING ALGEBRAIC RICCATI EQUATION FOR SINGULAR SYSTEM BASED ON MATRIX SIGN FUNCTION [J] . Chih-Cheng Huang, Jason Sheng-Hong Tsai, Shu-Mei Guo, International Journal of Innovative Computing Information and Control . 2013,第7期

机译：基于矩阵符号函数的奇异系统代数RICCATI方程求解
2. The Non-symmetric Discrete Algebraic Riccati Equation and Canonical Factorization of Rational Matrix Functions on the Unit Circle [J] . Frazho AE, Kaashoek MA, Ran ACM Integral equations and operator theory . 2010,第2期

机译：单位圆上非对称离散代数Riccati方程和有理矩阵函数的典范分解
3. A modified Newton method for solving non-symmetric algebraic Riccati equations arising in transport theory [J] . Lin YQ, Bao L, Wei YM IMA Journal of Numerical Analysis . 2008,第2期

机译：求解运输理论中出现的非对称代数Riccati方程的改进牛顿法
4. A method for solving the algebraic Riccati and Lyapunov equations using higher order matrix sign function algorithms [C] . Hasan, M.A., Jiann-Shiou Yang . 1999

机译：用高阶矩阵符号函数算法求解代数Riccati和Lyapunov方程的方法
5. Three numerical methods for solving generalized algebraic Riccati equations. [D] . Qian, Qingshan. 1997

机译：求解广义代数Riccati方程的三种数值方法。
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. Solving the algebraic Riccati equation with the matrix sign function [O] . Byers Ralph 1987

机译：用矩阵符号函数求解代数Riccati方程

Solving Parametrized Non-symmetric Algebraic Riccati Equations: A Matrix Sign Function Approach

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