Inheritance properties of Krylov subspace methods for continuous-time algebraic Riccati equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:371

Article

Zhang, Liping¹  Fan, Hung-Yuan²  Chu, Eric King-wah³ 

[1] Zhejiang Univ Technol, Dept Math, Hangzhou 310023, Peoples R China

[2] Natl Taiwan Normal Univ, Dept Math, Taipei 116, Taiwan

[3] Monash Univ, Sch Math, 9 Rainforest Walk, Clayton, Vic 3800, Australia

关键词: Continuous-time algebraic Riccati equation;    Krylov subspace;    LQR optimal control;    Projection method;   

DOI  :  10.1016/j.cam.2019.112685

来源: Elsevier

【 摘 要 】

We investigate the theory behind the Krylov subspace methods for large-scale continuous-time algebraic Riccati equations. We show that the solvability of the projected algebraic Riccati equation need not be assumed but can be inherited. This study of inheritance properties is the first of its kind. We study the stabilizability and detectability of the control system, the stability of the associated Hamiltonian matrix and perturbation in terms of residuals. Special attention is paid to the stabilizing and positive semi-definite properties of approximate solutions. Illustrative numerical examples for the inheritance properties are presented. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

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