The exact slow-fast decomposition of the algebraic Ricatti equation of singularly perturbed systems

Author

Su, Wu Chung ; Gajic, Zoran ; Shen, Xue Min

Author_Institution

Dept. of Electr. & Comput. Eng., Rutgers Univ., Piscataway, NJ, USA

Volume

37

Issue

9

fYear

1992

fDate

9/1/1992 12:00:00 AM

Firstpage

1456

Lastpage

1459

Abstract

The algebraic Riccati equation for singularly perturbed control systems is completely and exactly decomposed into two reduced-order algebraic Riccati equations corresponding to the slow and fast time scales. The pure-slow and pure-fast algebraic Riccati equations are asymmetric ones, but their O(ε) perturbations are symmetric. It is shown that the Newton method is very efficient for solving the obtained asymmetric algebraic Riccati equations. The method presented is very suitable for parallel computations. Due to the complete and exact decomposition of the Riccati equation, this procedure might produce new insight into the two-time-scale optimal filtering and control problems

Keywords

algebra; approximation theory; control systems; Newton method; algebraic Ricatti equation; asymmetric equations; exact slow-fast decomposition; fast time scale; singularly perturbed systems; slow time scale; two-time-scale optimal filtering; Concurrent computing; Control systems; Filtering; Newton method; Optimal control; Radio access networks; Riccati equations; Tin;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.159592

Filename

159592