A structure-preserving Lanczos-type algorithm with application to control problems

Author

Ferng, William R. ; Lin, Wen-Wei ; Wang, Chern-Shuh

Author_Institution

Dept. of Appl. Math., Nat. Chiao Tung Univ., Hsinchu, Taiwan

Volume

4

fYear

1997

fDate

10-12 Dec 1997

Firstpage

3855

Abstract

A Hamiltonian structure-preserving Lanczos-type method, named the J-Lanczos algorithm, is introduced for solving large sparse Hamiltonian eigenvalues problem which arises in both continuous-time and discrete-time optimal control applications. Shift and invert techniques are incorporated to approximate all stable eigenvalues and the associated invariant subspace. Numerical results for solving high order continuous-time Riccati equation arising from position and velocity control for a string of high speed vehicles are presented

Keywords

Riccati equations; continuous time systems; discrete time systems; eigenvalues and eigenfunctions; invariance; inverse problems; matrix algebra; optimal control; Hamiltonian matrix; J-Lanczos algorithm; Lanczos method; Riccati equation; continuous-time systems; discrete-time systems; eigenvalues; invariant subspace; optimal control; structure-preserving; Control theory; Cost function; Eigenvalues and eigenfunctions; Feedback; Kernel; Mathematics; Optimal control; Riccati equations; Sparse matrices; Strontium;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1997., Proceedings of the 36th IEEE Conference on

Conference_Location

San Diego, CA

ISSN

0191-2216

Print_ISBN

0-7803-4187-2

Type

conf

DOI

10.1109/CDC.1997.652463

Filename

652463