Generalized dilations and numerically solving discrete-time homogeneous optimization problems

Author

Tuna, S. Emre ; Teel, Andrew R.

Author_Institution

Dept. of Electr. & Comput. Eng., California Univ., Santa Barbara, CA, USA

Volume

5

fYear

2004

fDate

14-17 Dec. 2004

Firstpage

5403

Abstract

We introduce generalized dilations, a broader class of operators than that of dilations, and consider homogeneity with respect to this new class of dilations. For discrete-time systems that are asymptotically controllable and homogeneous (with degree zero) we propose a method to numerically approximate any homogeneous value function (solution to an infinite horizon optimization problem) to arbitrary accuracy. We also show that the method can be used to generate an offline computed stabilizing feedback law.

Keywords

approximation theory; asymptotic stability; discrete time systems; feedback; optimisation; asymptotically controllable systems; discrete-time homogeneous optimization problems; discrete-time systems; generalized dilations; homogeneous value function; infinite horizon optimization problem; numerical approximation; offline computed stabilizing feedback law; Control engineering; Control engineering computing; Control systems; Cost function; Feedback; Infinite horizon; Lyapunov method; Optimal control; Optimization methods; Table lookup;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2004. CDC. 43rd IEEE Conference on

ISSN

0191-2216

Print_ISBN

0-7803-8682-5

Type

conf

DOI

10.1109/CDC.2004.1429667

Filename

1429667