On dynamic gradient systems for solving linear programs: a sliding mode analysis

Author

Chong, Edwin K P ; Hui, Stefen ; Zak, Stanislaw H.

Author_Institution

Sch. of Electr. Eng. & Comput. Eng., Purdue Univ., West Lafayette, IN, USA

Volume

3

fYear

1995

fDate

13-15 Dec 1995

Firstpage

2109

Abstract

We use sliding modes to analyze a novel class of dynamic gradient systems that solve linear programming problems. The dynamic gradient systems we consider are constructed using a parametric family of exact penalty functions. We prove that for sufficiently large penalty parameters, any trajectory of the dynamic gradient systems associated with a given linear programming problem converges in finite time to its solution set. For our analysis we develop Lyapunov type theorems for finite time convergence of nonsmooth dynamic systems to invariant sets

Keywords

Lyapunov methods; convergence; linear programming; variable structure systems; Lyapunov type theorems; dynamic gradient systems; dynamic gradient systems trajectory; exact penalty functions parametric family; finite time convergence; invariant sets; linear programming; linear programs; nonsmooth dynamic systems; penalty parameters; sliding mode analysis; Convergence; Differential equations; Dynamic programming; Failure analysis; Linear programming; Sliding mode control;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1995., Proceedings of the 34th IEEE Conference on

Conference_Location

New Orleans, LA

ISSN

0191-2216

Print_ISBN

0-7803-2685-7

Type

conf

DOI

10.1109/CDC.1995.480512

Filename

480512