Linear programming solutions of periodic optimization problems: approximation of the optimal control

Luke Finlay; Vladimir Gaitsgory; Ivan Lebedev

doi:10.3934/jimo.2007.3.399

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2007, Volume 3, Issue 2: 399-413. Doi: 10.3934/jimo.2007.3.399

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Linear programming solutions of periodic optimization problems: approximation of the optimal control

1.
Centre for Industrial and Applicable Mathematics, University of South Australia, Mawson Lakes, SA 5095
2.
WorkCover Corporation of South Australia, 100 Waymouth St., Adelaide SA 5000

Received: October 2006

Revised: January 2007

Published: April 2007

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Abstract

Deterministic long run average problems of optimal control are ''asymptotically equivalent" to infinite-dimensional linear programming problems ( LPP ) and the latter are approximated by finite dimensional LPP. The solutions of this finite dimensional LPP can be used for numerical analysis of periodic optimization problems. In the present paper we establish the convergence of controls constructed on the basis of the solution of the finite dimensional LPP to the optimal control of a periodic optimization problem. Results are illustrated with a numerical example.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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