Use of approximations of Hamilton-Jacobi-Bellman inequality for solving periodic optimization problems

Vladimir Gaitsgory*, Ludmila Manic

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

1 Citation (Scopus)

Abstract

We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max–min type variational problem considered on the space of continuously differentiable functions. We approximate the latter with a maximin problem on a finite dimensional subspace of the space of continuously differentiable functions and show that a solution of this problem (existing under natural controllability conditions) can be used for construction of near optimal controls. We illustrate the construction with a numerical example.

Original languageEnglish
Title of host publicationOptimization and Control Techniques and Applications
EditorsHonglei Xu, Kok Lay Teo, Yi Zhang
Place of PublicationNew York
PublisherSpringer, Springer Nature
Pages91-114
Number of pages24
Volume86
ISBN (Electronic)9783662434031
DOIs
Publication statusPublished - 2014
Externally publishedYes
EventInternational Conference on Optimization and Control with Applications (OCA5) (5th : 2012) - Beijing, China
Duration: 4 Dec 20128 Dec 2012

Conference

ConferenceInternational Conference on Optimization and Control with Applications (OCA5) (5th : 2012)
CountryChina
CityBeijing
Period4/12/128/12/12

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