Analysis of extremum value theorems for function spaces in optimal control under numerical uncertainty

P. Osinenko, S. Streif

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

The extremum value theorem for function spaces plays the central role in optimal control. It is known that computation of optimal control actions and policies is often prone to numerical errors which may be related to computability issues. The current work addresses a version of the extremum value theorem for function spaces under explicit consideration of numerical uncertainties. It is shown that certain function spaces are bounded in a suitable sense, i.e., they admit finite approximations up to an arbitrary precision. The proof of this fact is constructive in the sense that it explicitly builds the approximating functions. Consequently, existence of approximate extremal functions is shown. Applicability of the theorem is investigated for finite-horizon optimal control, dynamic programming and adaptive dynamic programming. Some possible computability issues of the extremum value theorem in optimal control are shown on counterexamples.

Original languageEnglish
Pages (from-to)1015-1032
Number of pages18
JournalIMA Journal of Mathematical Control and Information
Volume36
Issue number3
DOIs
Publication statusPublished - 1 Sep 2019
Externally publishedYes

Keywords

  • approximate
  • dynamic programming
  • extremum
  • optimal control

Fingerprint

Dive into the research topics of 'Analysis of extremum value theorems for function spaces in optimal control under numerical uncertainty'. Together they form a unique fingerprint.

Cite this