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- Title
On Balder’s Existence Theorem for Infinite-Horizon Optimal Control Problems.
- Authors
Besov, K. O.
- Abstract
Balder’s well-known existence theorem (1983) for infinite-horizon optimal control problems is extended to the case in which the integral functional is understood as an improper integral. Simultaneously, the condition of strong uniform integrability (over all admissible controls and trajectories) of the positive part max{<italic>f</italic>0, 0} of the utility function (integrand) <italic>f</italic>0 is relaxed to the requirement that the integrals of <italic>f</italic>0 over intervals [<italic>T</italic>, <italic>T</italic>′] be uniformly bounded above by a function <italic>ω</italic>(<italic>T</italic>, <italic>T</italic>′) such that <italic>ω</italic>(<italic>T</italic>, <italic>T</italic>′) → 0 as <italic>T</italic>, <italic>T</italic>′→∞. This requirement was proposed by A.V. Dmitruk and N.V. Kuz’kina (2005); however, the proof in the present paper does not follow their scheme, but is instead derived in a rather simple way from the auxiliary results of Balder himself. An illustrative example is also given.
- Subjects
OPTIMAL control theory; EXISTENCE theorems; TRAJECTORIES (Mechanics); MATHEMATICAL functions; IMPROPER integrals
- Publication
Mathematical Notes, 2018, Vol 103, Issue 1/2, p167
- ISSN
0001-4346
- Publication type
Article
- DOI
10.1134/S0001434618010182