Year: 2017
Type: preprint
Abstract: Balder's well-known existence theorem (1983) for infinite-horizon optimal control problems is extended to the case when 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 $\max\{f_0,0\}$ of the utility function (integrand) $f_0$ is relaxed to the requirement that the integrals of $f_0$ over intervals $[T,T']$ be uniformly bounded from above by a function $ω(T,T')$ such that $ω(T,T')\to 0$ as $T,T'\to\infty$. 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.
Source: arXiv (Cornell University)
Author: Besov, K. O.
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Russian Science Foundation
Awards: G4065927754, G7131804313
OpenAlex ID: W2611284470