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DOI: 10.23952/cot.2023.12
Received September 13, 2022; Accepted November 29, 2022; Published March 16, 2023
Abstract. Let be Borel. We consider the problem (
) of minimizing an integral functional
of the form
in the set of admissible pairs
such that
and satisfy the following linear controlled dynamics, state and control constraints:
We prove that if is radially convex on the control variable, locally Lipschitz in the time variable and a mild boundedness assumption (satisfied if
is locally bounded where it is finite), then there is a minimizing sequence of admissible pairs with bounded controls. In the calculus of variations (
) this corresponds to the non-occurrence of the Lavrentiev phenomenon for the problem with an initial constraint.
How to Cite this Article:
C. Mariconda, Non-occurrence of the Lavrentiev gap for a Bolza type optimal control problem with state constraints and no end cost, Commun. Optim. Theory 2023 (2023) 12.