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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.