We present a version of the Pontryagin maximum principle for the general infinitehorizon optimal control problem with an additional specific asymptotic endpoint constraint under weak regularity assumptions. Such problems arise in economics when studying growth models. The proof is based on reducing the original problem to a family of finite-horizon problems for a mixed type functional containing a terminal term in the form of the conditional cost of the phase vector at a finite time. The results are illustrated by an example.
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Translated from Problemy Matematicheskogo Analiza 122, 2023, pp. 25-38.
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Aseev, S.M. The Pontryagin Maximum Principle Foroptimal Control Problem with an Asymptotic Endpoint Constraint Under Weak Regularity Assumptions. J Math Sci 270, 531–546 (2023). https://doi.org/10.1007/s10958-023-06364-7
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DOI: https://doi.org/10.1007/s10958-023-06364-7