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Characterizations of an approximate minimum in optimal control

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Abstract

By using the classical variational methods based on geodesic coverings of a domain and on Hilbert's independent integral, further characterizations of an approximate solution in problems of control are described. The starting point is the Ekeland-type characterization, the variational principle. As consequences, sufficient conditions for optimality are obtained in a form similar to the Weierstrass conditions from the calculus of variations.

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Authors and Affiliations

  1. Institute of Mathematics, Lódź University, Lódź, Poland

    A. Nowakowski (Associate Professor)

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  1. A. Nowakowski
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Communicated by D. Q. Mayne

The author is grateful to the referee for the valuable counterexamples to the first version of the paper.

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Nowakowski, A. Characterizations of an approximate minimum in optimal control. J Optim Theory Appl 66, 95–120 (1990). https://doi.org/10.1007/BF00940535

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