Abstract
In this paper, we extend Carathéodory's concept of equivalent variational problems to infinite-horizon optimal control problems. In such a setting, the usual concept of a minimum need not exist, and we therefore consider a weaker definition of optimality, known as catching up optimality. The extension presented here leads us to a Hamilton-Jacobi theory for infinite-horizon optimal control problems that closely parallels the classical work of Carathéodory as well as providing sufficient conditions for optimality. Finally, we show that the results given here subsume several previously known results as a special case.
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Communicated by L. Cesari
This research forms part of the author's doctoral dissertation, written at the University of Delaware, Newark, Delaware, under the supervision of Professor T. S. Angell.
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Carlson, D.A. A Carathéodory-Hamilton-Jacobi theory for infinite-horizon optimal control problems. J Optim Theory Appl 48, 265–287 (1986). https://doi.org/10.1007/BF00940673
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DOI: https://doi.org/10.1007/BF00940673