On transversality condition for overtaking optimality in infinite horizon control problem
Abstract
In this paper we investigate necessary conditions of optimality for infinite-horizon optimal control problems with overtaking optimality as an optimality criterion. For the case of local Lipschitz continuity of the payoff function, we construct a boundary condition on the co-state arc that is necessary for the optimality. We also show that, under additional assumptions on the payoff function's asymptotic behavior, the Pontryagin Maximum Principle with this condition becomes a complete system of relations, and this boundary condition points out the unique co-state arc through a Cauchy-type formula. An example is given to clarify the application of this formula as an explicit expression of the co-state arc. The cornerstone of this paper is the theorem on convergence of subdifferentials.
Cite
@article{arxiv.1704.03053,
title = {On transversality condition for overtaking optimality in infinite horizon control problem},
author = {Dmitry Khlopin},
journal= {arXiv preprint arXiv:1704.03053},
year = {2017}
}