On boundary conditions at infinity for infinite horizon control problem

摘要

In this paper we consider necessary conditions of optimality for infinite-horizon optimal control problems with overtaking optimality and with weakly overtaking optimality as optimality criterions. We propose a boundary conditions on the co-state arc that are necessary for the optimality. We also show that, under additional assumptions on the payoff function's asymptotic behavior, the Pontryagin Maximum Principle with these conditions becomes a complete system of relations, and this boundary condition points out the unique co-state arc through a Cauchy-type formula. Examples are given to clarify the application of this formula as an explicit expression of the co-state arc.