On the usage of the Henstock-Kurzweil integral in infinite horizon optimal control problems

Abstract

In the present paper we motivate the incorporation of a more general integral notion, namely the Henstock- Kurzweil integral, in a formulation of infinite horizon optimal control problems and investigate its impact. This results from the necessity of distinguishing between different interpretations of the improper integral objective (e.g. Lebesgue, improper Riemann etc.) which was addressed in [18]. A first result concerning sufficient optimality conditions for the new class of optimal control problems is obtained. Relations between admissible sets and optimal solutions of the new control problem and the problems involving Lebesgue or improper Riemann integrals are discussed by means of an example. The applicability of sufficient optimality conditions is also shown.