This paper addresses the optimal control problems with an interval-valued objective function. We consider a type of total order relationships \(\le _{adm}\) between two intervals. For each total order relationship, Kuhn–Tucker sufficient conditions for the optimal control problems with an interval-valued objective function are obtained. A numerical example is considered and solved. Kuhn–Tucker sufficient conditions provided under the total order relationship \(\le _{adm}\) are sufficient conditions under the partial order relationship \(\preceq _{LU}\) for interval-valued optimal control problems. The results of this paper could help construct evolutionary algorithms to solve interval-valued optimal control problems.
