the solution of the interval optimal control problem using the lu-order relation

In this paper, the solution of the optimal control problem with an interval-valued objective functional has been considered. first, the lu-solution concept has been defined for the interval space to reach this goal. then, using hukuhara's concepts of extreme and generalized differentiability, the necessary and sufficient optimality conditions have been obtained for the interval value function under the convexity hypotheses for solving the mentioned problem. these results have been obtained considering a particular optimal control problem, according to lagrange's formulation. furthermore, two numerical examples have been developed seeking to exemplify such results.