Sufficient Conditions for Optimality in Uncertain Optimal Control Problems

This work addresses the challenge of handling uncertainty in objective functions within optimal control problems by embedding an admissible order relation into the decision-making framework. Within this structure, the classical Bolza and Mayer problems are extended to interval-valued formulations using admissible ordering, thereby overcoming the limitations of traditional interval comparison methods such as the LU order. Furthermore, sufficient conditions for optimality are established, revealing a novel connection among admissible order structures, interval-valued Hamiltonian formulations, and the convexity or pseudo-convexity properties of the objective functional. Illustrative examples from management applications demonstrate how the proposed conditions enable the direct identification of admissible solutions. Moreover, given the increasing importance of advanced evolutionary algorithms, this research offers a foundation for advancing the solution of optimal control problems with interval-valued objectives.