A class of multiobjective control problems

We introduce the class of MP-pseudoinvex multiobjective optimal control problems. We show that the concept of MP-pseudoinvexity is a sufficient condition of optimality and, further, that problems such that every control process satisfying Pontryagin's maximum principle is an optimal process are necessarily MP-pscudoinvex problems. Moreover, a sub-class of the MP-pseudoinvex problems, which we call MP-invex multiobjective optimal control problems, is defined. We prove that the set of optimal solutions of MP-invex multiobjective problems coincides with the set of optimal solutions of a related scalar problem.