On Some Characterization Theorems for New Classes of Multiple-Objective Control Models

This paper introduces a new class of multiple-objective control models driven by path-independent curvilinear integrals involving the partial derivatives of the control variable. We investigate its solution set by considering a dual problem. Various duality results are formulated and proved in order to study and investigate the relationships between the set of solutions for these two variational control problems. Specifically, first, we establish that the value of the cost functional associated with the primal model cannot be greater than the value of the cost functional associated with the dual model. Secondly, the following two results present a strong-type duality between the variational models considered. At the end, we illustrate the main findings of the current paper with a numerical example.