Isoperimetric-type constrained variational control problem with uncertainty: robust optimality and duality

In this paper, we introduce a new class of variational control problem (VCP) with isoperimetric-type constraints involving uncertainty and study to find its optimal solution. For this, we construct a robust variational control problem with isoperimetric-type constraints associated with the problem (VCP) and derive the robust necessary optimality conditions using the Lagrange functional. We prove its sufficiency by imposing the convexity assumption over-involved functionals. We also construct the Wolfe type dual and its robust counterpart associated with the problem (VCP) to prove robust weak, strong and converse duality results. Further, an illustrative algorithm is given, and the theoretical results are accompanied by applications to determine their utility.