In this article, for a given class of multi-dimensional scalar variational control problems (named $urn:x-wiley:rnc:media:rnc5767:rnc5767-math-0001$ ) with mixed constraints implying second-order partial differential equations and inequations, we introduce an auxiliary (modified) class of variational control problems (named $urn:x-wiley:rnc:media:rnc5767:rnc5767-math-0002$ ), which is much easier to study, and provide some characterization results of $urn:x-wiley:rnc:media:rnc5767:rnc5767-math-0003$ and $urn:x-wiley:rnc:media:rnc5767:rnc5767-math-0004$ by using the notions of normal weak robust optimal solution and robust saddle-point associated with a Lagrange functional corresponding to $urn:x-wiley:rnc:media:rnc5767:rnc5767-math-0005$ . For this aim, we consider scalar multiple integral cost functionals and the notion of convexity associated with a multiple integral functional driven by an uncertain multi-time controlled second-order Lagrangian.

CONFLICT OF INTEREST

The author declared no conflict of interest to this work.

Open Research

DATA AVAILABILITY STATEMENT

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

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