Robust saddle-point criteria for multi-dimensional control optimisation problems with data uncertainty

Abstract

This paper deals with some new outcomes on the multi-dimensional control optimisation problem with data uncertainty (UMCOP). By employing the exact penalty function method, we formulate an equivalent unconstrained control optimisation problem and obtain the robust saddle-point criteria for (UMCOP). After that, we show the equivalences between the robust saddle-point of the considered control problem (UMCOP) and a robust minimiser of its associated penalised unconstrained control optimisation problem (UMCOP). We also provide some numerical illustrations to verify the developed results in this paper.