Saddle point criteria for robust isoperimetric constrained variational control problems
摘要
In this paper, we investigate a class of isoperimetric constrained variational control problems with data uncertainty and the robust approach is applied for solving such control problems. We construct the uncertain Lagrange functional, by changing the isoperimetric constraints into the system of ODE constraints and then the robust optimality conditions are analyzed for the considered variational control problem involving data uncertainty. Further, we define a robust saddle point for the associated uncertain Lagrange functional and show that it provides a variational characterization of the robust optimal solution. This characterization not only offers a deeper theoretical insight but also facilitates the verification of optimality under uncertainty. In addition, numerical applications are provided to illustrate the applicability of the proposed methodology and to demonstrate the effectiveness and robustness of the derived optimal solutions.