Analytic regularity and GPC approximation for control problems constrained by linear parametric elliptic and parabolic PDEs (Q2848594)

The paper is about optimal control problems of uncertain systems governed by linear parametric or stochastic PDEs. The authors present a convergent and efficient adaptive algorithm for solving linear-quadratic optimal control problems constrained by elliptic or parabolic PDEs with stochastic or possibly infinitely many countable parametric coefficients and with distributed and boundary controls. They prove analytic parameter dependence of the state, the adjoint. They also develop sparsity of generalized polynomial chaos expansions for state and control, and give convergence rates of best \(N\)-term truncations of these expansions.