The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solution of the nonlinear discrete problem and characterize it through first order optimality conditions. Furthermore, we systematically develop a priori as well as a posteriori error estimates. Our proposed method can be applied to a wide range of constrained optimal control problems subject to, e.g., scalar second-order PDEs and the Stokes equations. Numerical experiments that illustrate our theoretical findings are presented.

翻译：本文研究具有最优检验函数的DPG方法求解带控制约束的线性二次最优控制问题。我们证明了该非线性离散问题存在唯一最优解，并通过一阶最优性条件对其进行刻画。此外，我们系统地发展了先验误差估计和后验误差估计。所提出的方法可广泛应用于受标量二阶偏微分方程及Stokes方程等约束的各类约束最优控制问题。文中给出了验证理论结果的数值实验。