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arXiv · 2308.09169

A DPG method for linear quadratic optimal control problems

Thomas Führer·Francisco Fuica
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Abstract

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.

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Thomas Führer, Francisco Fuica. 2023-08-17. A DPG method for linear quadratic optimal control problems. https://arxiv.org/abs/2308.09169

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