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Abstract An auxiliary optimal control problem is formulated that provides with its unique solution, a continuous representation of the global error of a numerical approximation to the solution of a linear quadratic optimal control problem. The resulting error functions are characterized as the unique solutions to an optimality system that is reformulated as a boundary value problem. With this formulation, reliable pointwise error estimates can be generated utilizing well-established techniques of defect control. A novel algorithm based on defect correction and defect control is presented that generates pointwise approximations to the global error of numerical optimal control solutions on a uniform grid. It is proven and numerically validated that this algorithm can generate pointwise estimates that approximate the true global error with a prescribed accuracy.
Hofmann et al. (Mon,) studied this question.