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.

制定了一个辅助最优控制问题，它提供了其唯一的解，即线性二次最优控制问题解的数值逼近的全局误差的连续表示。由此产生的误差函数被描述为最优系统的唯一解，该系统被重新表述为边值问题。通过这种公式，可以利用完善的缺陷控制技术生成可靠的逐点误差估计。提出了一种基于缺陷校正和缺陷控制的新算法，该算法在均匀网格上生成数值最优控制解的全局误差的逐点近似。经证明和数值验证，该算法可以生成以规定精度近似真实全局误差的逐点估计。