We propose and analyze a posteriori error estimates for a control-constrained optimal control problem with bang-bang solutions. We consider a solution strategy based on the variational approach, where the control variable is not discretized; no Tikhonov regularization is made. We design, for the proposed scheme, a residual-type a posteriori error estimator that can be decomposed as the sum of two individual contributions related to the discretization of the state and adjoint equations. We explore reliability and efficiency properties of the aforementioned error estimator. We illustrate the theory with numerical examples.

翻译：本文针对具有bang-bang解的控制约束最优控制问题，提出并分析了一种后验误差估计方法。我们采用基于变分法的求解策略，其中控制变量未被离散化，且未引入Tikhonov正则化。针对所提方案，我们设计了一种残差型后验误差估计器，该估计器可分解为与状态方程及伴随方程离散化相关的两个独立贡献之和。我们深入探讨了该误差估计器的可靠性与有效性。最后通过数值算例对理论进行了验证。