Higher-order numerical scheme for linear quadratic problems with bang–bang controls
针对控制函数线性且取值于超立方体的线性二次最优控制问题，假设最优控制为纯bang-bang类型，提出一种离散化格式，使收敛速度比欧拉格式提高一倍，并利用最优解对扰动的稳定性证明精度估计。
This paper considers a linear-quadratic optimal control problem where the control function appears linearly and takes values in a hypercube. It is assumed that the optimal controls are of purely bang-bang type and that the switching function, associated with the problem, exhibits a suitable growth around its zeros. The authors introduce a scheme for the discretization of the problem that doubles the rate of convergence of the Euler's scheme. The proof of the accuracy estimate employs some recently obtained results concerning the stability of the optimal solutions with respect to disturbances.