Higher-order numerical scheme for linear quadratic problems with bang–bang controls
Higher-order numerical scheme for linear quadratic problems with bang–bang controls
复制标题
具有 Bang-Bang 控制的线性二次问题的高阶数值方案
DOI：
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发表时间：
2017
影响因子：
2.2
通讯作者：
V. Veliov
中科院分区：
文献类型：
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作者：
T. Scarinci;V. Veliov
本文考虑线性二次最优控制问题，其中控制函数呈线性出现并在超立方体中取值。假设最优控制是纯粹的爆炸式控制，并且与问题相关的切换函数在其零点附近表现出适当的增长。作者引入了一种问题离散化方案，使欧拉方案的收敛速度加倍。精度估计的证明采用了一些最近获得的关于最优解相对于干扰的稳定性的结果。
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.