Error analysis of discrete approximations to bang-bang optimal control problems: the linear case
Error analysis of discrete approximations to bang-bang optimal control problems: the linear case
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bang-bang 最优控制问题的离散逼近误差分析：线性情况
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
V. Veliov
中科院分区：
文献类型：
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作者：
V. Veliov
本文提出了线性系统终端最优控制问题的龙格-库塔直接离散化的误差估计。此类问题的最优控制通常是不连续的，并且解相对于扰动的 Lipschitz 稳定性不一定成立。如果某些最近获得了结构稳定性保持的充分条件，则估计（就最优控制而言）是一阶的，否则是分数阶的。证明中的主要工具是可达集的局部凸性指数与与问题相关的适当切换函数的零重数之间建立的关系。
The paper presents an error estimate for Runge- Kutta direct discretizations of terminal optimal control problems for linear systems. The optimal control for such problems is typically discontinuous, and Lipschitz stability of the solution with respect to perturbations does not necessarily hold. The estimate (in terms of the optimal controls) is of first order if certain recently obtained sufficient conditions for structural stability hold, and of fractional order, otherwise. The main tool in the proof is the established rela- tion between the local convexity index of the reachable set and the multiplicity of zeros of appropriate switching functions associated with the problem.