Degenerate Optimal Control Problems with State Constraints
Degenerate Optimal Control Problems with State Constraints
复制标题
具有状态约束的退化最优控制问题
DOI：
10.1137/s0363012998340223
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
R. Vinter
中科院分区：
文献类型：
--
作者：
F. Rampazzo;R. Vinter
具有路径状态约束的最优控制问题的标准必要条件在许多感兴趣的情况下不提供有关最小化器的有用信息，例如，当状态轨迹的左端点固定在 x0 且 x0 位于状态约束集的边界时；在这些情况下，存在一组非零但微不足道的乘数。我们给出了非平凡乘数存在的条件。这些条件的一个特点是它们允许非凸速度集和可测量的时间相关数据。证明技术基于对给定状态轨迹与满足状态约束的状态轨迹集合的距离的精确估计，源自动态规划文献。
Standard necessary conditions for optimal control problems with pathwise state constraints supply no useful information about minimizers in a number of cases of interest, e.g., when the left endpoint of state trajectories is fixed at x0 and x0 lies in the boundary of the state constraint set; in these cases a nonzero, but nevertheless trivial, set of multipliers exists. We give conditions for the existence of nontrivial multipliers. A feature of these conditions is that they allow nonconvex velocity sets and measurably time-dependent data. The proof techniques are based on refined estimates of the distance of a given state trajectory from the set of state trajectories satisfying the state constraint, originating in the dynamic programming literature.