Regularity results for a time-optimal control problem in the space of probability measures
Regularity results for a time-optimal control problem in the space of probability measures
复制标题
概率测度空间中时间最优控制问题的规律性结果
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Giulia Cavagnari
中科院分区：
文献类型：
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作者：
Giulia Cavagnari
本文在概率测度空间中研究了时间最优控制问题的最小时间函数的正则性。导致我们将经典理论推广到这个框架的主要动机是对我们只有初始状态的概率知识的情况进行建模，因为它发生在可能发生噪声和测量误差的真实的设置中。我们考虑了一个确定性的演化控制的连续性方程统治的系统，追求的目标是研究一个推广的经典结果，这种设置，我们证明了一个可达性的结果和局部Lipschitz连续性的广义最小时间函数。
This paper investigates some regularity properties of the minimum time function for a time-optimal control problem in the space of probability measures endowed with the topology induced by the Wasserstein metric. The main motivation leading us to the generalization of the classical theory to this framework is to model situations in which we have only a probabilistic knowledge of the initial state, as it happens in real settings where noises and measurement errors may occur. We consider a deterministic evolution for a system ruled by a controlled continuity equation and, pursuing the goal of studying a generalization of the classical results for this setting, we prove an attainability result and a locally Lipschitz continuity property for the generalized minimum time function.