Hamilton-Jacobi-Bellman Equation for a Time-Optimal Control Problem in the Space of Probability Measures
Hamilton-Jacobi-Bellman Equation for a Time-Optimal Control Problem in the Space of Probability Measures
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概率测度空间中时间最优控制问题的 Hamilton-Jacobi-Bellman 方程
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
G. Orlandi
中科院分区：
文献类型：
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作者：
Giulia Cavagnari;A. Marigonda;G. Orlandi
在本文中，我们制定了一个时间最优控制问题的概率测度空间赋予Wasserstein度量作为相应的经典问题的自然推广（{mathbb {R}}^d），其中的控制动力学是由一个微分包含。主要的动机是建模的情况下，我们只有一个概率知识的初始状态。特别是，我们证明了第一个动态规划原理，然后我们给出了一个Hamilton-Jacobi-Bellman方程的概率测度的空间，解决了一个推广的最小时间函数在适当的粘性意义。
In this paper we formulate a time-optimal control problem in the space of probability measures endowed with the Wasserstein metric as a natural generalization of the correspondent classical problem in ({mathbb {R}}^d) where the controlled dynamics is given by a differential inclusion. The main motivation is to model situations in which we have only a probabilistic knowledge of the initial state. In particular we prove first a Dynamic Programming Principle and then we give an Hamilton-Jacobi-Bellman equation in the space of probability measures which is solved by a generalization of the minimum time function in a suitable viscosity sense.