Optimal Steering of a Linear Stochastic System to a Final Probability Distribution-Part III
Optimal Steering of a Linear Stochastic System to a Final Probability Distribution-Part III
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DOI：
10.1109/tac.2018.2791362
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发表时间：
2018-09-01
影响因子：
6.8
通讯作者：
Pavon, Michele
中科院分区：
文献类型：
--
作者：
Chen, Yongxin;Georgiou, Tryphon T.;Pavon, Michele
这项工作的主题有其根源，在所谓的Schrodginer桥问题（SBP），要求布朗粒子在其通道之间观察到的经验边际分布在两个不同的时间点的最可能的分布。随机控制语言的重新表述激发了人们对这个问题的新兴趣。在早期的作品中，作为第一部分和第二部分，我们探讨了一个推广的原始SBP，相当于最佳的转向状态分布之间的线性随机动力系统，在两个时间点，在全状态反馈。在这些工作中，成本在控制输入中是二次的，即，控制能量。目前的工作的目的是详细的技术步骤，在扩展框架的情况下，在国家的二次成本也存在。因此，主要的贡献是在这种情况下，实际上是在封闭形式（定理1）给出的最优控制。在零噪声极限下，我们还得到了一般二次费用的（确定性）质量运输问题的解。
The subject of this work has its roots in the so-called Schrodginer bridge problem (SBP) which asks for the most likely distribution of Brownian particles in their passage between observed empirical marginal distributions at two distinct points in time. Renewed interest in this problem was sparked by a reformulation in the language of stochastic control. In earlier works, presented as Part I and Part II, we explored a generalization of the original SBP that amounts to optimal steering of linear stochastic dynamical systems between state-distributions, at two points in time, under full state feedback. In these works, the cost was quadratic in the control input, i.e., control energy. The purpose of the present work is to detail the technical steps in extending the framework to the case where a quadratic cost in the state is also present. Thus, the main contribution is to derive the optimal control in this case which in fact is given in closed-form (Theorem 1). In the zero-noise limit, we also obtain the solution of a (deterministic) mass transport problem with general quadratic cost.