Continuity of the Value Function for Stochastic Sparse Optimal Control

被引：0

作者：

Ito, Kaito ^{[1
]}

Ikeda, Takuya ^{[2
]}

Kashima, Kenji ^{[1
]}

机构：

[1] Kyoto Univ, Kyoto, Japan

[2] Univ Kitakyushu, Kitakyushu, Fukuoka, Japan

来源：

IFAC PAPERSONLINE | 2020年 / 53卷 / 02期

关键词：

sparsity; optimal control; stochastic systems; value function; continuity; DIRECTIONAL SPARSITY;

D O I：

10.1016/j.ifacol.2020.12.537

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we investigate the continuity of the value function for a stochastic sparse optimal control. The most common method to solve stochastic optimal control problems is the dynamic programming Specifically, if the value function is smooth, it satisfies the associated Hamilton-Jacobi-Bellman (HJB) equation. However, in general, the value function for our problem is not differentiable because of the nonsmoothness of the L-0 cost functional. Instead, we can expect that the value function is a viscosity solution to the HJB equation. This paper shows the continuity of our value function as a first step for showing that the value function is a viscosity solution. Copyright (C) 2020 The Authors.

引用

页码：7179 / 7184

页数：6

共 16 条

[1]

[Anonymous], 2008, OPTIMAL CONTROL VISC

[2]

Boyd Stephen, 2014, Foundations and Trends in Optimization, V1, P1, DOI 10.1561/2400000001

[3] Compressed sensing [J].