Stochastic Control of Multidimensional Systems With Relative Optimization

被引：0
|
作者：
Cao, Xi-Ren [1 ,2 ]
机构：
[1] Shanghai Jiao Tong Univ, Dept Automat, Key Lab Syst Control & Informat Proc, Minist Educ, Shanghai 200240, Peoples R China
[2] Hong Kong Univ Sci & Technol, Hong Kong, Peoples R China
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2020年 / 65卷 / 05期
基金：
美国国家科学基金会;
关键词：
Calculus; Optimization; Viscosity; Control systems; Indium tin oxide; Taylor series; Standards; Ito-Tanaka formula; local time; relative optimization theory; semismooth function; viscosity solution;
D O I：
10.1109/TAC.2019.2925469
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We derive the Tanaka formula for multidimensional semismooth functions with the local time on the semismooth curve along the gradient direction. With this formula, we extend the relative optimization based approach to stochastic control to multidimensional systems. Optimality conditions are derived for systems with semismooth value functions, and no viscosity solution is involved. This approach provides new insights and motivates the research on stochastic control and stochastic calculus, in particular, for problems with nonsmooth features and degenerate points.
引用
收藏
页码：1886 / 1900
页数：15
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