Proximal Analysis and the Minimal Time Function of a Class of Semilinear Control Systems

被引：3

作者：

Jiang, Yi ^{[1
,2
]}

He, Yiran ^{[1
,2
]}

Sun, Jie ^{[3
,4
]}

机构：

[1] Sichuan Normal Univ, VC VR Lab, Chengdu, Peoples R China

[2] Sichuan Normal Univ, Dept Math, Chengdu, Peoples R China

[3] Natl Univ Singapore, Dept Decis Sci, Bentley, WA, Australia

[4] Curtin Univ, Dept Math & Stat, Bentley, WA, Australia

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2016年 / 169卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Hamilton-Jacobi-Bellman equation; Minimal time function; Subdifferential; Time optimal control; SUBDIFFERENTIALS; EQUATIONS;

D O I：

10.1007/s10957-015-0848-z

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

The minimal time function of a class of semilinear control systems is considered in Banach spaces, with the target set being a closed ball. It is shown that the minimal time functions of the Yosida approximation equations converge to the minimal time function of the semilinear control system. Complete characterization is established for the subdifferential of the minimal time function satisfying the Hamilton-Jacobi-Bellman equation. These results extend the theory of finite dimensional linear control systems to infinite dimensional semilinear control systems.

引用

页码：784 / 800

页数：17

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