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

共 20 条

[1] Regularity results for the minimum time function of a class of semilinear evolution equations of parabolic type
Albano, P
Cannarsa, P
Sinestrari, C
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2000, 38 (03) : 916 - 946
[2] A BOUNDARY-VALUE PROBLEM FOR THE MINIMUM-TIME FUNCTION
BARDI, M
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1989, 27 (04) : 776 - 785
[3] Bardi M., 1997, Optimal control and viscosity solutions of HamiltonJacobi-Bellman equations
[4] On the Bellman equation for the minimum time problem in infinite dimensions
Cannarsa, P
Cârja, O
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2004, 43 (02) : 532 - 548
[5] On the minimum time function and the minimum energy problem;: a nonlinear case
Cârja, O
[J]. SYSTEMS & CONTROL LETTERS, 2006, 55 (07) : 543 - 548
[6] Clarke F. H., 1983, OPTIMIZATION NONSMOO
[7] The subgradient formula for the minimal time function in the case of constant dynamics in Hilbert space
Colombo, G
Wolenski, PR
[J]. JOURNAL OF GLOBAL OPTIMIZATION, 2004, 28 (3-4) : 269 - 282
[8] Colombo G, 2004, J CONVEX ANAL, V11, P335
[9] Fattorini H. O., 1996, Infinite Dimensional Optimization and Control Theory
[10] Subdifferentials of a minimum time function in Banach spaces
He, Yiran
Ng, Kung Fu
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 321 (02) : 896 - 910

← 1 2 →