On the "bang-bang" principle for nonlinear evolution hemivariational inequalities control systems

被引：10

作者：

Bin, Maojun ^{[1
]}

Liu, Zhenhai ^{[1
,2
]}

机构：

[1] Nanjing Univ Sci & Technol, Sch Sci, Nanjing 210094, Jiangsu, Peoples R China

[2] Yulin Normal Univ, Guangxi Coll & Univ Key Lab Complex Syst Optimiza, Yulin 537000, Guangxi Provinc, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 480卷 / 01期

基金：

欧盟地平线“2020”;

关键词：

Hemivariational inequalities; Extremal trajectory; Generalized Clarke subdifferential; Bang-bang" principle; L(P)-CONTINUOUS EXTREME SELECTORS; DECOMPOSABLE VALUES; INCLUSIONS; EXISTENCE; MULTIFUNCTIONS; RELAXATION;

D O I：

10.1016/j.jmaa.2019.07.054

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to discuss the control systems of nonlinear evolution hemivariational inequalities and their "bang-bang" principle in Banach space. At first, we show that extremal trajectories are in fact dense in the trajectories of the original system with convexified feedback control. Second, by using the density results, the nonlinear and infinite dimensional versions of the "bang-bang" principle for hemivariational inequalities control systems is derived. In the end, an example is provided to illustrate the application of the obtained theory. (C) 2019 Elsevier Inc. All rights reserved.

引用

页数：21

共 36 条

[1]

Aubin J., 1984, Differential Inclusions: Set-Valued Maps and Viability Theory

[2]

BRESSAN A., 1990, DIFFERENTIAL INTEGRA, V3, P633

[3]

Brezis H, 1973, Operateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert

[4] Extremal solutions of quasilinear parabolic inclusions with generalized Clarke's gradient [J].

Carl, S ;

Motreanu, D .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 191 (01) :206-233

[5]

Carl S, 2007, SPRINGER MONOGR MATH, P1

[6]

Clarke F.R., 1983, Optimization and Nonsmooth Analysis, DOI DOI 10.1137/1.9781611971309

[7] Baire's category and the bang-bang property for evolution differential inclusions of contractive type [J].

De Blasi, F. S. ;

Pianigiani, G. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 367 (02) :550-567

[8] A class of optimal control problems for piezoelectric frictional contact models [J].

Denkowski, Zdzislaw ;

Migorski, Stanislaw ;

Ochal, Anna .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (03) :1883-1895

[9]

Duvaut G., 1972, INEQUATIONS MECANIQU, P387

[10] CONTINUOUS-SELECTIONS FOR A CLASS OF NON-CONVEX MULTIVALUED MAPS [J].

FRYSZKOWSKI, A .

STUDIA MATHEMATICA, 1983, 76 (02) :163-174

← 1 2 3 4 →