Control systems described by a class of fractional semilinear evolution hemivariational inequalities and their relaxation property

Optimization ◽  
2021 ◽  
pp. 1-23
Author(s):  
Jing Li ◽  
Maojun Bin
Keyword(s):  
Control Systems ◽  
Relaxation Property ◽  
Hemivariational Inequalities ◽  
Evolution Hemivariational Inequalities

scholarly journals Optimal control of feedback control systems governed by systems of evolution hemivariational inequalities

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5205-5220 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Zhenhai Liu ◽  
Jen-Chih Yao ◽  
Yonghong Yao
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Feedback Control ◽  
Control Systems ◽  
Existence Result ◽  
Sufficient Conditions ◽  
Hemivariational Inequalities ◽  
Feedback Control System ◽  
Feedback Control Systems ◽  
Evolution Hemivariational Inequalities

In this paper, we introduce and consider a feedback control system governed by the system of evolution hemivariational inequalities. Several sufficient conditions are formulated by virtue of the properties of multimaps and partial Clarke?s subdifferentials such that the existence result of feasible pairs of the feedback control systems is guaranteed. Moreover, an existence result of optimal control pairs for an optimal control system is also established.

scholarly journals Results on the approximate controllability of fractional hemivariational inequalities of order $1< r<2$

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. Mohan Raja ◽  
V. Vijayakumar ◽  
Le Nhat Huynh ◽  
R. Udhayakumar ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Fixed Point ◽  
Control Systems ◽  
Approximate Controllability ◽  
Hemivariational Inequalities ◽  
Evolution Inclusions ◽  
Fractional Systems ◽  
Cosine Families ◽  
Fixed Point Approach ◽  
Semilinear Control Systems ◽  
Theoretical Results

AbstractIn this paper, we investigate the approximate controllability of fractional evolution inclusions with hemivariational inequalities of order $1< r<2$ 1 < r < 2 . The main results of this paper are verified by using the fractional theories, multivalued analysis, cosine families, and fixed-point approach. At first, we discuss the existence of the mild solution for the class of fractional systems. After that, we establish the approximate controllability of linear and semilinear control systems. Finally, an application is presented to illustrate our theoretical results.

Dynamic contact problem with thermal effect

2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Justyna Ogorzaly
Keyword(s):  
Thermal Effect ◽  
Frictional Contact ◽  
Dynamic Contact ◽  
The Body ◽  
Constitutive Law ◽  
Hemivariational Inequalities ◽  
Banach Fixed Point Theorem ◽  
Dynamic Contact Problem ◽  
System Of Inequalities ◽  
Evolution Hemivariational Inequalities

AbstractWe consider a model of a dynamic frictional contact between the body and the foundation. In this model the contact is bilateral. The behaviour of the material is described by the elastic-viscoplastic constitutive law with thermal effect. The variational formulation of this model leads to a system of two evolution hemivariational inequalities. The aim of this paper is to prove that this system of inequalities has a unique solution. The proof is based on the Banach fixed point theorem and some results for hemivariational inequalities.

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