Optimal control problems for a semi-linear integro-differential evolution system with infinite delay

被引：1

作者：

Huang, Hai ^{[1
]}

Fu, Xianlong ^{[2
]}

机构：

[1] Hangzhou Dianzi Univ, Sch Sci, Hangzhou, Peoples R China

[2] East China Normal Univ, Sch Math Sci, Shanghai Key Lab PMMP, Shanghai 200241, Peoples R China

来源：

OPTIMAL CONTROL APPLICATIONS & METHODS | 2022年 / 43卷 / 02期

关键词：

infinite delay; integro-differential equation; optimal control; resolvent operator; time optimal control; FUNCTIONAL-DIFFERENTIAL EQUATIONS; APPROXIMATE CONTROLLABILITY; RESOLVENT OPERATORS; INTEGRAL-EQUATIONS; HILBERT-SPACES; EXISTENCE; SOLVABILITY; INCLUSIONS; STABILITY; DRIVEN;

D O I：

10.1002/oca.2819

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 study in this work the optimal control and time optimal control problems for a semi-linear integro-differential evolution system with infinite delay in Hilbert space. We first study the existence and uniqueness result of mild solutions in space X alpha for the considered system, and the main tools here are the theory of resolvent operators and fractional powers of operators and alpha-norm. In this way the obtained results are more general and can be applied to the systems involving terms having spatial derivatives. Then we discuss the Lagrange optimal control problem for the system via limit arguments. The time optimal control problem is also proposed and investigated deliberately for it. Finally, an example is provided to show the applications of the obtained results.

引用

页码：459 / 475

页数：17

共 41 条

[1] Stochastic neutral evolution equations on Hilbert spaces with partially observed relaxed control and their necessary conditions of optimality [J].

Ahmed, N. U. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 101 :66-79

[2] Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with infinite delay [J].

Bahuguna, D. ;

Sakthivel, R. ;

Chadha, A. .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2017, 35 (01) :63-88

[3]

Balakrishnan AV., 1965, SIAM Series A Control, V3, P152

[4] The Solvability and Optimal Controls for Impulsive Fractional Stochastic Integro-Differential Equations via Resolvent Operators [J].

Balasubramaniam, P. ;

Tamilalagan, P. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2017, 174 (01) :139-155

[5] NECESSARY AND SUFFICIENT CONDITIONS FOR L1-STRONG WEAK LOWER SEMICONTINUITY OF INTEGRAL FUNCTIONALS [J].

BALDER, EJ .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1987, 11 (12) :1399-1404

[6] Existence and exponential stability for impulsive neutral stochastic functional differential equations driven by fBm with noncompact semigroup via Monch fixed point [J].

Deng, Sufang ;

Shu, Xiao-Bao ;

Mao, Jianzhong .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 467 (01) :398-420

[7] SOME CONSIDERATIONS FOR LINEAR INTEGRODIFFERENTIAL EQUATIONS [J].

DESCH, W ;

GRIMMER, R ;

SCHAPPACHER, W .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1984, 104 (01) :219-234

[8] Optimal control problem for some integrodifferential equations in Banach spaces [J].

Diallo, Mouhamadou Alpha ;

Ezzinbi, Khalil ;

Sene, Abdoulaye .

OPTIMAL CONTROL APPLICATIONS & METHODS, 2018, 39 (02) :563-574

[9] Exponential Behavior of Solutions to Stochastic Integrodifferential Equations with Distributed Delays [J].

Diop, Mamadou Abdoul ;

Caraballo, Tomas ;

Ndiaye, Abdoul Aziz .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2015, 33 (03) :399-412

[10]

El-Borai MM., 2009, INT J CONT MATH SCI, V4, P1361

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