Sensitivity analysis for optimal control problems governed by nonlinear evolution inclusions

Advances in Nonlinear Analysis

article

Nikolaos S. Papageorgiou¹  Vicenţiu D. Rădulescu²  Dušan D. Repovš⁴ 

[1] Department of Mathematics, National Technical University, Zografou Campus;Department of Mathematics, Faculty of Sciences, King Abdulaziz University;Department of Mathematics, University of Craiova;Faculty of Education and Faculty of Mathematics and Physics, University of Ljubljana

关键词: Evolution triple;    evolution inclusion;    PG and G convergence;    compact embedding;    Hadamard well-posedness;   

DOI  :  10.1515/anona-2016-0096

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We consider a nonlinear optimal control problem governed by a nonlinear evolution inclusion and depending on a parameter λ. First we examine the dynamics of the problem and establish the nonemptiness of the solution set and produce continuous selections of the solution multifunction ξ↦S⁢(ξ)${\xi\mapsto S(\xi\/)}$ (ξ being the initial condition). These results are proved in a very general framework and are of independent interest as results about evolution inclusions. Then we use them to study the sensitivity properties of the optimal control problem. We show that we have Hadamard well-posedness (continuity of the value function), and we establish the continuity properties of the optimal multifunction. Finally, we present an application on a nonlinear parabolic distributed parameter system.

【 授权许可】

CC BY