Optimal Control Problem for Bianchi Equation in Variable Exponent Sobolev Spaces

被引：0
作者：
Rovshan A. Bandaliyev
Vagif S. Guliyev
Ilgar G. Mamedov
Yasin I. Rustamov
机构：
[1] Institute of Mathematics and Mechanics of NAS of Azerbaijan,Department of Mathematics
[2] S.M. Nikolskii Institute of Mathematics at RUDN University,undefined
[3] Ahi Evran University,undefined
[4] Institute of Control Systems of NAS of Azerbaijan,undefined
来源：
Journal of Optimization Theory and Applications | 2019年 / 180卷
关键词：
3D optimal control; Pontryagin’s maximum principle; Bianchi equation; Goursat problem; Variable exponent Sobolev spaces; 37D30; 49B20; 49K20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, a necessary and sufficient condition, such as the Pontryagin’s maximum principle for an optimal control problem with distributed parameters, is given by the third-order Bianchi equation with coefficients from variable exponent Lebesgue spaces. The statement of an optimal control problem is studied by using a new version of the increment method that essentially uses the concept of the adjoint equation of the integral form.
引用
收藏
页码：303 / 320
页数：17
相关论文
共 19 条
  • [1] Egorov AI(1964)Optimal control in some distributed parameter systems Autom. Remote Control 25 613-623
  • [2] Idczak D(2003)Bang-bang principle for linear and non-linear Goursat-Darboux problem Internat. J. Control 76 1089-1094
  • [3] Idczak D(2003)Stability analysis of solutions to an optimal control problem associated with a Goursat-Darboux problem Int. J. Appl. Sci. Comput. 13 29-44
  • [4] Majewski M(1984)Necessary conditions for optimality of singular controls in systems governed by partial differential equations J. Optim. Theory Appl. 43 639-661
  • [5] Walczak S(1986)On optimality of controls singular in the classical sense in Goursat-Darboux systems Dokl. Akad. Nauk SSSR 286 808-812
  • [6] Kazemi-Dehkordi MA(1991)Optimality conditions for a Bolza problem governed by a hyperbolic system of Darboux-Goursat type Ann. Polon. Math. 53 7-14
  • [7] Mansimov KB(2015)Generalized Morrey estimates for the gradient of divergence form parabolic operators with discontinuous coefficients J. Differ. Equ. 259 2368-2387
  • [8] Walczak S(1983)Fundamental solution to some local and non-local boundary value problems and their representations Dokl. Akad. Nauk SSSR 271 265-269
  • [9] Guliyev VS(1985)Riemann function equation with dominant mixed derivative of arbitrary order Dokl. Akad. Nauk SSSR 283 783-787
  • [10] Softova L(2002)The local boundary value problem for an integro-differential equation Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb. 17 96-101
12