Optimal Control Problem for Bianchi Equation in Variable Exponent Sobolev Spaces

Rovshan A. Bandaliyev (), Vagif S. Guliyev (), Ilgar G. Mamedov () and Yasin I. Rustamov ()
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Rovshan A. Bandaliyev: Institute of Mathematics and Mechanics of NAS of Azerbaijan
Vagif S. Guliyev: Institute of Mathematics and Mechanics of NAS of Azerbaijan
Ilgar G. Mamedov: Institute of Control Systems of NAS of Azerbaijan
Yasin I. Rustamov: Institute of Control Systems of NAS of Azerbaijan

Journal of Optimization Theory and Applications, 2019, vol. 180, issue 1, No 16, 303-320

Abstract: Abstract 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.

Keywords: 3D optimal control; Pontryagin’s maximum principle; Bianchi equation; Goursat problem; Variable exponent Sobolev spaces; 37D30; 49B20; 49K20 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-018-1290-9

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