Optimal Control Problem for Fourth-Order Bianchi Equation in Variable Exponent Sobolev Spaces

Abstract

This work proposes a necessary and sufficient condition such as Pontryagin’s maximum principle for an optimal control problem with distributed parameters, which is described by the fourth-order Bianchi equation involving coefficients in variable exponent Lebesgue spaces. The problem is studied by aid of a novel version of the increment method that essentially uses the concept of the adjoint equation of integral type.

Keywords

• 4d optimal control
• Pontryagin's maximum principle
• Bianchi equation
• variable exponent Lebesgue spaces
• variable exponent Sobolev spaces

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