Research of the Optimal Control Problem for One Mathematical Model of the Sobolev Type

At the moment, optimal control problems for various linear and nonlinear Sobolev-type equations have been widely studied. This article is devoted to the study of optimal control for one mathematical model of the Sobolev type, which is based on the model equation, which describes various processes (for example, deformation processes, processes occurring in semiconductors, wave processes, etc.) depending on the parameters and can belong either to the class of degenerate (for lambda> 0) equations or to the class of nondegenerate (for lambda <0) equations. This work is the first attempt to study the control problem for mathematical semilinear models of the Sobolev type in the absence of the property of non-negative definiteness of the operator at the time derivative, i.e. the construction of a singular optimality system in accordance with the singular situation caused by the instability of the model. Conditions for the existence of a control-state pair are presented, and conditions for the existence of an optimal control are found.

Keywords

Sobolev type equations; phase space method; optimal control problem.

References

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