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In this chapter, we consider a linear-quadratic optimal control problem where the control variable enters the state equation via the Neumann boundary conditions. We refer to this type of problem as Neumann boundary control problem. We derive optimality conditions and discuss the regularity of optimal control, state, and adjoint state. The numerical analysis for this class of problems is then based on finite element estimates for the error on the boundary from Sect. 3.5 .

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Neumann Control

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  • 发表日期：

    2025年

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  • Boris Vexler,
  • Dominik Meidner

摘要

In this chapter, we consider a linear-quadratic optimal control problem where the control variable enters the state equation via the Neumann boundary conditions. We refer to this type of problem as Neumann boundary control problem. We derive optimality conditions and discuss the regularity of optimal control, state, and adjoint state. The numerical analysis for this class of problems is then based on finite element estimates for the error on the boundary from Sect. 3.5 .