On the semicontinuity of the solution map to a parametric boundary control problem

Abstract

This paper studies solution stability of a parametric boundary control problem governed by semilinear elliptic equation and nonconvex cost function with mixed state control constraints. Using the direct method and the first-order necessary optimality conditions, we obtain the upper semicontinuity and continuity of the solution map with respect to parameters.

Keywords:

• Parametric optimal control
• solution stability
• upper semicontinuity
• continuity
• boundary control
• mixed pointwise constraint

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

The research is funded by the Hanoi University of Science and Technology [project number T2016-PC-206].